Proceedings of the Second International Workshop on EGS - KEK

KEK <strong>Proceedings</strong> 2000-20
December 2000
A/H/M/R/D
<strong>Proceedings</strong> <strong>of</strong>
<strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong>
on EGS
August 8 - 12, 2000.
KEK, Tsukuba, Japan
Edited by
H. Hirayama, Y.Namito and S. Ban
High Energy Accelerator Reserach Organization

FOREWARD
The First <strong>International</strong> <strong>Workshop</strong> on EGS4 was held at KEK during August 26-29, 1997 to
exchange information about EGS4 itself as well as researches related to EGS4 internationally.
It provided useful information among researchers who use EGS4 as <strong>the</strong> tool in various elds.
As decided at this workshop, <strong>the</strong> second workshop was held again at KEK during August
8-12, 2000.
The workshop, sponsored by High Energy Accelerator Reserach Organization in Japan
(KEK), attracted over 100 EGS4 users from seven nations.
At <strong>the</strong> workshop, 42 talks including poster session were presented from <strong>the</strong> low-energy
problems to <strong>the</strong> high-energy ones in <strong>the</strong> various research elds like <strong>the</strong> medical physics, particle
or nuclear physics etc. These proceedings include all <strong>of</strong> <strong>the</strong> presentations at this workshop.
Finally, we would like to express our great appreciations to all authors who prepared <strong>the</strong>ir
manuscripts quickly in order to speed up <strong>the</strong> publication <strong>of</strong> <strong>the</strong>se proceedings.
The organizing committee,
S. Ban (KEK)
A. F. Bielajew (U. Michigan)
H. Hirayama (KEK)
Y. Namito (KEK)
W. R. Nelson (SLAC)

CONTENTS
Innovative Electron Transport Methods in EGS5 1
A. F. Bielajew and S. J. Wilderman
Improvements <strong>of</strong> Low Energy Photon Transport for EGS5 11
Y. Namito, H. Hirayama and S. Ban
Status <strong>of</strong> <strong>the</strong> Object-oriented EGS Interface Project 23
A. M. Yacout, W. L. Dunn, W. R. Nelson, P. Lui, A.F. Bielajew
H. Hirayama and Y. Namito
Application <strong>of</strong> EGS4 Code to Whole-body Counting 31
S. Kinase, M. Yoshizawa, J. Kuwabara and H. Noguchi
Fluence to E ective Dose Conversion Coe cients for
Electrons from 1MeV to 100GeV 40
S. Tsuda, A. Endo, Y. Yamaguchi and O. Sato
Analysis <strong>of</strong> Dose in Teeth for Estimation <strong>of</strong> E ective Dose by
<strong>the</strong> Electron Spin Resonance (ESR) Dosimetry Using Dental Enamels 48
F. Takahashi, Y. Yamaguchi, K. Saito, M. Iwasaki,
C. Miyazawa and T. Hamada
An EGS4 User Code with Voxel Geometry and
a Voxel Phantom Generating System 56
J. Funabiki, M. Terabe, M. Zankl, S. Koga and K. Saito
Applications <strong>of</strong> EGS4 on Leksell Gamma Unit 64
Joel YC Cheung, KN Yu, Robert TK Ho and CP Yu
Dosimetric Characterization <strong>of</strong> Low Energy Brachy<strong>the</strong>rapy Sources:
An EGS4 Monte Carlo Study 74
E. Mainegra and R. Capote
Optimization <strong>of</strong> PET Scanner Geometry 92
Lars-Eric Adam and J. S. Karp
Dose Distribution <strong>of</strong> Stereotactic Irradiation for Thorax 100
R. Sakai, H. Saitoh, T. Fujisaki, S. Abe, K. Fukuda,
M. Fukushi and E. Kunieda
The Caluculation <strong>of</strong> 3D Saptial Dose Distribution Around
a Shielded Vaginal Cylinder with Iridium-192 Source
Calculated by using Monte Carlo Code EGS4 107
I. J. Chen, R. D. Sheu, B. J. Chang Y. M. Liu, L. S. Chao, S. H. Yen
i

Polarization Study for NLC Positron Source Using EGS4 115
J. C. Liu, T. Kotseroglou, W. R. Nelson, and D. Schultz
EGS4 Simulation <strong>of</strong> <strong>the</strong> Positron Converter at <strong>the</strong> BEPC Linac-Based
Slow Positron Beam 124
R. S. Yu, C. X. Ma, G.X. Pei, L. Wei, B. Y. Wang, and T. B. Chang
Measurements <strong>of</strong> Photoneutron Spectra from Thick Pb Target
Bombarded by 1.2 and 2.0 GeV Electrons 130
S. Ban, Y. Namito, H. Hirayama, N. Terunuma, J. Urakawa, T. Sato,
R. Yuasa, K. Shin, H. S. Lee, and J. S. Bak
Response Calculations <strong>of</strong> <strong>the</strong> CdZnTe Detector Using EGS4 135
J. C. Liu, W. R. Nelson and R. Seefred
Development <strong>of</strong> Gamma Ray Monitor Using CdZnTe Semiconductor
Detector 144
A. H. D. Rasolonjatovo, T. Shiomi, T. Nakamura, H. Nishizawa,
Y. Tsudaka, H. Fujiwara, H. Araki, and K. Matsuo
A Monte Carlo Method for Determining Absolute Scintillation-Photon
Yields and Energy Resolution <strong>of</strong> Scintillators for Gamma Rays 152
H. Tawara, S. Sasaki, K. Saito and E. Shibamura
Development <strong>of</strong> Gamma-Ray Direction Detector Based on MSGC 161
T. Nagayoshi, H. Kubo, A. Ochi, S. Koishi, T. Tanimori, and Y. Nishi
Response Function <strong>of</strong> a NE213 Liquid Saintillation Detector
Simulated by EGS4/PRESTA Code for a Collimated -Ray Beam 168
N. Takeda, K. Kudo, S. Koshikawa, H. Ohgaki, H. Toyokawa, and T. Sugita
The E ect <strong>of</strong> <strong>the</strong> Build-up Wall at <strong>the</strong> TLD Calibration Using Co-60 176
N. Nariyama
A Convolution Method for Determining Temperature Rise in Targets
Struck by Beams <strong>of</strong> Various Size 182
W. R. Nelson, S. Ecklund and S. Rokni
Application <strong>of</strong> EGS4 for <strong>the</strong> Evaluation <strong>of</strong> Material Damage
Due to Gamma-ray Irradiation 193
O. Sato, T. Tobita and H. Suzuki
Examination <strong>of</strong> <strong>the</strong> X-Ray Piping Diagnostic System using EGS4
(Examination <strong>of</strong> <strong>the</strong> Film and Iron Rust) 199
G. Kajiwara
E ective Bending Point to Reduce Dose-Equivalent <strong>of</strong>
a Bending Duct Streaming System 209
K. Ueki
ii

EGS4 Simulation <strong>of</strong> Compton Scattering for Nondestructive Testing 216
N. Shengli, Z. Jun, and H. Liuxing
Implementation and Performance Evaluation <strong>of</strong> Iterative
Reconstruction Algorithms in SPECT: A Simulation Study
Using EGS4 224
T. Yokoi, H. Shinohara, T. Hashimoto, T. Yamamoto, and Y. Niio
Correction <strong>of</strong> Measurement by HP-Ge Detector
for Incident Diagnostic X-ray Photons 235
K. Koshida, K. Shimizu and T. Kasuga
Response <strong>of</strong> CdZnTe Detector in Measurement <strong>of</strong> Diagnostic
X-ray Spectra 242
S. Miyajima, H. Sakuragi and M. Matsumoto
Evaluation <strong>of</strong> Reponse Function <strong>of</strong> 16"x16"x4" Large-sized NaI
Scintillation Detctor for Environmental Gamma-ray Survey 250
H. Itadzu, T. Iguchi, A. Uritani and J. Kawarabayashi
Beam Dump for High Current Electron Beam at JNC 255
H. Takei and Y. Takeda
Variation <strong>of</strong> Dose Distribution by Detectors for Narrow Beam 264
T. Fujisaki, H. Saitoh, T. Inada, S. Abe, M. Fukushi and K. Fukuda
Returning Electron Simulation for a Klystron Collector Using EGS4 272
Z. Fang, S. Fukuda, S. Yamaguchi, and S. Anami
Direct Measurement <strong>of</strong> Electron-Tracks Using a Charge Coupled
Device 280
S. Kitamoto, M. Ohta, T. Okada, T. Kohmura, K. Mori,
H. Awaki, and K. Tachibana
Simulation <strong>of</strong> Angular Distribution <strong>of</strong> Gas Bremsstrahlung
Depending on <strong>the</strong> Residual Gas Pressure <strong>of</strong> Storage Ring 286
Y. Asano
Study on Spatial Distribution <strong>of</strong> Electromagnetic Shower
Around a Lead Block Irradiated by 700-MeV Bremsstrahlung 293
S. Oki, Y. Takashima, M. Yamakage, H. Kobayakawa K. Yoshida,
and K. Goto
Support <strong>of</strong> Low Energy X-ray Polarization with EGS4 299
K. Asamura, S. Gunji, Y. Inoue, T. Suzuki, T. Maeda, and H. Sakurai
iii

Unfolding <strong>of</strong> <strong>the</strong> Measured Spectra and <strong>the</strong> Determination <strong>of</strong>
Correction Factor <strong>of</strong> Free Air Ion Chamber using EGS4 Simulations 308
Y. Gwang-Ho
Simulation <strong>of</strong> Ionization and Scintillation Signals
in a Liquid Ionization Drift Chamber 316
T. Shimoyama, E. Shibamura, M. Miyajima
Observation <strong>of</strong> Intense Radiation During Thunderstorm and
Monte Carlo Simulation <strong>of</strong> Bremsstrahlung Generation 324
T. Torii, M. Takeishi, T. Hosono and T.Sugita
Predicted Angular Distribution <strong>of</strong> Fast Charged Particles with
Ionization 330
T. Nakatsuka
Lists <strong>of</strong> Participants 341
iv

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.1-10
Innovative Electron Transport Methods in EGS5
A. F. Bielajew and S. J. Wilderman
Department <strong>of</strong> Nuclear Engineering and Radiological Sciences
The University <strong>of</strong> Michigan
Cooley Building (North Campus)
2355 Bonisteel Boulevard
Ann Arbor, Michigan 48109-4540, USA
Abstract
The initial formulation <strong>of</strong> a Monte Carlo scheme for <strong>the</strong> transport <strong>of</strong> high-energy (> 100 keV)
electrons was established by Berger in 1963. Calling his method <strong>the</strong> \condensed history <strong>the</strong>ory",
Berger combined <strong>the</strong> <strong>the</strong>oretical results <strong>of</strong> <strong>the</strong> previous generation <strong>of</strong> research into developing approximate
solutions <strong>of</strong> <strong>the</strong> Boltzmann transport equation with numerical algorithms for exploiting
<strong>the</strong> power <strong>of</strong> computers to permit iterative, piece-wise solution <strong>of</strong> <strong>the</strong> transport equation in a computationally
intensive but much less approximate fashion. The methods devised by Berger, with
comparatively little modi cation, provide <strong>the</strong> foundation <strong>of</strong> all present dayMonte Carlo electron
transport simulation algorithms. Only in <strong>the</strong> last 15 years, beginning with <strong>the</strong> development and
publication <strong>of</strong> <strong>the</strong> PRESTA algorithm, has <strong>the</strong>re been a signi cant revisitation <strong>of</strong> <strong>the</strong> problem
<strong>of</strong> simulating electron transport within <strong>the</strong> condensed history framework. Research in this area
is ongoing, highly active, and far from complete. It presents an enormous challenge, demanding
derivation <strong>of</strong> new analytical transport solutions based on underlying fundamental interaction mechanisms,
intuitive insight in<strong>the</strong>development <strong>of</strong> computer algorithms, and state <strong>of</strong> <strong>the</strong> art computer
science skills in order to permit deployment <strong>of</strong> <strong>the</strong>se techniques in an e cient manner. The EGS5
project, a modern ground-up rewrite <strong>of</strong> <strong>the</strong> EGS4 code, is now in <strong>the</strong> design phase. EGS5 will take
modern photon and electron transport algorithms and deploy <strong>the</strong>m in an easy-to-maintain, modern
computer language|ANSI-standard C++. Moreover, <strong>the</strong> well-known di culties <strong>of</strong> applying EGS4
to practical geometries (geometry code development, tally routine design) should be made easier
and more intuitive through <strong>the</strong> use <strong>of</strong> a visual user interface being designed by Quantum Research,
Inc., work that is presented elsewhere in this conference. This report commences with a historical
review <strong>of</strong> electron transport models culminating with <strong>the</strong> proposal <strong>of</strong> a new, previously unpublished
algorithm, for <strong>the</strong> EGS5 project.
1 Introduction
Berger's founding paper[1], Monte Carlo Calculation <strong>of</strong> <strong>the</strong> penetration and di usion <strong>of</strong> fast
charged particles, ushered in <strong>the</strong> modern era <strong>of</strong> electron transport in Monte Carlo applications. The
principle di culty in applying <strong>the</strong> Monte Carlo method to electron transport lies in <strong>the</strong> fact that
electrons interact frequently until <strong>the</strong>ir kinetic energy is exhausted. A relativistic electron may have
10 4 {10 5 elastic interactions and 10 5 {10 6 inelastic interactions before falling to an energy so low that it
stops ionizing or exciting atoms individually or collectively in <strong>the</strong> material through which itisbeing
transported. Clearly, it was not feasible to model all <strong>of</strong> <strong>the</strong>se interactions in an analog Monte Carlo
code in <strong>the</strong> early 1960's, <strong>the</strong> era when Berger issued his famous report 1 . To overcome this di culty,
Berger devised <strong>the</strong> \condensed history <strong>the</strong>ory" (CHT). The CHT ga<strong>the</strong>rs toge<strong>the</strong>r many elastic and
1 Analog calculations are feasible today only in 1D geometries and are used, primarily, to study <strong>the</strong> physics <strong>of</strong> multiple
interactions. Analog calculations are not feasible for many applications requiring 3D geometries or applications that may
require millions or billions <strong>of</strong> primary source particles.
1

inelastic interactions into \virtual" interactions, permitting e ciency gains <strong>of</strong> up to 3 or 4 orders <strong>of</strong>
magnitude.
The computational speed-up achieved with Berger's CHT is impressive, but comes at a cost. The
electron transport becomes approximate! Consider, for example, an electron initially positioned at <strong>the</strong>
origin, ~x = ~0, directed along <strong>the</strong> ~z-axis with some initial energy E 0. This electron is to be moved a
total prescribed pathlength <strong>of</strong> some distance, say, t. For <strong>the</strong> moment, <strong>the</strong> method we adopt to choose
t is not pertinent to <strong>the</strong> discussion 2 . Let us now ask, after <strong>the</strong> electron is transported a distance t,
where will its path terminate? The only thing we can say with absolute certainty is that its path will
terminate at some position ~x, such that ~x t. The direction <strong>of</strong> <strong>the</strong> electron will be ( )'s selected
from an elastic multiple scattering <strong>the</strong>ory and <strong>the</strong> electron will have a lower energy, E, determined
from an inelastic multiple scattering <strong>the</strong>ory. The nal position <strong>of</strong> <strong>the</strong>se electrons should look something
like <strong>the</strong> depiction in gure 1. Because <strong>of</strong> <strong>the</strong> energy dependence <strong>of</strong> <strong>the</strong> di erential scattering cross
Figure 1: The termination points <strong>of</strong> 1000 electrons starting at <strong>the</strong> origin, ~x = ~0, directed along <strong>the</strong> ~z-axis, and
transported a total pathlength t.
section, <strong>the</strong> distribution that one observes depends on <strong>the</strong> energy <strong>of</strong> <strong>the</strong> electron. At high energies
where <strong>the</strong> elastic scattering is forward directed, <strong>the</strong>re is a strong clustering <strong>of</strong> <strong>the</strong> endpoints in <strong>the</strong>
forward direction with a few electrons scattered widely and even fewer that terminate in <strong>the</strong> reverse
hemisphere. At lower energies where <strong>the</strong> scattering becomes more isotropic, <strong>the</strong> sphere gets populated
more uniformly.
2 The distance t is usually chosen to satisfy a number <strong>of</strong> constraints: 1) t is <strong>the</strong> distance to a discrete event, like
a M ller or bremsstrahlung interaction, 2) t is small enough so that <strong>the</strong> energy <strong>of</strong> <strong>the</strong> electron over <strong>the</strong> pathlength is
approximately constant, 3) t is small enough so that <strong>the</strong> determination <strong>of</strong> <strong>the</strong> scattering angle is accurate.
2
t

2 Transport Mechanics
Given an elastic scattering cross section <strong>of</strong> arbitrary form and ignoring energy losses along <strong>the</strong>
transport step, <strong>the</strong> directions <strong>of</strong> <strong>the</strong> electrons after a pathlength t is known exactly from <strong>the</strong> multiple
scattering <strong>the</strong>ory <strong>of</strong> Goudsmit and Saunderson[2, 3] or Lewis's adaptation[4], assuming that <strong>the</strong> electron
loses energy continuously (an approximation in itself that only applies at high energies). O<strong>the</strong>r
successful multiple scattering <strong>the</strong>ories make assumptions which are rigorously applicable only for small
angles, for speci c forms <strong>of</strong> <strong>the</strong> elastic cross section, or for a restricted range <strong>of</strong> t[5,6,7,8,9,10,11].
While <strong>the</strong> direction is well characterized, <strong>the</strong> ending position is not. Indeed, <strong>the</strong>re is very little <strong>the</strong>oretical
development along <strong>the</strong>se lines and that which exists is not accurate enough for general-purpose
Monte Carlo. Therefore, we must \invent" a scheme to give a recipe for where to place <strong>the</strong> electron
at <strong>the</strong> end <strong>of</strong> <strong>the</strong> step and how to deduct energy losses. These schemes have come to be known as
\transport mechanics".
Although transport <strong>the</strong>ory solutions derived from <strong>the</strong> Boltzmann equation directly have not been
successful in predicting <strong>the</strong> coupled space-angle-energy distributions, <strong>the</strong>y do provide expressions for
<strong>the</strong> moments <strong>of</strong> spatial distributions and <strong>the</strong> couplings <strong>of</strong> moments between space and angle which
may be evaluated easily, independent <strong>of</strong> <strong>the</strong> form <strong>of</strong> <strong>the</strong> scattering cross sections employed. This
development, attributed to Lewis[4], may be employed to evaluate a mechanics scheme once it is
devised. In addition, Larsen has developed an analysis[12] that predicts <strong>the</strong> convergence rate <strong>of</strong> a
mechanics scheme compared to <strong>the</strong> solution obtained by analog (event-by-event) simulation. The
dependence <strong>of</strong> Monte Carlo tallies on electron step-size is known as \step-size dependence" and is
a function <strong>of</strong> <strong>the</strong> nature <strong>of</strong> <strong>the</strong> tally, <strong>the</strong> mechanics scheme employed and <strong>the</strong> treatment <strong>of</strong> electron
transport in <strong>the</strong> vicinity <strong>of</strong>interfaces where <strong>the</strong> interaction cross sections or densities change[13, 14].
It should be mentioned that Larsen convergence requires that <strong>the</strong> multiple elastic scattering scheme
be robust (exhibit no numerical or physical artifacts) as <strong>the</strong> pathlength is reduced to zero. This limit
is problematic for both <strong>the</strong> original implementations <strong>of</strong> Goudsmit-Saunderson <strong>the</strong>ory[2, 3] and Moliere
<strong>the</strong>ory[5, 6], although <strong>the</strong> di culties with both <strong>the</strong>se <strong>the</strong>ories have now been treated successfully[10,
11].
2.1 ETRAN, ITS, MCNP
Berger[1] recommended <strong>the</strong> following scheme for determining <strong>the</strong> position <strong>of</strong> <strong>the</strong> endpoint <strong>of</strong> a
transport step:
x + iy = t
2
0
@sin e i + k
s
hcos 2 i
6
z = t
(1 + cos ) (1)
2
where

2.2 EGS4, PRESTA
The EGS4 Monte Carlo code[25, 26, 27] employed a small variation on <strong>the</strong> ETRAN <strong>the</strong>me. The
EGS4 mechanics is expressed as ~x = f(t Z E)t^z where <strong>the</strong> function f(t Z E) is called a pathlength
or detour correction. The idea behind this scheme comes from <strong>the</strong> recognition that <strong>the</strong> forward
penetration distance z must be shorter than t. An approximate <strong>the</strong>ory based upon <strong>the</strong> developments
<strong>of</strong> Yang's[28] adaptation <strong>of</strong> Fermi-Eyges <strong>the</strong>ory[29] is employed. It has subsequently been shown that
<strong>the</strong> amount <strong>of</strong> correction applied by this method over-predicts by a factor <strong>of</strong> about two[30], one <strong>of</strong> <strong>the</strong>
motivating reasons for <strong>the</strong> development <strong>of</strong> <strong>the</strong> Parameter Reduced Electron-Step Transport Algorithm
(PRESTA)[30, 14].
PRESTA's mechanics scheme can be summarized as:
x + iy = t
sin ei
2
z = tf 0 (t Z E) (2)
whichintroduces a more robust detour correction, f 0 (t Z E), and a lateral transport that is correlated
to <strong>the</strong> angle, as suggested by Berger[1].
2.3 PENELOPE
Primarily intended to address <strong>the</strong> problems <strong>of</strong> low-energy electron transport (1 keV

according to a recipe that can be found in <strong>the</strong> reference[39]. PENELOPE's random hinge iterated
twice appears to perform as well, although a moments analysis <strong>of</strong> a two-step random hinge has not
been undertaken.
The PRESTA-II mechanics adds an important new physical feature. The nal direction implied by
( ) and <strong>the</strong> nal direction with respect to <strong>the</strong> starting point ~x=j~xj are now decoupled, as physically
<strong>the</strong>y should be. (They are strongly correlated but not rigidly coupled.)
2.5 An extension to PENELOPE's mechanics
The PRESTA-II mechanics removes <strong>the</strong> rigid coupling between <strong>the</strong> direction and position vector,
but requires two samplings <strong>of</strong> <strong>the</strong> multiple scattering angle, whichistypically <strong>the</strong> most computationally
costly part <strong>of</strong> <strong>the</strong> transport algorithm. Moreover, <strong>the</strong> ve moments hzi, hx sin cos + y sin sin i,
hz cos i, hx 2 + y 2 i, and hz 2 i can not all be perfectly preserved by <strong>the</strong> PRESTA-II/EGSnrc scheme.
A new mechanics scheme has been found[40] which doeshave all <strong>the</strong>se features and requires only one
sampling <strong>of</strong> <strong>the</strong> multiple scattering angle. This scheme takes <strong>the</strong> form:
x + iy = t[frsin e 1 + cos e 2 ]
z = t[k(1 ; r)+c +(kr + d) cos ] (5)
where <strong>the</strong> ve constants f kcdcan be xed so as to reproduce <strong>the</strong> above ve moments exactly. This
improvement in moment compliance is obtained with only a single sampling <strong>of</strong> <strong>the</strong> multiple-scattering
angle, although <strong>the</strong>re are two azimuthal angle samplings (which are relatively inexpensive). However,
in initial tests <strong>of</strong> this extension to PENELOPE's mechanics, <strong>the</strong>re appears to be no advantage to using
<strong>the</strong> extension over a double sampling <strong>of</strong> PENELOPE's simpler scheme, ei<strong>the</strong>r from <strong>the</strong> standpoint <strong>of</strong>
computational e ciency or compliance with higher order moments.
2.6 EGS5 mechanics
Given that <strong>the</strong> simpler PENELOPE mechanics, when sampled twice appears to be more useful
ei<strong>the</strong>r <strong>the</strong> PRESTA-II/EGSnrc or extended PENELOPE mechanics, we have decided to adopt <strong>the</strong>
PENELOPE mechanics with a new extension which accounts for energy changes to rst order in an
elegant way. The algorithm is best expressed in <strong>the</strong> followed pseudo-code:
1) SAMPLE two uniformly distributed random numbers, r1 and r2.
2) IF r1

2. De ect <strong>the</strong> particle by sampling from <strong>the</strong> multiple scattering angular distribution assuming
that it has gone <strong>the</strong> full step t at <strong>the</strong> starting energy E = E0.
3. Transport <strong>the</strong> electron in <strong>the</strong> forward direction a distance (r1 ; r2)t assuming that <strong>the</strong>
energy is constant at <strong>the</strong> starting energy.
4. Deduct energy according to some energy loss model as if it had gone <strong>the</strong> complete step.
The electron now has energy E = E0 ; (E0t).
5. Transport <strong>the</strong> electron in <strong>the</strong> new direction a distance (1 ; r1)t assuming that <strong>the</strong> energy
is constant at <strong>the</strong> revised energy.
Note that <strong>the</strong> energy-loss processes can occur on ei<strong>the</strong>r side (in a time-wise fashion) <strong>of</strong> <strong>the</strong> direction
change and that <strong>the</strong> energy employed in <strong>the</strong> selection <strong>of</strong> <strong>the</strong> angle is, on average, <strong>the</strong> mean energy <strong>of</strong>
<strong>the</strong> step. This gives <strong>the</strong> correct rst-order correction for energy loss in <strong>the</strong> de ection process.
2.6.1 Accounting for discrete interactions
Conventionally, as in <strong>the</strong> EGS4 code, an initial distance to a discrete interaction is determined
and <strong>the</strong>n broken up into multiple scattering sub-steps, using some mechanics scheme. A drawback
to this approach is that <strong>the</strong> cross sections employed to sample <strong>the</strong> distance to a discrete interaction
depends on <strong>the</strong> energy <strong>of</strong> <strong>the</strong> particle, which changes during <strong>the</strong> course <strong>of</strong> transporting <strong>the</strong> particle
according to a given mechanics scheme.
In <strong>the</strong> revised EGS5 model, we permit discrete interactions to occur within <strong>the</strong> multiple scattering
step. If we consider <strong>the</strong> transport segments to occur without energy change (energy change is e ected
at <strong>the</strong> energy \hinge points" only) and resample <strong>the</strong> distance to discrete interaction after each change
in energy, we can account for <strong>the</strong> variation in <strong>the</strong> cross sections with respect to energy along <strong>the</strong>
path. Note that when an interaction occurs, energy is deducted, daughter particles are created and
directions may change. These are allowed to occur in accordance with <strong>the</strong> laws <strong>of</strong> physics. One simply
has to resample <strong>the</strong> distance to <strong>the</strong> next interaction point andtransport <strong>the</strong> remaining distance <strong>the</strong>
<strong>the</strong> next real or virtual event.
2.6.2 Transport across interfaces
The most accurate way to cross interfaces is to choose a step-size that guarantees that <strong>the</strong>
transport step does not cross <strong>the</strong> interface, reducing <strong>the</strong> electron step-size to such a degree that
<strong>the</strong> multiple-interaction condensed history physics \evaporates" and <strong>the</strong> electron is permitted to cross
<strong>the</strong> interface in analog mode without approximation[41]. This technique, while perfectly accurate,
is computationally very costly. Therefore, we seek a technique that is approximate, yet su ciently
accurate for most applications, and faster, with <strong>the</strong> increase in speed coming about by allowing
electrons to drift across interfaces during <strong>the</strong> sub-step segments.
Since <strong>the</strong> step-size is no longer constrained by geometry, we consider several constraints on <strong>the</strong>
electron step-size. The rst, measured in terms <strong>of</strong> <strong>the</strong> rst elastic scattering transport moment (which
is proportional to <strong>the</strong> average amount <strong>of</strong> de ection), controls <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong> geometrical development
<strong>of</strong> <strong>the</strong> electron track. The second, measured in terms <strong>of</strong> <strong>the</strong> rst inelastic scattering transport
moment (which is proportional to <strong>the</strong> average amount <strong>of</strong> energy loss), controls <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong>
energy-loss modeling along <strong>the</strong> electron track. Superimposed upon this is <strong>the</strong> discrete interaction
physics.
Assume that <strong>the</strong> elastic scattering constraint is expressed as a distance T elastic such that a prescribed
average amount <strong>of</strong> scattering has occurred and that <strong>the</strong> inelastic scattering constraint is de ned by a
distance T inelastic such that a prescribed average amount <strong>of</strong> energy loss has occurred. The algorithm
takes <strong>the</strong> following form:
1. Determine <strong>the</strong> distance to a cumulative elastic scattering event, t elastic = r1T elastic, where r1 is
a uniformly sampled random number between 0 and 1. Note that <strong>the</strong> algorithm is su ciently
general to allow for o<strong>the</strong>r prescriptions for choosing this distance.
6

2. Determine <strong>the</strong> distance to a cumulative inelastic scattering event, t inelastic = r2T inelastic, where
r2 is ano<strong>the</strong>r uniformly sampled random number between 0 and 1.
3. Determine <strong>the</strong> distance to a discrete scattering event, t discrete = ; ;1 ln(r3), where r3 is ano<strong>the</strong>r
uniformly sampled random number between 0 and 1 and is <strong>the</strong> macroscopic cross section in
units <strong>of</strong> cm ;1 .
4. Determine <strong>the</strong> distance, tgeom, <strong>the</strong> distance along <strong>the</strong> particle's current direction to an interface.
5. Determine <strong>the</strong> minimum <strong>of</strong> <strong>the</strong> 4 distances: tgeom, t elastic, t inelastic, and t discrete. Subtract this
distance from all 4.
6. Transport <strong>the</strong> electron this distance along its current direction <strong>of</strong> motion.
7. If tgeom =0:
(a) Rescale <strong>the</strong> distances t elastic and t inelastic, and resample t discrete accounting for <strong>the</strong> new
interaction physics, if <strong>the</strong> medium on <strong>the</strong> o<strong>the</strong>r side <strong>of</strong> <strong>the</strong> interface is di erent.
8. Else if t elastic =0:
(a) Sample <strong>the</strong> interaction using <strong>the</strong> parameters <strong>of</strong> <strong>the</strong> current medium and de ect <strong>the</strong> electron.
(b) Calculate <strong>the</strong> new t elastic, t elastic =(T elastic;t elastic)+r4T elastic, where r4 is ano<strong>the</strong>r uniformly
sampled random number between 0 and 1.
9. Else if t inelastic =0:
(a) Sample <strong>the</strong> interaction using <strong>the</strong> parameters <strong>of</strong> <strong>the</strong> current medium and deduct energy from
<strong>the</strong> electron.
(b) Calculate <strong>the</strong> new t inelastic, t inelastic =(T inelastic ; t inelastic)+r4T inelastic, where r4 is ano<strong>the</strong>r
uniformly sampled random number between 0 and 1.
10. Else if t discrete =0:
(a) Sample <strong>the</strong> interaction using <strong>the</strong> parameters <strong>of</strong> <strong>the</strong> current medium. Create daughter
particles, de ect <strong>the</strong> parent particle and deduct <strong>the</strong> energy <strong>of</strong> <strong>the</strong> daughter particles from
it, as appropriate.
(b) Calculate <strong>the</strong> new t discrete, t discrete = ; ;1 ln(r4), where r4 is ano<strong>the</strong>r uniformly sampled
random number between 0 and 1.
11. Go to step 4 unless <strong>the</strong> electron's energy has fallen below <strong>the</strong> transport threshold.
Note that this scheme has characterized 4types <strong>of</strong> interaction, interface intercept, discrete interaction,
energy loss due to cumulative events, and direction change due to cumulative events. It places
all <strong>the</strong>se \interactions" on a more-or-less equal footing and deals with each separately. Uniformly
randomizing <strong>the</strong> position at which energy loss due to cumulative events occurs e ectively samples <strong>the</strong>
average energy for <strong>the</strong> elastic and discrete events, <strong>the</strong> correct prescription to rst order. Note also that
we interpret any event that can cause any change in <strong>the</strong> phase space <strong>of</strong> <strong>the</strong> particles in <strong>the</strong> problem to
have equal status. This would allow ustointroduce many forms <strong>of</strong> variance reduction as a new class
<strong>of</strong> event, and facilitate <strong>the</strong> introduction <strong>of</strong> variance reduction techniques.
If we treat <strong>the</strong> above algorithm in an in nite medium, tgeom = 1 we note that it collapses to <strong>the</strong>
algorithm described previously. Similarly, itis easy to avoid any species <strong>of</strong> interaction by setting its
interaction distance to in nity. Note that this algorithm can be used to model analog transport, which
is accomplished by setting t inelastic = t elastic =0. Therefore, this algorithm can be applied to photon
transport as well. Indeed, as far as <strong>the</strong> algorithm is concerned, an electron is transported in a similar
fashion to a photon except that an electron has two extra interaction channels.
7

3 Conclusions
Transport mechanics algorithms have been reviewed. Based upon recent developments in EGS4/
PRESTA-II, EGSnrc and extensions to <strong>the</strong> PENELOPE code, an e cient algorithm which takes into
account energy losses and provides realistic spatial-angular correlations has been described. Future
work will demonstrate <strong>the</strong> step-size stability <strong>of</strong> this algorithm under a variety <strong>of</strong> conditions.
Acknowledgements
We would like to thank Pr<strong>of</strong>. Ed Larsen <strong>of</strong> <strong>the</strong> University <strong>of</strong> Michigan and Pr<strong>of</strong>. Francesc Salvat <strong>of</strong>
<strong>the</strong> University <strong>of</strong> Barcelona for lively discussions on transport mechanics. This project was supported
by funds from Quantum Research Services, Inc. under an award from <strong>the</strong> Department <strong>of</strong> Energy.
The ndings, opinions and recommendations expressed <strong>the</strong>rein are those <strong>of</strong> <strong>the</strong> author and are not
necessarily those <strong>of</strong> Quantum Research Services, Inc. or <strong>the</strong> Department <strong>of</strong> Energy.
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10

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.11-22
Improvements <strong>of</strong> Low Energy Photon Transport for EGS5
Y. Namito, H. Hirayama and S. Ban
High Energy Accelerator Research Organization (KEK)
Oho, Tsukuba-shi, Ibaraki-ken, 305-0801, Japan
Abstract
We have implemented additional functions to EGS4 code [1]. We describe each modi cation
<strong>of</strong> EGS4 after <strong>the</strong> 1st international EGS4 workshop [2]. The items are i) L-X ray ii) Electron
impact ionization, iii) Auger electron and iv) X ray and Auger from compound and mixture. Then,
we describe two systematic comparison <strong>of</strong> improved EGS4 code and measurements, which were
performed to verify <strong>the</strong> validity <strong>of</strong> <strong>the</strong> improvement. The comparison are \20-40 keV synchrotron
radiation scattering experiment" and "Electron beam induced K-X ray intensity". Agreement <strong>of</strong>
calculation and experiment were satisfying level in both comparisons.
1 Introduction
In <strong>the</strong> 1st international EGS4 workshop in 1997, we presented improvements <strong>of</strong> low energy photon
transport <strong>of</strong> EGS4 code. The items <strong>of</strong> <strong>the</strong> improvements were,
Linearly polarized photon scattering [3],
Doppler broadening in Compton scattering [4],
L-X ray [5],
Electron impact ionization [6].
We continue an improvement<strong>of</strong>low energy photon transport <strong>of</strong> EGS4 code which will be integrated
as part <strong>of</strong> EGS5 code. The new improvements are,
Revision <strong>of</strong> L-X ray,
Revision <strong>of</strong> Electron impact ionization,
Auger electron,
Xray/Auger from compound/mixture.
In Sec. 2, <strong>the</strong>se new improvements are described.
Two systematic comparisons <strong>of</strong> measurements and EGS4 code were performed to verify <strong>the</strong> validity
<strong>of</strong> <strong>the</strong> improvement. These comparisons were described in Sec 3. The rst comparison is \20-40 keV
synchrotron radiation scattering experiment". Targets are C, Cu, Ag, and Pb. Compton, Rayleigh,
K-X, L-X rays are observed using Ge detectors. L-X rays from Gd sample were also measured.
The second comparison is \Electron beam induced K-X ray". Electron beam <strong>of</strong> 10-3000 keV
incident normally on targets (Al,Ti,Cu,Ag and Au) and K-X ray intensity was calculated at 120 and
180 . Comparison <strong>of</strong> photon spectra from Cu and Sn target due to electron beam incident were also
performed.
All <strong>the</strong> improvements until now areavailable as programs [7] and manuals [8, 9].
1

2 Improvements <strong>of</strong> Programs
2.1 L-X ray
2.1.1 Energy dependent L subshell cross sections
In 1996 version <strong>of</strong> L-X ray calculation [5], <strong>the</strong> ratio <strong>of</strong> L subshell photoelectric e ect cross sections
at <strong>the</strong> energy <strong>of</strong> L-edges was used and any energy dependence <strong>of</strong> <strong>the</strong> ratio was ignored. This introduced
an error greater than negligible level. We implemented energy dependence <strong>of</strong> <strong>the</strong> ratio <strong>of</strong> L subshell
photoelectric e ect cross sections using Matese and Johnson's calculated L subshell photoelectric e ect
cross sections [10].
2.1.2 Emission rates library based on experiment values
In 1996 version <strong>of</strong> L-X ray calculation [5], we used Sco eld's calculated K and L emission rates
[11]. In <strong>the</strong> current version, we use Salem's experimental K and L emission rates [12]. EGS4 calculation
using Salem's value gives better agreement with measurements comparing to calculation using
Sco eld's value.
2.1.3 Local extrapolation method (LEM)
To avoid possible underestimation <strong>of</strong> X rays near edge-energy two modi cations were applied.
1. Improvement <strong>of</strong> piecewise linear tting named `Local extrapolation method'(LEM) to treat mean
free path and branching ratio near to edge. [13]
2. Increasing <strong>the</strong> number <strong>of</strong> photon energy intervals from 200 to 1000.
2.2 EII
In 1999, we implemented EII into EGS4 code. [6] We updated EII calculation function so that it
is ready to built up for EGS5. Here, following modi cations were applied to EII calculation.
1. Common subroutine with photoelectric e ect is used in K-X calculation.
2. EII<strong>of</strong>any element in compound and mixture is treated.
In <strong>the</strong> same time, <strong>the</strong> treatment <strong>of</strong> photoelectric e ect related phenomena in EGS4 code was also
changed. As a result <strong>of</strong> this, following points were also modi ed,
1. Fluorescent yield was updated from [14, 15] to [16, 17]. The ratio <strong>of</strong> currently used and previously
used uorescent yield is shown in Fig.1.
2. Possible underestimation <strong>of</strong> K is now avoided by means <strong>of</strong> LEM and increasing <strong>the</strong> number <strong>of</strong>
photon energy intervals.
3. The number <strong>of</strong> <strong>the</strong> energy <strong>of</strong> K-X ray is increased from 4 to 10.
2.3 Auger electron
Auger electron calculation was added to EGS4 code. Data and method <strong>of</strong> calculation is described
in [9].
Guadala et al measured electron spectra from Al and Ti target using monochronized synchrotron
radiation photon at BNL. [18] Electron emitted to forward direction <strong>of</strong> 10 opening angle were measured
with energy resolution <strong>of</strong> 3%. We simulated Guadala's experiment using <strong>the</strong> improved EGS4
code. As <strong>the</strong> photon energy was not measured, we adjusted incident photon energy from Compton
recoil energy. Comparison <strong>of</strong> measurement and calculation is shown in Fig. 2. EGS4 underestimated
Auger electron from Al sample. EGS4 reproduced Auger electron from Ti sample and Compton recoil
electron from both <strong>the</strong> samples.
2

Table 1: Incident photon energy and linear polarization
Energy (keV) 40 30 20
Linear Polarization (P ) 0.885 0.877 0.873
Table 2: Samples and <strong>the</strong>ir thickness
Sample C Cu Ag Pb
T (g/cm 2 ) 0.1325 1.79 0.525 0.568
2.4 X ray/Auger from compound/mixture.
We modi ed pegs4 program so that <strong>the</strong> ratio <strong>of</strong> photo electric e ect cross sections <strong>of</strong> each element
in compound and mixture is output as a function <strong>of</strong> photon energy. We also modi ed EGS4 program
to read in this ratio and to use it to select element in photoelectric e ect in compound and mixture.
After <strong>the</strong> element is sampled in <strong>the</strong> calculation, ei<strong>the</strong>r X ray or Auger electron from that element is
followed. The detail <strong>of</strong> <strong>the</strong> calculation method is described in [9].
3 Systematic Comparison <strong>of</strong> Measurement and Calculation
3.1 Photon Beam Incident
We performed a mono-energy photon-scattering experiment at a BL-14C in a 2.5 GeV synchrotron
light facility (PF). The experimental arrangement is shown in Fig.3. Photons from a vertical wiggler
were used after being monochronized by a Si(1,1,1) double crystal monochrometer. A linearly polarized
mono-energy photon beam was scattered by a sample located at point O with its normal vector
1
; ) <strong>the</strong> scattered photons were detected by two high-purity Ge detectors located at =90 .
(; 1 2
p 2 1 2
Incident photon energies and linear polarization are shown in Table 1. Sample and <strong>the</strong>ir thickness
are shown in Table 2. One Ge detector (Ge2) was located in <strong>the</strong> plane <strong>of</strong> <strong>the</strong> incident polarization
vector( = 0 ), and <strong>the</strong> o<strong>the</strong>r (Ge1) in <strong>the</strong> plane perpendicular to it ( = 90 ). Samples were
contained in a vacuum chamber, and vacuum pipes were placed between <strong>the</strong> vacuum chamber and
<strong>the</strong> Ge detectors in order to reduce any scattering due to <strong>the</strong> air. Collimators <strong>of</strong> 5.01 mm aperture
were placed in front <strong>of</strong> Ge detectors (C1C2). The distance from <strong>the</strong> surface <strong>of</strong> <strong>the</strong> sample to <strong>the</strong>
collimator was 420 mm. The opening angle <strong>of</strong> this collimator was 0:33 and <strong>the</strong> energy spread <strong>of</strong>
a Compton-scattered photon due to this opening angle (without Doppler broadening) was negligibly
small, 31eV for incident beam<strong>of</strong> 40 keV. The incident photon intensity was monitored in a free{air
ionization chamber, which was calibrated using a calorimeter [19].
Two stage EGS4 calculation was performed. In <strong>the</strong> rst stage, photon beam incident on <strong>the</strong>
sample and emergent photons (A) are scored. In <strong>the</strong> second stage, energy deposition in Ge detector
was calculated while using `A' as a photon source.
Measured and calculated photon spectra are shown in Fig. 4. The spectrum by EGS4 calculation
is smeared by Gaussian function <strong>of</strong> FWHM=0.3 keV to account for <strong>the</strong> resolution <strong>of</strong> Ge detector. The
shape <strong>of</strong> Compton scattering, Rayleigh scattering, K-X ray and L-X ray peaks are well reproduced by
<strong>the</strong> EGS4 calculation.
The ratio <strong>of</strong> measured and calculated peaks are shown in Fig. 5. In <strong>the</strong> L-X ray comparison,
preliminary data <strong>of</strong> Gd sample are also shown. jC=M ; 1j 0.03 for Compton, 0.6 for Rayleigh, 0.04
for K-X and 0.15 for L-X.
3

Table 3: Geometric average <strong>of</strong> C/M <strong>of</strong> K-X ray yields. Gr and Ca means <strong>the</strong> calculation result using Gryzinski's
and Casnati's cross section, respectively.
3.2 Electron Beam Incident
Target Al Ti Cu Ag Au Av
EGS4 0.0027 0.023 0.053 0.31 0.85 0.061
EGS4+EII(Gr) 0.96 1.12 0.86 0.91 1.07 0.98
EGS4+EII(Ca) 1.16 1.40 1.18 1.11 1.16 1.21
We simulated following three measurements.
1. Dick et al performed a systematic measurement <strong>of</strong> K-X ray when electron beam <strong>of</strong> 10, 20, 40,
100, 200, 500, 1500 and 3000 keV hits target(Al, Ti, Cu, Ag and Au) normally. [20] K-X ray
yield per incident electron was measured at = 120 and 180 .
2. Acosta et al measured photon spectra emitted from Cu target at = 140 using Si detector
when an electron beam <strong>of</strong> 20 keV incident normally on <strong>the</strong> target [23].
3. Placious measured bremsstrahlung photons and K-X rays from Sn targets iat =70 and 140
for <strong>the</strong> normal incidence <strong>of</strong> 100 keV electrons [21, 22].
EGS4 calculation with and without <strong>the</strong> improvement to treat EII were performed. As a K-shell
EII cross section, Gryzinski's relativistic cross section [24] were used. All <strong>the</strong> comparisons were done
in absolute, i.e. no normalization between <strong>the</strong> measurement and <strong>the</strong> calculation were done.
To simulate Acosta's experiment, two stage calculation was done. In <strong>the</strong> rst stage, photons
emerging from <strong>the</strong> target to =125-135 was scored (A). In <strong>the</strong> second stage, we calculated energy
deposition in Si detector using "A" as a source. All <strong>the</strong> absorbing layers in Si detector were considered.
3.2.1 K-X ray yield
The calculated and measured K-X ray yields are shown in Fig. 1. The statistical error in <strong>the</strong>
calculation is within 3% for EGS4+EII, 10% and 5% for EGS4 <strong>of</strong> Al and o<strong>the</strong>r targets, respectively.
The geometric average <strong>of</strong> <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> calculated K-X ray yield to <strong>the</strong> measured one is shown
for each target in Table 1. Here, a result <strong>of</strong> EGS4+EII calculation using Casnati's EII cross section
[25, 26] is also shown, whose agreement with measurement isworse comparing to <strong>the</strong> calculation using
Gryzinski's cross section.
The EGS4 calculation apparently becomes underestimated with decreasing Z <strong>of</strong> <strong>the</strong> target. C/M
is only 0.0027 for Al, but C/M is 0.85 for Au. The degree <strong>of</strong> underestimation depends weakly on <strong>the</strong>
electron incident energy and <strong>the</strong> scoring angle.
For Al, Ti, Cu and Ag sample, dominant contribution <strong>of</strong> K-X ray isEII.For Au sample, dominant
contribution <strong>of</strong> K-X ray is photoelectric e ect <strong>of</strong> bremsstrahlung photon.
3.2.2 Photon spectra from a Cu target
The calculated and measured photon spectra from Cu target are shown in Fig. 2. C/M=0.92, 0.83
and 0.85 for energy intervals <strong>of</strong> 1-7.6 (low energy bremsstrahlung), 7.6-9.2 (K-X) and 9.2-20 keV (high
energy bremsstrahlung) when EII is considered in a calculation. When EII is ignored, C/M=0.07 in
K-X region. Gauss smearing <strong>of</strong> FWHM=1.6 keV were applied to <strong>the</strong> EGS4 result to simulate energy
resolution <strong>of</strong> <strong>the</strong> Si detector.
4

3.2.3 Photon spectra from a Sn target
The calculated and measured photon spectra from Sn target are shown in Fig. 3. C/M=0.74
and 0.88 at =70 and = 110 , respectively for energy intervals <strong>of</strong> 10.0-36.0 keV (K-X) when EII
is considered in a calculation. When EII is ignored, C/M=0.52 and 0.67 at = 70 and = 110 ,
respectively for energy region <strong>of</strong> 10.0-36.0 keV.
As NaI detector was used in this measurement, energy resolution is not good comparing to Acosta's
measurement. Then, large amount <strong>of</strong> bremsstrahlung photon contributed to <strong>the</strong> counts in <strong>the</strong> K-X
ray energy region. Gauss smearing <strong>of</strong> FWHM=8 keV were applied to <strong>the</strong> EGS4 result to simulate
energy resolution <strong>of</strong> <strong>the</strong> NaI detector.
4 Discussion
4.1 Photon beam incident
4.1.1 Rayleigh scattering
As shown in Fig.5(b), measured and calculated intensity <strong>of</strong>Rayleigh scattered photon di ers by
factor <strong>of</strong> 1.5 or more. This is due to interference between Rayleigh scattered photons.
About C and Pb sample, jM=Cj ;1 < 0:15. This means <strong>the</strong> e ect <strong>of</strong> interference is small for
<strong>the</strong>se samples, The di erence between that in horizontal and vertical directions are small. This means
that <strong>the</strong> azimuth angle dependence is small. It may be possible to simulate interference <strong>of</strong> Rayleigh
scattering from C and Pb sample by modifying <strong>the</strong> form factor <strong>of</strong> Rayleigh scattering in <strong>the</strong> same way
as that <strong>of</strong> water [27].
4.1.2 L-X ray
M/C 1.07 and 0.85 for Gd and Ag. There are possible sources <strong>of</strong> errors both in experimental
side and calculation side.
Measuring Ag L-X ray is more di cult comparing to o<strong>the</strong>r measurements because <strong>of</strong> its low energy
(2.5-4 keV). The e ciency <strong>of</strong> Ge detectors change largely depending on energy and attenuation due
to air and Kapton lm is also evident. The measurement <strong>of</strong>GdL-Xray is only preliminary and <strong>the</strong>se
data may bechanged in <strong>the</strong> future measurement.
The error <strong>of</strong> L-shell uorescent yields ( L1, L2 and L3) are 30-20, 25-10 and 20-10% respectively
for Ag, 15, 10-5 and 5% respectively for Gd. [16]
4.2 EII
Among 62 comparison between Dick's K-X ray yield measurement and EGS4 calculation, jC=M;1j
was within 0.15 for 41 cases. We guess <strong>the</strong> largest source <strong>of</strong> <strong>the</strong> discrepancy between measurement
and calculation is <strong>the</strong> error in EII cross section.
In <strong>the</strong> comparison <strong>of</strong> Dick's measurement and EGS4 calculation, C/M=0.79 when electron energy=20
keV, target=Cu and = 120 . In <strong>the</strong> comparison <strong>of</strong> Acosta's measurement and EGS4
calculation, C/M=0.83. The close agreement <strong>of</strong>two C/M values suggest that both experiment values
are consistent.
In <strong>the</strong> comparison <strong>of</strong> Acosta's measurement and EGS4 calculation, high energy part <strong>of</strong> bremsstrahlung
photon was underestimated. Similar underestimation <strong>of</strong> bremsstrahlung at high photon
energy side was also seen in <strong>the</strong> comparison <strong>of</strong> photon spectra from a Sn target. We guess <strong>the</strong>se
underestimation can be xed by using better bremsstrahlung photon generation cross section.
5

5 Conclusion
Two systematic comparisons <strong>of</strong> measurements and EGS4 code were performed to verify <strong>the</strong> validity
<strong>of</strong> <strong>the</strong> improvement. The rst comparison is \20-40 keV synchrotron radiation scattering experiment".
Targets are C, Cu, Ag, and Pb. Compton, Rayleigh, K-X, L-X rays are observed using Ge detectors.
L-X rays from Gd sample were also measured. The agreement <strong>of</strong> EGS4 and <strong>the</strong> measurement was
good both in <strong>the</strong> energy spectral shape and intensity: jC=M ;1j 0.03 for Compton, 0.6 for Rayleigh,
0.04 for K-X and 0.15 for L-X.
Systematic comparison <strong>of</strong> measured and calculated K-X ray yield from various target for electron
beam <strong>of</strong> 0.01 to 3 MeV was performed without any normalization. General agreement between
measurement and calculation show <strong>the</strong> validity <strong>of</strong> improved EGS4 code. For Al, Ti, Cu and Ag sample,
dominant contribution <strong>of</strong> K-X ray is EII. For Au sample, dominant contribution <strong>of</strong> K-X ray is
photoelectric e ect <strong>of</strong> bremsstrahlung photon.
References
[1] W. R. Nelson, H. Hirayama, D. W. O. Rogers, SLAC-265 (Stanford University, Stanford, 1985)
[2] Y. Namito, H. Hirayama and S. Ban, \Improvements <strong>of</strong> Low-Energy Photon Transport in EGS4",
In 1st <strong>International</strong> <strong>Workshop</strong> on EGS4, Japan, Aug. 26-29 1997 ed. by. H. Hirayama, Y. Namito
and S. Ban, KEK Proc. 99-16, (1997) pp.32-50
[3] Y. Namito, S. Ban and H. Hirayama, Nucl. Instrum. and Meth. A 332(1993)277.
[4] Y. Namito, S. Ban and H. Hirayama, Nucl. Instrum. and Meth. A 349(1994)489.
[5] H. Hirayama, Y. Namito and S. Ban, \Implementation <strong>of</strong> an L-Shell Photoelectron and an L
X-ray for Elements into <strong>the</strong> EGS4 Code", KEK Internal 96-10 (1996).
[6] Y. Namito and H. Hirayama, Nucl. Instrum. and Meth. A423(1999)238.
[7] ftp://ftp.kek.jp/kek/kek egs4/kek improve/kek improve.*
[8] Y. Namito and H. Hirayama, \LSCAT: Low-energy Photon-scattering Expansion for <strong>the</strong> EGS4
Code (Inclusion <strong>of</strong> Electron Impact Ionization)", KEK Internal 2000-4 (2000).
[9] H. Hirayama and Y. Namito, \General Treatment <strong>of</strong> Photoelectric Related Phenomena for Compounds
and Mixtures in EGS4", KEK Internal 2000-3 (2000).
[10] J. J. Matese and W. R. Johnson, Phys. Rev. 140(1965)A1.
[11] J. M. Sco eld, At. Data and Nucl. Data Tables 14(1974)121.
[12] S. I. Salem and P. L. Lee, At. Data and Nucl. Data Tables 18(1976)233.
[13] Y. Namito and H. Hirayama, \Improvement <strong>of</strong> <strong>the</strong> Cross-section and Branching-ratio Evaluation
in EGS4 in <strong>the</strong> Energy Interval Which Has an Absorption-edge", In 8th EGS4 Users' Meeting
in Japan, Japan, Aug. 1-3 1999 ed. by. H. Hirayama, Y. Namito and S. Ban, KEK Proc. 99-15,
(1999) pp.1-6.
[14] Ed C. M. Lederer V. S. Shirley, Table <strong>of</strong> Isotopes 7th edn (Wiley-Interscience, New York, 1978).
[15] W. Bambynek et al., Rev. Mod. Phys. 44(1972)716.
[16] Ed V. S. Shirley, Table <strong>of</strong> Isotopes 8th edn. (Wiley-Interscience, New York, 1996).
[17] W. Bambynek, post-deadline abstract published in <strong>the</strong> Proc. <strong>of</strong> <strong>the</strong> Conference on X-ray and
inner-shell processes in atoms, molecules and solids, Leipzig, Aug 20-24 (1984).
6

7
Figure 1: Ratio <strong>of</strong> currently used uorescent yield and previously used one.
0.95
0 20 40 60 80 100
Z
Ω k (84)/Ω k (72)
1
+3%@Ti
+2%@Cu
+0%@Ag,Sn,Au
1.05
+9%@Al
1.1
[27] L. R. M. Morin, J. Phys. Chem. Ref. Data 11 (1982)1091.
[26] E. Casnati, A. Tartari, C. Baraldi, J. Phys. B 16 (1983)505.
[25] E. Casnati, A. Tartari, C. Baraldi, J. Phys. B 15 (1982)155
[24] M. Gryzinski, Phys. Rev. 138, A 305, A 322, A 336 (1965).
[23] E. Acosta, X. Llovet, E. Coleoni, J. A. Riveros, F. Salvat, J. Apply. Phys. 83(1998)6038.
[22] M. J. Berger, In Monte Carlo transport <strong>of</strong> Electron and Photons, eds. T. M. Jenkins, W. R. Nelson
and A. Rindi (Plenum, New York, 1988) pp.216, Figure 8.27b.
[21] R. Placious, J. Appl. Phys. 38(1967)2030.
[20] C. E. Dick, A. C. Lucas, J. M. Motz, R. C. Placious, J. H. Sparrow, J. Appl. Phys. 44(1973)815.
[19] H. Nakashima et al., Nucl. Instr. Meth. A 310(1991)696.
[18] N. A. Guadala et al., Nucl. Instr. Meth. A 347(1994)504.

Number<strong>of</strong>Electron(arb.)
700
600
500
400
300
200
100
(a)Al48.1nm,57.0keV
Auger ComptonRecoil
Exp
EGS4
0
0 5 10 15
ElectronKineticEnergy(keV)
Number<strong>of</strong>Electron(arb.)
2500
2000
1500
1000
500
Auger
(b)Ti68nm,57.25keV
Exp
EGS4
ComptonRecoil
0
0 5 10 15
ElectronKineticEnergy(keV)
Figure 2: Comparison <strong>of</strong> <strong>the</strong> electron spectra. Incident is monochronized synchrotron radiation photon. Measurement
by Guadala et al is shown by lled circles. EGS4 calculations are shown in solid line. Target materials,
thickness and incident photon energies are, (a) Al 48.1 nm, 57.0 keV (b) Ti 68 nm, 57.25 keV. Incident photon
energy was adjusted from Compton recoil electron energy.
Figure 3: Experiment arrangement. A mono-energetic linearly polarized synchrotron radiation photon beam
was scattered by a sample (S) <strong>the</strong> scattered photons were counted by two high-purity Gedetectors for lowenergy
photons (Ge1, Ge2). The aperture <strong>of</strong> <strong>the</strong> C0 collimator was 2 mm. A free air ion chamber (FAIC)
was located in front <strong>of</strong> <strong>the</strong> sample to monitor incident photon intensity. The sample was placed at point O
its normal vector is (; 1
2 ; 1p
2 1
2 ). Collimators(C1C2) de ne <strong>the</strong> opening angle <strong>of</strong> Ge detectors. The distance
from <strong>the</strong> surface <strong>of</strong> <strong>the</strong> sample to <strong>the</strong> exit <strong>of</strong> collimator (L1) was 420 mm and <strong>the</strong> aperture <strong>of</strong> Collimator(D1)
was 5.01 mm.
8

Counts(/keV/sr/source)
Counts(/keV/sr/source)
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
(a)C40keV
COUNTH
COUNTV
EGS4H
EGS4V
GeCompton
Edge
GeK-XEscape
M.S.
Compton
Rayleigh
0 5 10 15 20 25 30 35 40
EnergyDeposition(keV)
COUNTH
COUNTV
EGS4H
EGS4V
L-X
FeK-X
(c)Ag20keV
GeK-XEscape
ResonantRaman
Rayleigh
Compton
0 5 10 15 20
EnergyDeposition(keV)
Counts(/keV/sr/source)
Counts(/keV/sr/source)
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -2
10 -3
10 -4
10 -5
10 -6
K-X
PileUp
(b)Cu40keV
COUNTH
COUNTV
EGS4H
EGS4V
GeK-X
Escape
Rayleigh
Compton
0 5 10 15 20 25 30 35 40
EnergyDeposition(keV)
GeK-X
Escape
Ll
Lα Lβ
Lγ
(d)Pb40keV
PileUp
COUNTH
COUNTV
EGS4H
EGS4V
GeK-X
Escape
Rayleigh
Compton
0 5 10 15 20 25 30 35 40
EnergyDeposition(keV)
Figure 4: Comparison <strong>of</strong> <strong>the</strong> photon spectra. Measurement is shown by lled (horizontal) and open circles
(vertical). EGS4 calculations are shown in solid (horizontal) and dashed (vertical). Targets and incident
photon energy are, (a) C-40 keV (b) Cu-40 keV (c) Ag-20 keV (d) Pb-40 keV.
9

M/C
M/C
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
CH
CuH
AgH
PbH
CV
CuV
AgV
PbV
(a)Compton
0.8
15 20 25 30 35 40 45
IncidentPhotonEnergy(keV)
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
(c)K-X
CuH
AgH
CuV
AgV
0.8
15 20 25 30 35 40 45
IncidentPhotonEnergy(keV)
M/C
M/C
1.4
1.3
1.2
1.1
1
0.9
0.8
CuH
PbV
PbH
CH
CV
(b)Rayleigh
CuV
0.7
AgV
AgH
0.6
5 10 15 20 25 30 35 40 45
IncidentPhotonEnergy(keV)
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
(d)L-X
Gd
Pb
Ag
0.8
0 10 20 30 40 50
IncidentPhotonEnergy(keV)
Figure 5: Ratio <strong>of</strong> measured and calculated intensity <strong>of</strong> each peak. `H' and `V' means horizontal and vertical
respectively. (a) Compton scattering (b) Rayleigh scattering (c) K-X ray (d) L-X ray.
10
H
V
H
V
V
H

K-Xrayyield(photons/sr/e-)
K-Xrayyield(photons/sr/e-)
K-Xrayyield(photons/sr/e-)
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -3
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -2
10 -1
10 -2
10 -3
10 -4
10 -5
10 -6
10 -2
(a)Al
Exp(Dick)180 o
Exp(Dick)120 o
EGS4+EII(GR)
EGS4
(c)Cu
(e)Au
10 -2
180 o
120 o
180 o
120 o
10 -1
C/M=0.96
C/M=0.0027
10 0
Incidentelectronkineticenergy(MeV)
10 -1
C/M=0.86
C/M=0.053
Exp(Dicketal)180 o
Exp(Dicketal)120 o
EGS4+EII(GR)
EGS4
10 0
Incidentelectronkineticenergy(MeV)
10 -1
10 0
C/M=1.07
C/M=0.85
180 o
120 o
180 o
120 o
Exp(Dick)
EGS4+EII(GR)
EGS4
Incidentelectronkineticenergy(MeV)
180 o
10 1
10 1
10 1
K-Xrayyield(photons/sr/e-)
K-Xrayyield(photons/sr/e-)
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -3
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -2
(b)Ti
(d)Ag
10 -2
10 -1
180 o
120 o
180 o
120 o
Exp.(Dick)180 o
Exp.(Dick)120 o
EGS4+EII(GR)
EGS4
10 0
C/M=1.12
Incidentelectronkineticenergy(MeV)
10 -1
C/M=0.91
C/M=0.31
Exp(Dick)180 o
EGS4+EII(GR)
EGS4
10 0
Incidentelectronkineticenergy(MeV)
C/M=0.023
Figure 6: Comparison <strong>of</strong> <strong>the</strong> K-X ray yield. The measured values by Dicketal. are indicated by lled boxes
( =180 ) and lled triangles ( = 120 ). EGS4: EGS4 calculation without EII EGS4+EII: EGS4 calculation
with EII using Gryzinski's cross section. (a) Al (b) Ti (c) Cu (d) Ag (e) Au.
11
180 o
10 1
10 1

Counts(/keV/sr./source)
10 -3
10 -4
10 -5
10 -6
10 -7
Exp.(Acosta)
EGS4+EII
EGS4
0 5 10
PhotonEnergy(keV)
15 20
Figure 7: Spectra <strong>of</strong> <strong>the</strong> bremsstrahlung and K-X rays from a Cu target toward =130 . A20keV electron
beam is normally incident on <strong>the</strong> target. The closed circle indicates a measurement using a Si detector by
Acosta et al. The solid and dashed lines indicates <strong>the</strong> EGS4 calculation with EII using Gryzinski's cross section
and without EII.
Photons(/MeV/sr./electron)
10 -1
10 -2
10 -3
10 -4
(a)θ=70 o
Exp.(Placious)
EGS4+EII(GR)
EGS4
0 0.02 0.04 0.06 0.08 0.1 0.12
Photonenergy(MeV)
Photons(/MeV/sr./electron)
10 -1
10 -2
10 -3
10 -4
Exp.(Placious)
EGS4+EII(GR)
EGS4
(b)θ=110 o
0 0.02 0.04 0.06 0.08 0.1 0.12
Photonenergy(MeV)
Figure 8: Spectra <strong>of</strong> <strong>the</strong> bremsstrahlung and K-X rays from a Sn target toward (a) = 70 and (b) =
120 , respectively. A 100 keV electron beam is normally incident on <strong>the</strong> target. The closed circle indicates a
measurement using an NaI detector by Placious. The solid and dashed lines indicates <strong>the</strong> EGS4 calculation
with EII using Gryzinski's cross section and without EII.
12

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.23-30
Status <strong>of</strong> <strong>the</strong> Object-oriented EGS Interface Project
A. M. Yacout, W. L. Dunn, W. R. Nelson 1 , P. Lui 1 ,
A. F. Bielajew 2 , H. Hirayama 3 and Y. Namito 3
Quantum Research Services, PO Box 52391, Durham, NC 27717, USA
1 Stanford Linear Accelerator Center, PO Box 4349, Stanford, CA 94309, USA
2 The University <strong>of</strong> Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109, USA
3 High Energy Accelerator Research Organization (KEK), Oho, Tsukuba-shi,
Ibaraki-ken 305-0801, Japan
Abstract
The object-oriented EGS interface project seeks to simplify { using modern object-oriented
and visual user interface techniques { <strong>the</strong> geometry and scoring aspects <strong>of</strong> <strong>the</strong> process <strong>of</strong> running
<strong>the</strong> EGS code. The project will create an extremely user-friendly EGS package that retains and
exploits <strong>the</strong> well documented physics advantages <strong>of</strong> EGS but removes <strong>the</strong> requirement that <strong>the</strong>
user write HOWFAR and AUSGAB subroutines to de ne <strong>the</strong> geometry and scoring aspects <strong>of</strong> each
new problem. In addition, several physics enhancements will be incorporated in EGS5. Although
EGS5 will be able to be used in <strong>the</strong> traditional way { in a stand-alone fashion with users writing
<strong>the</strong>ir own geometry and scoring subroutines { it is designed to be used in a completely new way
{ linked to a user interface through which users can manage all aspects <strong>of</strong> problem speci cation
and code operation. This paper concentrates on <strong>the</strong> object-oriented user interface, which will
dramatically simplify de ning problem-speci c detail for EGS. The \EGS5+VUI1" package will
allow users to solve independent problems by run-time linking <strong>of</strong> <strong>the</strong> EGS5 code with class libraries
that encapsulate <strong>the</strong> geometry and scoring aspects <strong>of</strong> each problem. Some simple example problems
are considered in order to illustrate features <strong>of</strong> <strong>the</strong> EGS5+VUI1 package.
1 Introduction
The Electron Gamma Shower (EGS) Monte Carlo coupled electron-photon transport code has
enjoyed much success and broad acceptance over a period <strong>of</strong> manyyears. However, <strong>the</strong> currentversion,
EGS4[1], has now been released for over a decade without formal upgrading and re-release. Fur<strong>the</strong>r,
EGS4 requires that <strong>the</strong> user be pro cient enough to program <strong>the</strong> geometry and scoring aspects <strong>of</strong>
each problem in subroutines that must be compiled and linked to <strong>the</strong> static part <strong>of</strong> <strong>the</strong> code. Use <strong>of</strong>
<strong>the</strong> Mortran pre-processor[2] and several \canned" geometry macros (e.g., $PLAN1,$PLAN2P,$CYLNDR,
etc.[3]) can simplify <strong>the</strong> process, but solving di erent problems never<strong>the</strong>less requires compilation and
linking <strong>of</strong> user code to EGS physics code. This places a substantial burden on <strong>the</strong> user and, not
insigni cantly, permits errors in logic or implementation, especially among inexperienced users.
O<strong>the</strong>r general-purpose Monte Carlo radiation transport codes, such as MCNP and GEANT, deal
with <strong>the</strong> geometry/scoring problem by building extensive libraries and tools. This approach has <strong>the</strong>
disadvantages <strong>of</strong> creating a large code overhead and limiting <strong>the</strong> user to those geometry and scoring
estimators that are built-in. EGS, on <strong>the</strong> o<strong>the</strong>r hand, has allowed user exibility by allowing <strong>the</strong>
user to write <strong>the</strong> geometry/scoring aspects <strong>of</strong> each problem. This leads to a leaner code but adds
time and requires that <strong>the</strong> user be a competent programmer. The application <strong>of</strong> object-oriented
(OO) programming techniques allows <strong>the</strong> \best <strong>of</strong> both worlds." In our OO approach, we respresent
geometrical shapes, sources, and scoring estimators as classes. Objects selected from <strong>the</strong>se classes are
linked to <strong>the</strong> physics code at run time, without <strong>the</strong> need to compile and link user code. Use <strong>of</strong> a
scripted input provides a exible way to build objects at run time.
1

In <strong>the</strong> following, we discuss our e orts to signi cantly upgrade <strong>the</strong> EGS4 code and to develop an
object-oriented EGS interface that will obviate <strong>the</strong> need for <strong>the</strong> user to write problem-speci c code.
2 The EGS5 and Object-oriented EGS Interface Projects
The authors are involved in a multi-institutional e ort to signi cantly upgrade <strong>the</strong> EGS4 code.
This e ort will result in an enhanced version <strong>of</strong> EGS, EGS5, and an OO user interface to <strong>the</strong> enhanced
physics code. The user interface will contain a visual user interface (VUI) through which <strong>the</strong> user
will communicate with <strong>the</strong> rest <strong>of</strong> <strong>the</strong> code <strong>the</strong> combined package will be called EGS5+VUI1. It is
anticipated that EGS5+VUI1 will be released before <strong>the</strong> end <strong>of</strong> <strong>the</strong> year 2001.
To date, EGS4 has been modi ed to conform to modern programming conventions (such as IN-
CLUDE statements for COMMON blocks, etc.) and to incorporate low-energy photon enhancements
developed at KEK. The resulting EGS4.2 version has been extensively benchmarked against EGS4.
Fur<strong>the</strong>r physics enhancements are being developed that will be incorporated into EGS. The nal EGS5
physics code will include at least <strong>the</strong> following enhancements:
Improved low-energy photon transport, e.g.[4]
Improved electron transport modeling, e.g.[5]
Low energy electron cross section handling[6]
Photoelectric angular distributions[7]
Improved bremsstrahlung photon angular distributions[8]
K and L shell uorescence[9]
Some <strong>of</strong> <strong>the</strong>se physics enhancements that will be incorporated in EGS5 are discussed in o<strong>the</strong>r presentations[10,
11] at this workshop. In addition, EGS5 will incorporate cross section generation within <strong>the</strong>
code, ra<strong>the</strong>r than requiring that <strong>the</strong> user run a pre-processor, such as PEGS, to create <strong>the</strong> necessary
cross section les for di erent problems.
The o<strong>the</strong>r signi cant e ort is to construct a powerful object-oriented user interface to EGS that
will revolutionize <strong>the</strong> way EGS is run in <strong>the</strong> future. The OO paradigm is well suited to support our
primary goal <strong>of</strong> producing a reusable code { reusable in <strong>the</strong> sense that modi cations to one component
do not require modi cations to <strong>the</strong> o<strong>the</strong>r components <strong>of</strong> <strong>the</strong> code package. The main components in
our case are <strong>the</strong> physics in EGS, <strong>the</strong> VUI, and <strong>the</strong> user code (including <strong>the</strong> geometry in HOWFAR
and <strong>the</strong> scoring estimators in AUSGAB). It is noted that "modifying" can be interpreted also in <strong>the</strong>
sense <strong>of</strong> "adding", so that in EGS5+VUI1 geometry and o<strong>the</strong>r classes can be added without having
to rebuild <strong>the</strong> rest <strong>of</strong> <strong>the</strong> package.
The encapsulation property <strong>of</strong> OO programming, in which each object encapsulates (contains) its
data and code (functions), provides <strong>the</strong> rst means <strong>of</strong> breaking <strong>the</strong> problem into meaningful components.
Each object is capable <strong>of</strong> manipulating its own data (properties) to independently provide <strong>the</strong>
information required by o<strong>the</strong>r parts <strong>of</strong> <strong>the</strong> system. Thus, for instance, tracking a particle inside a
particular geometrical shape is handled completely by <strong>the</strong> methods encapsulated in <strong>the</strong> object itself.
The implementation <strong>of</strong> <strong>the</strong> tracking code is thus completely hidden from <strong>the</strong> rest <strong>of</strong> <strong>the</strong> system. The
inheritance property <strong>of</strong> OO programming allows <strong>the</strong> construction <strong>of</strong> new object types (classes) based
on existing types. New classes "inherit" some or all <strong>of</strong> <strong>the</strong> properties and methods <strong>of</strong> <strong>the</strong> base class.
This property allows us to re-use existing code and, more importantly, provides a way to specify and
establish a common interface for all object types (existing or to be added) by deriving <strong>the</strong>m from
one common base class. For example, geometrical objects are derived from one common ancestor
this base class de nes <strong>the</strong> required methods for particle tracking (methods to determine if a speci ed
spatial point is inside an object, to determine if a track intersects an object surface, etc.). Classes
2

inherited from this class modify <strong>the</strong>se methods according to <strong>the</strong> geometry <strong>of</strong> <strong>the</strong> shape <strong>the</strong>y represent.
Finally, <strong>the</strong> objects created from <strong>the</strong>se classes are polymorphic: <strong>the</strong> methods in <strong>the</strong> di erent class
types have identical names, but at run time, <strong>the</strong> correct method is called according to <strong>the</strong> type <strong>of</strong> <strong>the</strong>
object being used. These properties <strong>of</strong> OO programming enable us to systematically implement <strong>the</strong>
tracking and scoring aspects <strong>of</strong> Monte Carlo in general, regardless <strong>of</strong> <strong>the</strong> details <strong>of</strong> a speci c problem.
3 Description <strong>of</strong> <strong>the</strong> User Interface
Aschematic <strong>of</strong> <strong>the</strong> EGS5+VUI1 package is given in gure 1. The block marked \EGS5" contains
Figure
Script
Parser read
Script
Generator
write
display
interface
Generic Code Interface
(OO HOWFAR, AUSGAB)
EGS5
Classes
VUI
1: Aschematic <strong>of</strong> <strong>the</strong> EGS5+VUI1 package.
<strong>the</strong> enhanced physics models. For <strong>the</strong> present, it will be programmed in Fortran77 and can be used
in <strong>the</strong> traditional way (write problem-speci c routines, prepare an input le, compile and link <strong>the</strong>
routines with EGS5, and execute <strong>the</strong> resulting code for <strong>the</strong> given problem). However, EGS5 can also
be used in a much simpler way, as part <strong>of</strong> <strong>the</strong> EGS5+VUI1 package. In this case, <strong>the</strong> user will set
up <strong>the</strong> problem by interacting only through <strong>the</strong> VUI, which will be a full-function interface that uses
icons, dialog boxes, menus, etc. to set up a speci c problem. Geometric objects, materials, sources,
and estimators will be selected from pre-de ned libraries. Dimensions, positions, etc. will be entered
into dialog boxes. Once an object has been registered, its methods will be used to draw it on <strong>the</strong>
screen. Geometrical objects can contain o<strong>the</strong>r objects, including o<strong>the</strong>r geometrical objects, allowing
transport in complex geometrical systems. Sessions can be saved and retrieved and <strong>the</strong> user can
initiate execution <strong>of</strong> EGS merely by clicking on an appropriate icon, after <strong>the</strong> problem has been fully
set up. The VUI will allow <strong>the</strong> user to construct a new problem from <strong>the</strong> ground up or by modifying
an old session.
The Script Generator will generate appropriate script from <strong>the</strong> speci c objects that <strong>the</strong> user selects
for a given problem. The script incorporates <strong>the</strong> descriptions <strong>of</strong> all objects representing <strong>the</strong> geometry,
materials, sources, and estimators in <strong>the</strong> problem using a simple syntax. Thus, no separate input data
3

le needs to be prepared. Also, no predetermined order <strong>of</strong> records is required, as in <strong>the</strong> numerical
input les used previously with EGS. Example scripts are given in <strong>the</strong> next section for three simple
problems.
EGS5+VUI1 will contain a Class Library, i.e. a library <strong>of</strong> geometry, source, material, and scoring
classes. The classes will contain methods that perform operations appropriate for <strong>the</strong>ir types. For
example, each geometric class contains <strong>the</strong> following methods:
1. Method to register its name, creator method, properties (names and read/write handlers), and
display methods
2. A creator method to instantiate a new object <strong>of</strong> <strong>the</strong> class
3. Property handlers (methods to read and write a value <strong>of</strong> a property)
4. Display methods to display di erent views <strong>of</strong> <strong>the</strong> object and an interface to query required
properties
5. A method to determine if a speci ed point is inside an object
6. A method to determine if a track intersects an object
7. A method to determine <strong>the</strong> entry point to an object along a speci ed track
8. A method to determine <strong>the</strong> exit point from an object along a speci ed track
One <strong>of</strong> <strong>the</strong> signi cant features <strong>of</strong> EGS5+VUI1 is that a procedure will exist for adding new classes.
Thus, if a user desires to incorporate for a speci c problem a special or unusual geometrical object or
scoring estimator that is not part <strong>of</strong> <strong>the</strong> existing Class Library, a procedure will exist for adding one
or more classes. The new classes are added to <strong>the</strong> run-time library without rebuilding <strong>the</strong> package
and will be available for all future problems. In this way <strong>the</strong> library <strong>of</strong> classes in EGS5+VUI1 can
grow as needed to handle essentially arbitrary problems. It is noted, however, that <strong>the</strong> initial Class
Library will be su cient to treat a very broad range <strong>of</strong> problems.
The Parser creates objects from <strong>the</strong> script at run time, using simple lexical rules. Objects created
by <strong>the</strong> Parser are instances <strong>of</strong> classes stored in <strong>the</strong> Class Library and registered at start-up by <strong>the</strong>
VUI. The Parser will provide high-level functions for developers <strong>of</strong> new classes. The HOWFAR and
AUSGAB routines are reduced to generic (universal) routines that implement systematic tracking and
scoring algorithms and pass information between <strong>the</strong> EGS5 code and <strong>the</strong> problem-speci c objects. The
use<strong>of</strong>genericHOWFAR and AUSGAB routines is possible because <strong>of</strong> <strong>the</strong> OO organization. A single
query is issued to a container called <strong>the</strong> "Mo<strong>the</strong>r Volume." The Mo<strong>the</strong>r Volume queries all internal
geometrical objects and volumes, which in turn query <strong>the</strong>ir internal gometric objects and volumes. In
this way, particle location and transport can be tracked with a single call at each transport step.
4 Demonstration
We consider three simple problems as a means to demonstrate <strong>the</strong> EGS5+VUI1 approach. These
problems were run in an early part <strong>of</strong> <strong>the</strong> project using EGS4. Problem 1 is similar to <strong>the</strong> standard EGS
demonstration problem, namely a mono-directional source emitting 1-MeV photons into a polyethylene
slab along <strong>the</strong> +z direction <strong>the</strong> slab is bounded on one side by a vacuum and on <strong>the</strong> o<strong>the</strong>r by air
(see gure 2). We desire <strong>the</strong> total energy deposited in <strong>the</strong> polyethylene slab. The second and third
problems involve a sphere <strong>of</strong> polyethylene surrounded by vacuum. A source similar to that in <strong>the</strong> rst
sample problem is located at <strong>the</strong> center <strong>of</strong> <strong>the</strong> sphere (see gure 3). We sought <strong>the</strong> energy deposited
in <strong>the</strong> sphere, for Problem 2, and <strong>the</strong> particle ux at <strong>the</strong> outside surface <strong>of</strong> <strong>the</strong> sphere, for Problem
3. This suite <strong>of</strong> problems, though simple, allows us to demonstrate <strong>the</strong> OO approach for di erent
geometries (slab versus sphere) as well as di erent estimators (energy deposition versus boundary
crossing).
4

Air
Polyethylene
Vacuum
1 cm thickness
Mono-directional, photon source
Figure 2: A mono-directional source emits 1-MeV photons into a polyethylene slab <strong>of</strong> thickness one cm. We
seek <strong>the</strong> energy deposited in <strong>the</strong> polyethylene slab.
y
r = 1 cm
Polyethylene
Point source x
Figure 3: A mono-directional source emits 1-MeV photons intoapolyethylene sphere <strong>of</strong> radius one cm. We seek
in Problem 2 <strong>the</strong> energy deposited in <strong>the</strong> sphere and in Problem 3 <strong>the</strong> ux <strong>of</strong> particles at <strong>the</strong> sphere boundary.
5

We solved all problems using EGS in <strong>the</strong> traditional manner. This required writing two HOWFAR
routines (one for <strong>the</strong> slabs and one for <strong>the</strong> sphere) and twoAUSGAB routines (one for energy deposition
and one for ux). The HOWFAR and AUSGAB routines were compiled and linked in various ways
with <strong>the</strong> EGS4 physics code to create three executable codes. We <strong>the</strong>n ran each code with 100,000
histories to obtain results in <strong>the</strong> conventional way. We also solved <strong>the</strong> three problems using <strong>the</strong> OO
approach. This involved writing a script for each problem (this task eventually will be performed by
<strong>the</strong> Script Generator, which has not yet been completed) and <strong>the</strong>n letting <strong>the</strong> parser take each script
and create <strong>the</strong> objects from a library which was linked at run time with <strong>the</strong> EGS4 object module.
The scripts for <strong>the</strong> three problems are given below.
Slab Energy Deposition Script (Problem 1)
TMaterial:POLY{tag="POLY"id=1}
TMaterial:AIR{tag="AIR"id=2}
TSource:Source{energy=1.id=0location=(0.0,0.0,+0.0)
number=100000seed=5555}
TEstimator:Estimator{id=1}
TVolume:Mo<strong>the</strong>rVolume{
TSlabZ:Vaccum{thickness=100.0TPoint=(0,0,-100.0)
ecut=0.01pcut=0.01}
TSlabZ:PolySlab{thickness=1.0TSource=Source
TPoint=(0,0,0)TMaterial=POLYTEstimator=Estimator
transport=1ecut=.01pcut=0.01}
TSlabZ:AirSlab{thickness=100.0TPoint=(0,0,1.0)
TMaterial=AIRtransport=0ecut=.01pcut=.01}
}
Sphere Energy Deposition Script (Problem 2)
TMaterial:POLY{tag="POLY"id=1}
TMaterial:AIR{tag="AIR"id=2}
TSource:Source{energy=1.id=0location=(0.0,0.0,+0.0)
number=100000seed=5555}
TEstimator:Estimator{id=1}
TVolume:"Mo<strong>the</strong>rVolume"{
TSphere:PolySphere{radius=1.0TSource=Source
center=(0,0,0)TMaterial=POLYTEstimator=Estimator
transport=1ecut=.01pcut=0.01}
TSlabZ:EMPTYSlab{thickness=100.0TPoint=(0,0,-50.0)
transport=0ecut=.01pcut=.01}
}
Sphere Flux Script (Problem 3)
TMaterial:POLY{tag="POLY"id=1}
TMaterial:AIR{tag="AIR"id=2}
TSource:Source{energy=1.id=0location=(0.0,0.0,+0.0)
number=100000seed=5555}
TFluxEstimator:Estimator{id=1}
TVolume:"Mo<strong>the</strong>rVolume"{
TSphere:PolySphere{radius=1.0TSource=Source
center=(0,0,0)TMaterial=POLYTEstimator=Estimator
transport=1ecut=.01pcut=0.01}
TSlabZ:EMPTYSlab{thickness=100.0TPoint=(0,0,-50.0)
transport = 0ecut=.01pcut=.01}
}
6

Review <strong>of</strong> <strong>the</strong> scripts indicates <strong>the</strong> simplicity <strong>of</strong> this approach. The user interactively selects
<strong>the</strong> type <strong>of</strong> source, <strong>the</strong> geometric objects, <strong>the</strong> materials, and <strong>the</strong> appropriate estimator and speci es
desired values for <strong>the</strong> necessary parameters. The script generator <strong>the</strong>n creates a script that embeds
this information. For instance, in all three problems, <strong>the</strong>re is only one source, which is located at <strong>the</strong>
origin and emits mono-energetic photons at 1 MeV. The number <strong>of</strong> hisotries for each source is also
embedded in <strong>the</strong> script. Fur<strong>the</strong>r, in Problem 1, <strong>the</strong> Mo<strong>the</strong>r Volume consists <strong>of</strong> three slabs: avacuum
slab that extends from z = -100 cm to z = 0, a polyethylene slab that extends from z =0toz = 1 cm,
and an air slab that extends from z =1cmtoz = 101 cm all three slabs are centered at x = 0 and y =
0. Only <strong>the</strong> polyethylene slab contains a source and an estimator. The Mo<strong>the</strong>r Volumes in Problems
2 and 3 each consist <strong>of</strong> a vacuum slab (arbitrarily extending from z = -50 cm to z = 50 cm) and an
embedded polyethylene sphere <strong>of</strong> radius 1 cm. In fact, <strong>the</strong> scripts <strong>of</strong> Problems 2 and 3 di er only in
<strong>the</strong> one line that identi es which estimator to use (TEstimator in Problem 2 and TFluxEstimator in
Problem 3). The classes for TEstimator and TFluxEstimator contain <strong>the</strong> necessary methods to score
<strong>the</strong> appropriate quantities.
The results obtained from <strong>the</strong> two approaches are compared in <strong>the</strong> Table. It is clear that <strong>the</strong> results
are equivalent, but that in <strong>the</strong> OO case no subroutines had to be re-written and no recompilation for
each problem had to be performed. Of course users <strong>of</strong> <strong>the</strong> EGS5+VUI1 package will not have to write
scripts like those shown above <strong>the</strong>se will be generated by <strong>the</strong> Script Generator part <strong>of</strong> <strong>the</strong> OO user
interface.
5 Conclusions
Table: Comparison <strong>of</strong> results for three sample problems.
FORTRAN OO VUI
Problem 1 0.0017520 0.0000158 0.0017528 0.0000158
Problem 2 0.0017054 0.0000146 0.0017063 0.0000147
Problem 3 0.230075 0.037540 0.230973 0.037547
A new version <strong>of</strong> EGS, EGS5, is being developed that will incorporate numerous physics and
programming enhancements. The owner, SLAC, intends to make EGS5 available to <strong>the</strong> user community
as previous versions <strong>of</strong> EGS were. However, EGS5 will also be made commercially available as
a package with an object-oriented user interface in <strong>the</strong> form <strong>of</strong> EGS5+VUI1. The package will allow
EGS5 to be used without <strong>the</strong> need to write problem-speci c subroutines and compile and link <strong>the</strong>m
to <strong>the</strong> EGS5 physics code. Instead, <strong>the</strong> user will interact with <strong>the</strong> code through a visual user interface
that will prepare a script that de nes <strong>the</strong> problem to be solved. This script will be interpreted by <strong>the</strong>
parser, which creates <strong>the</strong> problem objects for <strong>the</strong> EGS5 physics code at run time from classes stored in
a dynamic link library. The OO user interface package will include numerous geometry, scoring, and
source classes however, if <strong>the</strong> library <strong>of</strong> classes is insu cient for a given problem, a direct procedure
for <strong>the</strong> user to create new classes that can also be linked at run time is included. The new EGS5+VUI1
will enable users to address challenging radiation transport problems using <strong>the</strong> enhanced physics <strong>of</strong>
EGS5 without <strong>the</strong> need to write problem-speci c code.
Acknowledgements
This project was supported by <strong>the</strong> U.S. Department <strong>of</strong> Energy through Grant DE-FG02-
97ER82465.
7

References
[1] W.R. Nelson, H. Hirayama and D.W.O. Rogers, \The EGS4 Code System", SLAC-265, Stanford
Linear Accelerator Center, Stanford University, Stanford, CA (1985).
[2] A.J. Cook, \Mortran3 User's Guide", SLAC Computational Research Group Technical Memorandum
Number CGTM 209, Stanford Linear Accelerator Center, Stanford University, Stanford, CA
(1983).
[3] H. Hirayama and Y. Namito, \Lecture Notes <strong>of</strong> EGS4 Course at KEK", KEK Internal 99-5, KEK,
Tsukuba, Japan (1999).
[4] Y. Namito, S. Ban, and H. Hirayama, \Implementation <strong>of</strong> Linearly-polarized Photon Scattering
into <strong>the</strong> EGS4 Code", Nuc. Instr. Meth. A322(1993)277-283.
[5] A.F. Bielajew and Rogers, \PRESTA: The Parameter Reduced Electron-Step Transport Algorithm
for Electron Monte Carlo Transport", Nucl. Instr. Meth. Phys. Res B18(1987)165-181.
[6] C.-M. Ma and A. E. Nahum, \A new algorithm for EGS4 low-energy electron transport to account
for <strong>the</strong> change in discrete interaction cross-section with energy", Nucl. Instru. Meth. B72(1992)319-
330.
[7] A.F. Bielajew and D. W. O. Rogers, \Photoelectron Angular Distribution in <strong>the</strong> EGS4 Code
System", National Research Council <strong>of</strong> Canada Report PIRS-0058 (1986).
[8] A.F. Bielajew, R. Mohan and C.-S. Chui, \Improved Bremsstrahlung Photon Angular Sampling
in <strong>the</strong> EGS4 code system", Med. Phys. 17(1990)522.
[9] M. Conti, A. Del Guerra, D. Mazzei, P. Russo, W. Bencivelli, E. Bartolucci, A. Messineo, V. Rosso,
A. Stefanini, U. Bottigli, P. Randaccio and W. R. Nelson, \Use <strong>of</strong> <strong>the</strong> EGS4 Monte Carlo Code to
Evaluate <strong>the</strong> Response <strong>of</strong> HgI2 and CdTe Detectors for Photons in <strong>the</strong> Diagnostic Energy Range",
Nucl. Inst. Meth. A322(1992)591-595.
[10] Y. Namito and H. Hirayama, \Improvements <strong>of</strong> Low Energy Photon Transport for EGS5", Proc.
<strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, Aug. 8-10, 2000, KEK, Tsukuba, Japan (2000).
[11] A.F. Bielajew and S.J. Wilderman, \Innovative Electron Transport Methods in EGS5", Proc.
<strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, Aug. 8-10, 2000, KEK, Tsukuba, Japan (2000).
8

where Y is <strong>the</strong> counting e ciency ratio and X <strong>the</strong> surface area <strong>of</strong> <strong>the</strong> phantom (m 2 ).
The relationship between <strong>the</strong> 40 K contents in <strong>the</strong> total body and <strong>the</strong> lean body mass (LBM) <strong>of</strong> <strong>the</strong>
50 subjects is shown in Fig. 6 along with <strong>the</strong> regression lines and correlation coe cients (r). In <strong>the</strong>
gure, <strong>the</strong> heavy solid line represents <strong>the</strong> relationship between <strong>the</strong> LBM and <strong>the</strong> 40 Kcontents in <strong>the</strong>
total body on <strong>the</strong> following assumptions: <strong>the</strong> adipose tissue has much less K contents than <strong>the</strong> LBM
and <strong>the</strong> LBM contains, on <strong>the</strong> average, 2.663 g K kg ;1 [16]. The corrected 40 Kcontents for <strong>the</strong> LBM
give higher correlation coe cient than <strong>the</strong> non-corrected contents. The r values <strong>of</strong> <strong>the</strong> corrected and
<strong>the</strong> non-corrected 40 K contents for <strong>the</strong> LBM in regression are 0.90 and 0.69, respectively. It can be
seen that <strong>the</strong> slope <strong>of</strong> <strong>the</strong> regression equation on <strong>the</strong> corrected 40 Kcontents is similar to that <strong>of</strong> <strong>the</strong>
heavy solid line.
4 Conclusions
The EGS4 code was applied to <strong>the</strong> calibration <strong>of</strong> <strong>the</strong> JAERI whole-body counter. The following
conclusions were derived.
1. The calibration method by <strong>the</strong> calculation was validated by comparing <strong>of</strong> <strong>the</strong> calculated and
measured response functions. The calculated counting e ciencies are useful for routine and
unusual measurements. The counting e ciency curves for <strong>the</strong> child, adolescent and adult water
phantoms are nearly straight in logarithmic scale in <strong>the</strong> photon energy range 300-1,461 keV
when <strong>the</strong> peak counts integrated between double <strong>the</strong> FWHM <strong>of</strong> <strong>the</strong> peak. The scattering e ect
<strong>of</strong> photons on <strong>the</strong> counting e ciency regarding <strong>the</strong> water phantoms accounts for 10 1 % <strong>of</strong>
<strong>the</strong> counting e ciency for 662 keV photons.
2. The counting e ciencies <strong>of</strong> <strong>the</strong> whole-body counter strongly depend on <strong>the</strong> 137 Cs distribution
within <strong>the</strong> body. The 137 Cs body burdens would be underestimated by a factor <strong>of</strong> 3 in <strong>the</strong> worst
case.
3. Using <strong>the</strong> calculated counting e ciencies, <strong>the</strong> correction factors on 40 K whole-body counting
were determined. The correction factors for <strong>the</strong> 40 K whole-body counting shall be practical and
useful for <strong>the</strong> JAERI whole-body counter.
4

Table 1 The water phantoms for <strong>the</strong> Monte Carlo simulation
Adult Adolescent Child
Parts Height Width Length Height Width Length Height Width Length
(cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm)
Head 16.7 13.3 18.0 15.8 12.4 17.9 14.0 11.5 16.8
Neck 8.7 7.8 8.5 7.2 6.7 7.6 5.2 4.9 5.7
Chest 19.4 29.1 20.3 17.1 23.9 17.8 12.0 16.0 12.0
Abdomen 16.1 25.0 20.3 14.2 21.3 17.8 12.7 16.0 12.0
Arm 7.4 6.6 51.0 5.8 5.1 45.3 4.4 4.0 28.0
Pelvis 18.8 28.2 23.6 15.0 23.8 20.6 13.9 16.0 14.0
Thigh 12.7 11.4 33.0 10.5 9.4 27.5 6.8 6.1 14.0
Lower leg 8.6 7.7 37.7 6.8 6.1 34.4 5.1 4.6 19.0
Foot 16.8 8.4 6.6 12.9 6.9 5.8 9.5 5.0 4.5
Height 168.0 cm 149.4 cm 98.0 cm
Weight 60.2 kg 37.4 kg 14.9 kg
6

Photo.1 A photograph <strong>of</strong> a whole-body counter in JAERI.
7

X
Z
Phantom
0.5m
Y
Shieldingroom
Bed
NaI(Tl)detector
Figure 1: Geometry <strong>of</strong> <strong>the</strong> JAERI whole-bidy ciunter and adult water phantom.
Y
Figure 2: Comparison <strong>of</strong> <strong>the</strong> calculated and measured response functions for <strong>the</strong> adult water phantom.
8

ε
ε
ε
ε
ε
ε
Figure 3: Counting e ciencies " and peak e ciencies "' <strong>of</strong> <strong>the</strong> JAERI whole body counter for <strong>the</strong> child,
adolescent and adult water phantom.
1.2
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
Stomach/Wholebody
Figure 4: Response <strong>of</strong> <strong>the</strong> JAERI whole-body counter regarding various 137 Cs distributions.
9

2.5
2
1.5
1
0.5
0
Calculation
Experiment
0.5 1.0 1.5 2.0
Surfacearea<strong>of</strong>phantom(m 2 )
Figure 5: Counting e ciency <strong>of</strong> <strong>the</strong> JAERI whole-body counter regarding <strong>the</strong> surface area <strong>of</strong> <strong>the</strong> watewr
phantom.
7000
6000
5000
4000
3000
2000
1000
0
Non-corrected
r=0.69
Corrected
r=0.90
0 10 20 30 40 50 60 70
Leanbodymass(kg)
Figure 6: Relationship between <strong>the</strong> 40 K contents in <strong>the</strong> total body and <strong>the</strong> lean body mass.
10

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.40-47
Fluence to E ective Dose Conversion Coe cients
for Electrons from 1MeV to 100GeV
S. Tsuda, A. Endo, Y. Yamaguchi and O. Sato 1
Department <strong>of</strong> Health Physics, Japan Atomic Energy Research Institute
Tokai, Ibaraki 319-1195, Japan
1 Mitsubishi Research Institute, INC.
Otemachi, Chiyoda-ku, Tokyo 100-8141, Japan
Abstract
Fluence to e ective dose conversion coe cients have been calculated for electrons from 1MeV
to 100GeV using an anthropomorphic phantom and <strong>the</strong> EGS4 code. The conversion coe cients
were calculated for typical six di erent irradiation geometries by taking electro-magnetic cascade
shower and photonuclear reaction into account. The contribution due to photonuclear reaction in
energies up to 140MeV was evaluated to be less than 0.2% to absorbed dose.
1 Introduction
Dose limits are expressed in terms <strong>of</strong> <strong>the</strong> quantities, introduced in <strong>the</strong> Recommendation <strong>of</strong> <strong>the</strong>
<strong>International</strong> Commission on Radiological Protection (ICRP). The e ective dose, in ICRP publication
60 (ICRP60) [1], is de ned as <strong>the</strong> sum <strong>of</strong> risk-weighted organ doses and used as a radiological protection
quantity related to total stochastic e ect on human body. Since this quantity is not measurable
in practice, <strong>the</strong> conversion coe cient, calculated for standard conditions <strong>of</strong> exposure from physical
quantities such as particle uence to e ective dose, has been used for <strong>the</strong> external radiation protection.
ICRP has compiled <strong>the</strong> conversion coe cients against external radiations such as photons up to
10MeV, neutrons up to 180MeV and electrons up to 10MeV in ICRP Publication 74 (ICRP74) [2].
However, <strong>the</strong>re has been growing need <strong>of</strong> dose conversion coe cients for higher energy or various kinds
<strong>of</strong> radiation.
After <strong>the</strong> publication <strong>of</strong> ICRP74, <strong>the</strong> conversion coe cients have been calculated by several groups
for photons [3, 4] up to 10GeV and for neutrons [5, 6], protons [6, 7], muons [8] and pions [9] up to
10TeV. As for uence to e ective dose conversion coe cients for electrons up to GeV order, Ferrari
et al. [10] calculated <strong>the</strong> conversion coe cients for electrons up to 10GeV in four di erent types <strong>of</strong>
geometries using FLUKA [11], <strong>the</strong> Monte Carlo high energy radiation transport code. The conversion
coe cients for higher energy electrons will be needed for <strong>the</strong> radiation protection in synchrotron
electron facilities etc.
In <strong>the</strong> present study, uence to e ective dose conversion coe cients were calculated for electrons
in an energy range from 1MeV to 100GeV, using an anthropomorphic phantom and <strong>the</strong> photon
electron Monte Carlo simulation code EGS4 [13]. The calculations have included <strong>the</strong> evaluation <strong>of</strong> both
electro-magnetic process and photonuclear reaction, which are caused by high-energy bremsstrahlung
produced in a human body. In <strong>the</strong> calculation <strong>of</strong> e ective dose due to photonuclear reaction, <strong>the</strong>
reactions such as( , p), ( ,d),( ,t),( , 3 He), ( , ) and ( , n) were considered. The contribution
<strong>of</strong> photonuclear reaction to absorbed dose was also evaluated.
1

2 Method <strong>of</strong> Calculation
2.1 E ective dose
In ICRP60, e ective dose is de ned as
E = X
T
w T H T (1)
where w T is <strong>the</strong> tissue weighting factor for tissue or organ, T, and H T is <strong>the</strong> equivalent dose in tissue
or organ, T. The tissue weighting factors are given for 12 tissues or organs and remainder including
10 tissues or organs. H T is given by
HT = X
wRDTR (2)
R
where wR is <strong>the</strong> radiation weighting factor for radiation R and DTR is <strong>the</strong> absorbed dose for tissue or
organ, T, due to radiation R. For photons and electrons, wR is assigned to be unity. When it comes
to <strong>the</strong> treatment <strong>of</strong> colon, we treated <strong>the</strong> lower large intestine as colon and <strong>the</strong> upper large intestine
as one <strong>of</strong> <strong>the</strong> remainder tissues, according to ICRP60.
In <strong>the</strong> evaluation <strong>of</strong> electro-magnetic process, DTR was obtained by dividing deposited energy in
each organ or tissue by its own mass.
In <strong>the</strong> case <strong>of</strong> photonuclear reaction, using <strong>the</strong> averaged photon uence in each organ or tissue
calculated by EGS4, absorbed dose for charged particles were calculated by
D i = 1 X
j
Z
E i
E i
Z
E
N j ij(E ) f j(E iE ) (E )dE dE i (3)
where
D i : absorbed dose for charged particle i, such as proton (p), deuteron (d), triton (t), 3 He, and
-particle ( ),
: density <strong>of</strong> organs or tissue,
E i : energy <strong>of</strong> charged particle i,
E : photon energy,
N j : atom number density <strong>of</strong>j -nucleus such asC,N,O,
ij(E ):cross section <strong>of</strong> j -nucleus for i-particle production when photon energy is E ,
f j(E iE ): energy spectrum <strong>of</strong> secondary particle i by <strong>the</strong> reaction between photon and j -nucleus,
(E ):averaged photon uence in organs or tissue.
In this calculation, it is assumed that recoiled nuclei and secondary charged particles deposit
<strong>the</strong>ir whole energies on <strong>the</strong> spot <strong>of</strong> each organ or tissue where <strong>the</strong> particles are produced (kerma
approximation). However, we did not evaluate <strong>the</strong> contribution <strong>of</strong> secondary neutrons because <strong>of</strong> <strong>the</strong>
following reasons. The rst is that <strong>the</strong> contribution <strong>of</strong> neutron to absorbed dose will be overestimated
under <strong>the</strong> assumption <strong>of</strong> <strong>the</strong> kerma approximation. The second is, that it is reported <strong>the</strong> contribution
<strong>of</strong> neutron produced to absorbed dose is considerably small [14] when a 30cm-thick semi-in nite slab
phantom are irradiated by photons in <strong>the</strong> energy range up to 10GeV.
, was calculated by energy conservation law and
As for recoiled nuclei, <strong>the</strong> kinetic energy, E Recoil
i
dose equivalents were obtained by substituting E Recoil
i for Ei in Eq.(3). Total absorbed dose was
composed <strong>of</strong> those due to electro-magnetic cascade shower and photonuclear reaction. HT in each
organ or tissue was converted from <strong>the</strong> total absorbed dose in Eq.(2). Finally, we obtained E by
summating <strong>the</strong> product <strong>of</strong> HT for <strong>the</strong> organs or tissues and wT in Eq.(1).
2.2 Photonuclear cross section
Photonuclear cross sections <strong>of</strong> secondary particle production were taken from preliminary version
<strong>of</strong> JENDL Photonuclear Data Files (JENDL-PDF) [18]. We treated <strong>the</strong> main elements in a human
2

ody such as carbon, nitrogen and oxygen. The reaction types included were ( , p), ( ,d),( , t), ( ,
3 He), ( , ) and ( , n). The cross sections <strong>of</strong> <strong>the</strong> six reactions including <strong>the</strong> giant dipole resonance
peaks were given for <strong>the</strong> photon energy up to 140MeV. The photonuclear reaction was evaluated for
<strong>the</strong> components <strong>of</strong> photon uence with energy below 140MeV.
2.3 Ma<strong>the</strong>matical phantom and Monte Carlo code
An anthropomorphic phantom and EGS4 were used to calculate energy deposition and photon
uence averaged over each tissue or organ. The ma<strong>the</strong>matical phantom used in <strong>the</strong> calculation was a
modi ed MIRD-type phantom, in which oesophagus was added by Yamaguchi [15]. The phantom [15]
is designed as hermaphroditic and composed <strong>of</strong> <strong>the</strong> 61 regions, or 37 organs and tissues with di erent
densities and composition. Three tissues have been considered: s<strong>of</strong>t tissues, lungs and skeletal tissue.
The density assumed is 0.9869 g cm ;3 for s<strong>of</strong>t tissues, 0.2958 g cm ;3 for lungs and 1.4682 g cm ;3 for
skeletal tissue. The composition <strong>of</strong> <strong>the</strong> three tissues were limited to <strong>the</strong> 17 elements,H,C,N,O,Na,
Mg, P, S, Cl, K, Ca, Fe, Zn, Rb, Sr, Zr, Pb.
To incorporate <strong>the</strong> phantom into <strong>the</strong> EGS4 code system, UCGEN [16], <strong>the</strong> generalized user code
for EGS4, was used. The user code employs modi ed MARS geometry package [17] developed at
ORNL, and <strong>the</strong> MIRD-type anthropomorphic phantom was described with this geometry package.
The phantom was irradiated in a vacuum space by mono-energetic parallel electron beams. Selected
irradiation geometries were anterior-posterior (AP), posterior-anterior (PA), right lateral (RLAT), left
lateral (LLAT), isotropic (ISO) and rotational (ROT).
Cut o energies for photons and electrons were set to be 10keV and 100keV respectively since <strong>the</strong>
range for electrons with <strong>the</strong> cut o energies is short as compared with <strong>the</strong> tissue or organ size in <strong>the</strong>
phantom. Histories were selected to keep <strong>the</strong> statistical uncertainties below 10% for equivalent doses
<strong>of</strong> organ or tissue that were given <strong>the</strong> tissue weighting factors.
3 Results and Discussion
3.1 Dose contribution due to photonuclear reaction
The contribution <strong>of</strong> photonuclear reaction to absorbed dose is expressed by <strong>the</strong> ratio <strong>of</strong> absorbed
doses due to photonuclear reaction against <strong>the</strong> total absorbed dose, as shown in Fig.1. In AP irradiation
geometry, <strong>the</strong> maximum contribution <strong>of</strong> photonuclear reaction to <strong>the</strong> total absorbed dose
is about 0.1%. The predominant reactions were ( , n) and ( , p) reactions, due to <strong>the</strong> large cross
sections compared with o<strong>the</strong>r reactions. The contribution <strong>of</strong> photonuclear reaction to doses gradually
increases with incident electron energy up to about 500MeV and <strong>the</strong>n changes little up to 100GeV.
As for o<strong>the</strong>r irradiation geometries, <strong>the</strong> each energy dependence <strong>of</strong> <strong>the</strong> ratio was similar to that in AP
geometry and <strong>the</strong> maximum contributions to absorbed dose are within 0.2%.
In <strong>the</strong> present evaluation, <strong>the</strong> doses in <strong>the</strong> photon energy range above 140MeV were neglected
because <strong>of</strong> <strong>the</strong> lack <strong>of</strong> <strong>the</strong> cross section in JENDL-PDF. According to Sato et al. [14], <strong>the</strong> cross
sections above 140MeV are comparable or greater than <strong>the</strong> cross section at <strong>the</strong> energy <strong>of</strong> giant dipole
resonance peaks. In <strong>the</strong> case <strong>of</strong> <strong>the</strong> incident electron energy 100GeV in AP geometry, <strong>the</strong> ratio <strong>of</strong>
photon uences above 140MeV up to 100GeV amounted to more than 50% and <strong>the</strong> contribution <strong>of</strong>
photon uence above 140MeV was estimated to be over 50%. Then <strong>the</strong> contribution <strong>of</strong> photonuclear
reactions to absorbed doses has been underestimated. However, <strong>the</strong> contribution <strong>of</strong> photonuclear
reaction to absorbed dose was estimated to be within 1% and considerably small against total absorbed
doses, even if <strong>the</strong> absorbed doses in energies over 140MeV were considered.
3.2 Dose conversion coe cients
Fluence to e ective dose conversion coe cients are summarized and compared with Ferrari's
data [10] in Table 1. Statistical uncertainties (fractional standard deviation) are presented for each
3

value. The same data are also plotted in Fig.2. In <strong>the</strong> coe cients, both electro-magnetic cascade
process and photonuclear reaction were considered.
As shown in Fig.2, <strong>the</strong> coe cients sharply increase with incident electron energy up to 50MeV,
while those for electron energies over 50MeV increase gradually. The type <strong>of</strong> geometry with <strong>the</strong>
maximum E is dependent on incident electron energies. In <strong>the</strong> energy range below 50MeV, <strong>the</strong> E
values are higher for AP than for any o<strong>the</strong>r geometries. This is because <strong>the</strong> range <strong>of</strong> electron is short
and most <strong>of</strong> electron energies are deposited in <strong>the</strong> area near <strong>the</strong> surface <strong>of</strong> <strong>the</strong> phantom, where organs
or tissues with large w T such as testes and breast are located. At 50MeV, signi cant di erence in
<strong>the</strong> E values was not found among irradiation geometries. The reason is that <strong>the</strong> range <strong>of</strong> electron
with 50MeV is estimated to be about 16 cm and nearly equal to <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> phantom. For
electron energy over 100MeV, <strong>the</strong> E values for RLAT or ISO become <strong>the</strong> maximum. The range <strong>of</strong>
electron becomes larger and energy deposition increases in organs or tissues located inside and on <strong>the</strong>
rear <strong>of</strong> <strong>the</strong> phantom against its incident direction. The variation <strong>of</strong> organ dose conversion coe cients
decreases with incident electron energy in <strong>the</strong> energy range over 50MeV.
For LAT geometry, <strong>the</strong>re are some di erence in E between for right lateral (RLAT) and for left
lateral (LLAT). This result can be explained by <strong>the</strong> position <strong>of</strong> speci c organs, such as stomach and
colon, with high tissue weighting factor. E is about 10% higher for RLAT than for LLAT in <strong>the</strong>
energy range over 5GeV, mainly because stomach and colon, with relatively high w T ,were located at
<strong>the</strong> left side <strong>of</strong> phantom. The E values for ROT resulted in nearly averaged values for AP, PA and
LAT geometry.
The data are in a good agreement with Ferrari's data in <strong>the</strong> energy range up to 10GeV. In AP, <strong>the</strong>
results show agreement within 6% in <strong>the</strong> energy range over 20MeV. In o<strong>the</strong>r irradiation geometries,
<strong>the</strong>re is no signi cant di erence as well. As a result, <strong>the</strong> conversion coe cients calculated for <strong>the</strong>
energy range over 10MeV are valid data. On <strong>the</strong> o<strong>the</strong>r hand, some <strong>of</strong> <strong>the</strong> present results in <strong>the</strong> energy
range below 10MeV exceed by about 40% those <strong>of</strong> <strong>the</strong> reference data. These discrepancies might be
attributed to <strong>the</strong> di erence in phantom, compared <strong>the</strong> calculated organ doses with Ferrari's data.
The data calculated in <strong>the</strong> present study will contribute a determination <strong>of</strong> <strong>the</strong> dose limit for
electrons.
4 Conclusion
E ective dose per unit uence for electrons has been calculated from 1MeV to 100GeV using
<strong>the</strong> photon-electron Monte Carlo simulation code, EGS4, combined with an anthropomorphic phantom.
Photonuclear reaction has been also considered in <strong>the</strong> conversion coe cient below photon energy
140MeV. The calculated conversion coe cients are generally in agreement with those up to 10GeV
calculated by FLUKA. The dose contributions <strong>of</strong> photonuclear reaction to absorbed dose were estimated
to be less than 0.2% in any irradiation geometries and found to be not so signi cant even if
<strong>the</strong> cross section <strong>of</strong> photonuclear reaction above 140MeV were considered. We will provide a complete
dataset <strong>of</strong> uence to e ective dose conversion coe cients for electrons up to 100GeV.
References
[1] <strong>International</strong> Commission on Radiological Protection, \1990 Recommendations <strong>of</strong> <strong>the</strong> <strong>International</strong>
Commission on Radiological Protection", ICRP Publication 60. Ann. ICRP 21 (1-3) (1991).
[2] <strong>International</strong> Commission on Radiological Protection, \Conversion Coe cients for use in Radiological
Protection against External Radiation", ICRP Publication 74, Ann. ICRP26 (3/4) (1998).
4

[3] Sato, O., Iwai, S., Tanaka, S., Uehara, T., Sakamoto, Y., Yoshizawa, N. and Furihata, S. ,
\Clculation <strong>of</strong> Equivalent Dose and E ective Dose Conversion Coe cients for Photons from
1MeV to 10GeV", Radiat. Prot. Dosim. 62(1995)119-130.
[4] Ferrari, A., Pelliccioni, M. and Pillon, M., \Fluence to E ective Dose and E ective Dose Cnversion
Coe cients for Photons from 50keV to 10GeV", Radiat. Prot. Dosim. 67(1996)245-251.
[5] Ferrari, A., Pelliccioni, M. and Pillon, M., \Fluence to E ective Dose Conversion Coe cients for
Neutrons up to 10TeV", Radiat. Prot. Dosim. 71(1997)165-173.
[6] Yoshizawa, N., Sato, O., Takagi, S., Furihata, S., Iwai, S., Uehara, T., Tanaka, S. and Sakamoto,
Y., \External Radiation Conversion Coe cients using Radiation Weighting Factors and Quality
Factors for Neutron and Proton from 20MeV to 10GeV", Nucl. Sci. Tech. 35(12)(1998)928-942.
[7] Ferrari, A., Pelliccioni, M. and Pillon, M., \Fluence to E ective Dose Conversion Coe cients for
Protons from 5MeV to 10TeV", Radiat. Prot. Dosim. 71(2) (1997)85-91.
[8] Ferrari, A., Pelliccioni, M. and Pillon, M., \Fluence-to-E ective Dose Conversion Coe cients for
Muons", Radiat. Prot. Dosim. 74(4)(1997)227-233.
[9] Ferrari, A., Pelliccioni, M. and Pillon, M., \Fluence to E ective Dose Conversion Coe cients for
Negatively and Positively Charged Pions", Radiat. Prot. Dosim. 80(4)(1998)361-370.
[10] Ferrari, A., Pelliccioni, M. and Pillon, M., \Fluence to E ective Dose and E ective Dose
Equivalent Conversion Coe cients for Electrons from 5MeV to 10GeV", Radiat. Prot. Dosim.
69(2)(1997)97-104.
[11] Aarnio, P. A., Fasso, A., Ferrari, A., Mohring, J. -H., Ranft, J., Sala, P. R., Stevenson, G. R. and
Zazula, J. M., \FLUKA: Hadronic Benchmarks and Applications", In: Proc. MC93 Int. Conf. on
Monte Carlo Simulation in High Energy and Nuclear Physics, Tallahassee, 22-26 February 1993
(Ed. World Scienti c) (1994).
[12] Ranft, J. and Nelson, W. R., \Hadron Cascades Induced by Electron and Photon Beams in <strong>the</strong>
GeV Energy Range", Nucl. Instrm. Methods. A257(1987)177-184.
[13] Nelson, W. R., Hirayama, H. and Rogers, W. O., \The EGS-4 Code System", SLAC-265 (1985).
[14] Sato, O., Yoshizawa, N., Iwai, S., Uehara, T., Sakamoto, Y.and Tanaka, S., J. Nucl. Sci. Tech.
supplement 1(2000)861-864.
[15] Yamaguchi, Y., \Dose Conversion Coe cients for External Photons Based on ICRP 1990 Recommendations",
J. Nucl. Sci. Tech. 31(1994)716-725.
[16] Momose, T., Nojiri, I., Narita, O., Iwai, S., Rintsu, Y., Sato, O. and Nakamura, M., \mprovement
in <strong>the</strong> EGS4 code system - General Purpose Electron-Photon Monte Carlo Transport Code
System", In: Proc. The rst EGS4 User's Meeting in Japan, 48-73 (1990).
[17] West, J. T. and Emmett, M. B., \MARS: A Multiple Array System Using Combinatorial Geometry",
NUREG/CR-0200, vol.3, sect.M9 (1993).
[18] Fukahori, T. private communication.
5

Table 1. Fluence to E ective dose conversion coe cients.
6

γ
γ
γ
Figure 1. The ratio <strong>of</strong> absorbed dose by photonuclear reaction to total dose equivalent inAP
geometry. O<strong>the</strong>rs include secondaries and recoiled charged particles produced by <strong>the</strong> reactions such
as ( ,d),( , t), ( , 3 He), ( , ) and ( , n).
Effective dose per unit <strong>of</strong> fluence [pSvcm 2 ]
10 3
10 2
10 1
10 0
10 0
10 1
10 2
10 3
Electron energy [MeV]
10 4
Figure 2. E ective dose per unit uence as a function <strong>of</strong> incident electron energy.
7
10 5

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.48-55
Analysis <strong>of</strong> Dose in Teeth for Estimation <strong>of</strong> E ective Dose
by <strong>the</strong> Electron Spin Resonance (ESR) Dosimetry
Using Dental Enamels
F. Takahashi 1 , Y. Yamaguchi 1 , K. Saito 1 ,
M. Iwasaki 2 , C. Miyazawa 2 and T. Hamada 3
1 Japan Atomic Energy Research Institute,
Tokai-mura, Naka-gun, Ibaraki, 319-1195,Japan
2 School <strong>of</strong> Dentistry, Ohu University,
Tomita-machi, Koriyama-shi, Fukushima, 963-8611, Japan
3 Nuclear Safety Research Association,
5-18-7, Shimbashi, Minato-ku, Tokyo, 105-0004, Japan
Abstract
Dose in teeth was studied to develop a method that can predict e ective dose from results by
<strong>the</strong> Electron Spin Resonance (ESR) dosimetry using dental enamels for external photon exposure.
Absorbed dose in teeth and e ective dose were calculated by <strong>the</strong> Electron Gamma Shower Code
Version 4 (EGS4). In <strong>the</strong> Monte Carlo calculations, a region for teeth was newly added to a
ma<strong>the</strong>matical human model. Experiments were carried out with a head phantom, which is made <strong>of</strong>
tissue equivalent materials. ESR dosimetry was made with dental enamels irradiated at teeth-part
in <strong>the</strong> head phantom. The absorbed dose in a mouth was also measured with TLDs exposed to
gamma rays as <strong>the</strong> teeth. The Monte Carlo calculation and <strong>the</strong> experiment gave a quantitative
relationship between absorbed dose in teeth and e ective dose. The obtained data are considered to
be useful for <strong>the</strong> retrospective individual dose assessment with ESR dosimetry using dental enamels.
1 Introduction
Retrospective assessments <strong>of</strong> exposures to ionizing radiation have been performed to evaluate past
radiation events, where no useful information can be taken from a dosimeter or a radiation monitor.
The Electron Spin Resonance (ESR) dosimetry with teeth is based on measurements <strong>of</strong> radiationinduced
CO33- radicals in hydroxyapatite and one <strong>of</strong> <strong>the</strong> methods to assume past exposure[1, 2].
Since <strong>the</strong> hydroxypatite crystal in <strong>the</strong> dental can easily trap free electrons and <strong>the</strong> signal in exposed
dental enamel remains stable for a long time, this method has been applied to retrospective dose
assessments in atomic-bomb survivors[3, 4], residents a ected by <strong>the</strong> Chernobyl accident[5, 6] and
accumulated individual dose <strong>of</strong> workers in Russian nuclear facility \Mayak"[7, 8].
The ESR signal has been related to <strong>the</strong> dose accumulated in teeth[9, 10, 11, 12, 13]. For an
estimation <strong>of</strong> individual dose, <strong>the</strong> ultimate quantities are organ or tissue dose and e ective dose,
risk-weighted average <strong>of</strong> organ dose over a whole body. The intensity <strong>of</strong> ESR signal resulted from <strong>the</strong>
radicals, however, can directly indicate only absorbed dose in teeth. Then, <strong>the</strong> retrospective individual
dose assessment requires <strong>the</strong> information for conversion from <strong>the</strong> measured quantities to organ dose
<strong>of</strong> interest. In this work, Monte Carlo calculations with <strong>the</strong> Electron Gamma Shower Code Version 4
(EGS4)[14] and experiments with a realistic head phantom were carried out to correlate quantitatively
dose in teeth with e ective dose for external photon exposure.
1

2 Computation
EGS4 Code in conjunction with user's code UCGEN[15, 16] was used to calculate absorbed dose
to organ or tissues including teeth. A ma<strong>the</strong>matical human model used in <strong>the</strong> calculations was an
adult MIRD-5 type phantom designed by Cristy[17] and teeth-part was newly added in <strong>the</strong> head <strong>of</strong> <strong>the</strong>
phantom, where facial skeleton had been already de ned. Figure 1 shows an overview <strong>of</strong> <strong>the</strong> MIRD-5
type phantom and a cross section <strong>of</strong> <strong>the</strong> head at <strong>the</strong> level <strong>of</strong> newly de ned teeth region. The teeth
were grouped into ve parts to examine <strong>the</strong> distribution <strong>of</strong> absorbed dose to teeth (teeth-dose) in <strong>the</strong>
mouth. A s<strong>of</strong>t tissue area was also attached on <strong>the</strong> chest surface to assess a dosimeter reading.
Photon parallel beams were assumed to be incident on <strong>the</strong> phantom. Calculations were performed
for 12 incident angles with 30 degrees interval to study <strong>the</strong> angular characteristics <strong>of</strong> <strong>the</strong> teeth-dose
and e ective dose. The track length estimator was applied to calculate energy di erential uences in
each organ or tissue and <strong>the</strong> kerma approximation to convert <strong>the</strong>m into absorbed dose.
3 Experiment
Experiments were made with a realistic head phantom, which is made <strong>of</strong> tissue-equivalent plastic
and contains human skull. The head phantom was placed on <strong>the</strong> trunk <strong>of</strong> an Alderson RANDO
phantom. The phantom was set at 2.0 m distant from a 137 Cs or a 60 Co source. Teeth were inserted
in <strong>the</strong> upper and lower jaws <strong>of</strong> <strong>the</strong> phantom. After <strong>the</strong> irradiation, dental enamels were separated
mechanically from o<strong>the</strong>r parts <strong>of</strong> <strong>the</strong> teeth and subjected to ESR measurements[18]. In addition to <strong>the</strong>
teeth, <strong>the</strong> absorbed dose in <strong>the</strong> mouth was measured with <strong>the</strong>rmo-luminescence dosimeters (TLDs)
located at <strong>the</strong> teeth-part in <strong>the</strong> head phantom. The TLD is made <strong>of</strong> a CaSO4 crystal and has a
diameter <strong>of</strong> 4mm (UD-110s, Matsushita). The measured dose by <strong>the</strong> TLD could be directly compared
to <strong>the</strong> teeth-dose obtained by <strong>the</strong> calculations, since <strong>the</strong> energy absorption coe cient for tooth enamel
is closed to that for a CaSO4 crystal with <strong>the</strong> energy <strong>of</strong> photons emitted from a 137 Cs or a 60 Co source.
4 Results and Discussion
Figure 2 shows calculated photon energy dependences <strong>of</strong> dose in front-teeth, dose in back-teeth,
e ective dose and dose on chest surface in anterior-posterior (AP) and posterior-anterior (PA) geometries.
The values <strong>of</strong> dose are given in <strong>the</strong> unit <strong>of</strong> mSv/R, <strong>the</strong> ratio <strong>of</strong> equivalent dose or e ective
dose to exposure in free air. The equivalent dose <strong>of</strong> teeth was obtained with multiplying <strong>the</strong> absorbed
dose in teeth by radiation weighting factor (wR) for photons[19]. The teeth-dose indicates di erent
behavior from <strong>the</strong> e ective dose for low photon energies, because tooth contains element with a higher
atomic number such as Ca and P than those <strong>of</strong> s<strong>of</strong>t tissue and can receive higher dose due to energy
absorption through photoelectric e ect. On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> teeth-dose is near to e ective dose in
<strong>the</strong> energy region above 300keV, where <strong>the</strong> Compton scattering process is dominant interaction with
tissues.
Figure 3 shows dependences <strong>of</strong> teeth-dose in <strong>the</strong> mouth on incident direction <strong>of</strong> 50 keV and 1250
keV photons. The teeth-doses are more strongly dependent upon <strong>the</strong> incident direction <strong>of</strong> <strong>the</strong> photon
for 50 keV than for 1250 keV, because low-energy photons cannot penetrate materials with heavy
elements as high-energy photons. The angular dependence <strong>of</strong> teeth-dose changes apparently according
to <strong>the</strong> part <strong>of</strong> teeth for 50 keV photons.
Figure 4 depicts angular dependences <strong>of</strong> teeth-dose, e ective dose and dose on chest surface for
incidences <strong>of</strong> 1250 keV photons. The results suggest that <strong>the</strong> teeth-dose can be thought as <strong>the</strong> e ective
dose for <strong>the</strong> incidences <strong>of</strong> photons from <strong>the</strong> front <strong>of</strong>ahuman body within 60 degrees. The teeth-dose,
however, can underestimate <strong>the</strong> e ective dose for <strong>the</strong> photons from <strong>the</strong> back <strong>of</strong>ahuman body, because
<strong>the</strong> photon can be absorbed in <strong>the</strong> red-bone marrow in <strong>the</strong> spine. On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> teeth-dose
is more than <strong>the</strong> e ective dose for <strong>the</strong> geometry <strong>of</strong> lateral photon irradiation, because <strong>the</strong> organs in
<strong>the</strong> trunk principally contributing to <strong>the</strong> e ective dose are well shielded by <strong>the</strong> human body tissues.
2

The obtained teeth-doses and e ective doses are summarized in Table 1 with some cases <strong>of</strong> photon
irradiations. The values <strong>of</strong> dose in <strong>the</strong> rotational (ROT) geometry are average <strong>of</strong> <strong>the</strong> calculated doses
over all horizontal incident angles for each photon energy. It can be concluded from <strong>the</strong> results that
we can interpret <strong>the</strong> teeth-dose as e ective dose for more than 1 MeV photons in <strong>the</strong> AP and <strong>the</strong> ROT
geometries. These conversion coe cients from <strong>the</strong> teeth-dose to <strong>the</strong> e ective dose are to be essential
for <strong>the</strong> retrospective individual dose assessment by ESR dosimetry with teeth. However, it should be
mentioned that <strong>the</strong>se data are obtained with a mono-energetic eld. The teeth-dose can remarkably
overestimate <strong>the</strong> e ective dose for low energy photon as shown in 50 keV photons, so <strong>the</strong> measured
dose with ESR dosimetry is to be larger than <strong>the</strong> teeth-dose <strong>of</strong> 1250 keV in Table 1 for a retrospective
assessment <strong>of</strong> exposure with photons from a 60 Co source.
Table 2 summarizes distributions <strong>of</strong> <strong>the</strong> teeth-dose in <strong>the</strong> mouth by <strong>the</strong> ESR dosimetry, <strong>the</strong> measurements
with TLDs and <strong>the</strong> calculations for a 60 Co source. Since relationship between intensity <strong>of</strong>
<strong>the</strong> ESR signal and tooth-dose has not been determined yet, <strong>the</strong> signal intensity or <strong>the</strong> dose in teeth
at <strong>the</strong> middle- and <strong>the</strong> back- part are given with relative values to those at <strong>the</strong> front part, which are
normalized to 1.0. The values in <strong>the</strong> calculations are based on <strong>the</strong> result <strong>of</strong> 1250keV photons. The
results by <strong>the</strong> ESR dosimetry agreed with <strong>the</strong> measurements by TLDs and <strong>the</strong> calculations for both
<strong>of</strong> <strong>the</strong> AP and PA geometries.
Table 3 shows <strong>the</strong> comparison <strong>of</strong> <strong>the</strong> teeth-dose by <strong>the</strong> calculations and <strong>the</strong> experiments with
TLDs. The calculated teeth-doses are less than <strong>the</strong> measured doses for <strong>the</strong> PA geometry, whereas
<strong>the</strong> measured teeth-doses are valid to <strong>the</strong> results by <strong>the</strong> calculations for <strong>the</strong> AP geometry. The
disagreements in <strong>the</strong> PA geometry are due to <strong>the</strong> di erence <strong>of</strong> <strong>the</strong> head part between <strong>the</strong> modi ed
ma<strong>the</strong>matical human models for <strong>the</strong> calculations and <strong>the</strong> phantom used for <strong>the</strong> experiments. .
5 Construction <strong>of</strong> a Voxel type phantom (Veri cation <strong>of</strong> Experiments)
Since <strong>the</strong> calculated teeth-doses were less than <strong>the</strong> measured doses with TLDs (CaSO4) located
in <strong>the</strong> head phantom as shown in Table 3, <strong>the</strong> Monte Carlo calculations are to be performed for a
veri cation <strong>of</strong> <strong>the</strong> experiments. The computational human model for <strong>the</strong> veri cation is called as \voxel
(Volume-pixel) type" phantom[20].
A Voxel type phantom was developed based upon a computed topography (CT) image <strong>of</strong> <strong>the</strong>
head phantom, which hadbeen taken with 1mm interval. The CT image having 512x512 pixels was
segmented into s<strong>of</strong>t tissue, bone, teeth and air according to CT values as shown in Figure 4 (a). Figure
4shows that <strong>the</strong> teeth-part de ned in <strong>the</strong> Voxel type phantom is quite similar to <strong>the</strong> teeth-part added
to <strong>the</strong> MIRD type in <strong>the</strong> already performed calculations. Since CT images <strong>of</strong> <strong>the</strong> RANDO phantom
in <strong>the</strong> experiments were not taken, <strong>the</strong> trunk <strong>of</strong> <strong>the</strong> phantom is to be replaced by o<strong>the</strong>r human model.
These images are now being piled up to construct <strong>the</strong> computational ma<strong>the</strong>matical model for <strong>the</strong>
calculations.
6 Conclusion
The Monte Carlo calculations and <strong>the</strong> experiments have provided <strong>the</strong> quantitative relationship
between <strong>the</strong> teeth-dose and e ective dose for photon external exposure with 9 energies between 20
keV and 2500 keV. The obtained results are to be useful for <strong>the</strong> individual dose assessment by <strong>the</strong>
ESR dosimetry with teeth. To get <strong>the</strong> nal goal <strong>of</strong> this work, Monte Carlo calculations should be
performed to verify <strong>the</strong> experiments with a Voxel type phantom based upon <strong>the</strong> head phantom used
in <strong>the</strong> experiments.
3

Acknowledgements
The authors express cordial thanks to <strong>the</strong> Toshiba Medical Cooperation for taking CT image
photographs <strong>of</strong> <strong>the</strong> head phantom.
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L. I. Sukhovskaya, N. E. Schklovsky-Kordi, A. F. Vanin, N. V. Voevodskaya and
A. I. Vorobiev, \Radiation Dosimetry for Residents <strong>of</strong> <strong>the</strong> Chernobyl Region: A Comparison
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[7] A. A. Romanyukha, D. Regulla, E. Vasilenko and A. Wieser, \South Ural Nuclear Workers:
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Monitoring", Appl. Radiat. Isot. 45 (1994)1195-1199.
[8] A. A. Romanyukha, E. A. Ignatiev, E. K. Vasilenko, E. G. Drozhko, A. Wieser, P. Jacob,
I. B. Keirim-Markus, E. D. Kleschenko, N. Nakamura and C. Miyazawa, \EPR Dose Reconstruction
for Russian Nuclear Workers", Health Phys. 78-1 (2000)15-20.
[9] T. Shimano, M. Iwasaki, C. Miyazawa, T. Miki, A. Kai, and M. Ikeya, \Human Tooth Dosimetry
for Gamma-Rays and Dental X-Rays Using ESR," Appl. Radiat. Isot. 40(1989)1035-1038.
[10] M. Iwasaki, C. Miyazawa, A. Kubota, E. Suzuki, K. Sato, J. Naoi, A. Kato and K. Niwa, \Energy
Dependences <strong>of</strong> <strong>the</strong> CO 3;
3 Signal Intensity in ESR Dosimetry <strong>of</strong> Human Tooth Enamel",
Radioisotopes 40(1991)421-424.
[11] M. Iwasaki, C. Miyazawa, T. Uesawa, E. Suzuki, M. Hoshi, and K. Niwa, \Exposure Rate Dependence
<strong>of</strong> <strong>the</strong> CO 3;
3 Signal Intensity in ESR Dosimetry <strong>of</strong> Human Tooth Enamel", Radioisotopes
41(1992)642-644.
[12] M. Iwasaki, C. Miyazawa, T. Uesawa, I. Ito and K. Niwa \Di erences in Radiation Sensitivity <strong>of</strong>
Human Tooth Enamel in an Individual and among <strong>the</strong> Individuals in Dental ESR Dosimetry",
Radioisotopes 44(1995)785-788.
[13] M. Iwasaki, C. Miyazawa and T. Uesawa, \E ect <strong>of</strong> Tooth Position in <strong>the</strong> Oral Cavity for Various
Irradiation Geometries in Dental ESR Dosimetry", Radioisotopes 48(1999)530-534.
[14] W. R. Nelson, H. Hirayama and D. W. O. Rogers, \The EGS4 Code System", SLAC-265 (1985).
[15] I. Nojiri, S. Iwai, O. Sato, S. Takagi, S. Sawamura, and Y. Fukasaku, Power Reactor and Nuclear
Fuel Development Corporation Technical Report 102(1997) 59-66 (in Japanese).
4

[16] S. Takagi, O. Sato, S. Iwai, T. Uehara and I. Nojiri, \Development and Benchmarking <strong>of</strong> General
Purpose User Code <strong>of</strong> EGS4", Proc. <strong>of</strong> <strong>the</strong> 1st <strong>International</strong> <strong>Workshop</strong> on EGS4, 86-96, (1997).
[17] M. Cristy, \Ma<strong>the</strong>matical Phantom Representing Children <strong>of</strong> Various Ages for Use in Estimates
<strong>of</strong> Internal Doses", MUREG/CR-1159 (1980).
[18] M. Iwasaki, C. Miyazawa, T. Uesawa, I. Ito and K. Niwa, \E ect <strong>of</strong> Sample Grain Size on <strong>the</strong>
CO 3;
3 Signal Intensity in ESR Dosimetry <strong>of</strong> Human Tooth Enamel", Radioisotopes 42(1995)470-
473.
[19] ICRP, \1990 Recommendations for <strong>the</strong> <strong>International</strong> Commission on Radiological Protection",
ICRP Publication 60 (Oxford: Pergamon Press), 1991.
[20] M. Zankl, N. Petoussi and A. Wittmann, \The GSF voxel phantoms and <strong>the</strong>ir application in radiology
and radiation potection", Voxel Phantom Development, Proc. <strong>of</strong> an <strong>International</strong> <strong>Workshop</strong>
at <strong>the</strong> National Radiological Protection Board, p.98-104, (1995).
5

Table 1 Teeth-dose and E ective dose for some cases <strong>of</strong> photon external photon exposures.
1. 1250keV (A) Teeth-dose (B) E ective dose (B)/(A)
(mSv/R) (mSv/R)
AP Geometry 9.2 8.8 0.96
PA Geometry 5.4 7.9 1.46
LLAT Geometry 8.2 6.4 0.78
ROT Geometry 7.8 7.4 0.95
2. 50keV (A) Teeth-dose (B) E ective dose (B)/(A)
(mSv/R) (mSv/R)
AP Geometry 53 9.2 0.17
PA Geometry 6.5 5.3 0.82
LLAT Geometry 32 3.5 0.11
ROT Geometry 30 5.5 0.18
Table 2 Teeth-dose distributions in <strong>the</strong> mouth by <strong>the</strong> ESR dosimetry, <strong>the</strong> TLDs and
<strong>the</strong> calculations ( 60 Co source).
1. AP geometry Relative value
Front Middle Back
ESR dosimetry 1.0 1.0 0.9
TLDs 1.0 1.0 1.0
Calculation 1.0 1.0 0.9
2. PA geometry Relative value
Front Middle Back
ESR dosimetry 1.0 1.1 1.1
TLDs 1.0 1.1 1.2
Calculation 1.0 1.1 1.2
The signal intensities or teeth-doses at middle- and pack-parts are
relative values to those at front-part, which are normalized to 1.0.
Table 3 Comparison <strong>of</strong> Teeth-dose by <strong>the</strong> TLDs and <strong>the</strong> calculations ( 60 Co source).
1. AP geometry Teeth-dose (mSv/R) E ective Dose
Front Middle Back (mSv/R)
TLDs 9.4 9.7 9.1 |{
Calculation 9.4 9.4 8.8 8.8
2. PA geometry Teeth-dose (mSv/R) E ective Dose
Front Middle Back (mSv/R)
TLDs 6.2 6.5 7.1 |{
Calculation 4.8 5.2 5.9 7.5
6

Figure1 Schematicview<strong>of</strong>aMIRD-typephantomand<strong>the</strong>crosssection<strong>of</strong>headat<strong>the</strong>
level<strong>of</strong>newlydefinedteeth-part.
Doseperexposureinfreeair
(mSv/R)
Doseperexposureinfreeair
(mSv/R)
80
60
40
20
0
10 50 100 500 1000
Photonenergy(keV)
(a)APgeometry
20
15
10
5
Frontteeth
Backteeth
Chestsurface
Effectivedose
Frontteeth
Backteeth
Chestsurface
Effectivedose
0
10 50 100 500 1000
Photonenergy(keV)
(b)PAgeometry
Figure2 Teeth-dose,doseonchestsurfaceandeffectivedoseperunitexposureinfreeair
asafunction<strong>of</strong>photonenergyforAP(a)andPA(b)geometries.
7

Left
Front
60
40
20
0
Back
(a)50keV
Right Left
Front
10
Frontteeth
Left-middleteeth
Back
Right-backteeth
Unit:mSv/R
(b)1250keV
5
0
Right
Figure3 Angulardependence<strong>of</strong>teeth-dosesfor50keVand1250keVphotons.
Left
Front
10
5
0
Back
Right
Teeth-dose
Chestsurfacedose
Effectivedose
Unit:mSv/R
Figure4 Angulardependence<strong>of</strong>teeth-dose,doseonchestsurfaceandeffectivedose.
(a)Voxel-typephantom
(b)MIRD-typephantom
Figure5 Teeth-partin<strong>the</strong>twoma<strong>the</strong>maticalhumanmodels.
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.48-55
An EGS4 User Code with Voxel Geometry and
a Voxel Phantom Generation System
J. Funabiki 1 , M. Terabe 1 , M. Zankl 2 , S. Koga 3 , and K. Saito 4
1
Mitsubishi Research Institute, Inc.,
3-6 Otemachi 2-Chome Chiyoda-Ku, Tokyo 100-8141, Japan
2
GSF, Neuherberg D-85758 Oberschleissheim, Germany
3
Fujita Health University,
98 Dengakugakubo 1-Banchi Kutsukake-Cho Toyoake-Shi Aichi-Ken 470-1101, Japan
4
Japan Atomic Energy Research Institute,
2-4 Shirakatashirane Tokai-mura, Ibaragi-ken 319-1195 Japan
Abstract
An EGS4 user code with voxel geometry (<strong>the</strong> UCPIXEL code) has been developed in order to
make accurate dose evaluation by using human voxel phantoms. The voxel data have a format
devised by GSF. This format can compress so large amount <strong>of</strong> high-resolution voxel data that
required memory for computation is greatly reduced. UCPIXEL can treat 8 basic irradiation
geometries (AP, PA, RLAT, LLAT, ROT, ISO, AB, BA) and cylindrical pseudo-environmental
radiation source with arbitrary size, energy and directional distribution. In addition, UCPIXEL
can model contaminated soil with arbitrary area and depth under a phantom and radiation from
<strong>the</strong> soil. By using a post-processor, e ective dose equivalent, e ective doseand organ doses can
be evaluated from <strong>the</strong> output <strong>of</strong> UCPIXEL. Preliminary results <strong>of</strong> e ective dose calculated by
using UCPIXEL for a Japanese voxel phantom are demonstrated and compared with <strong>the</strong> previous
results for MIRD-type phantoms. Wehave also developed an intelligent system which automatically
constructs a voxel phantom from CT data. We introduce this system and preliminary results are
shown.
1 Introduction
Fluence to e ective dose equivalent or e ective dose conversion coe cients for photons or electrons
have beenevaluated by some researchers[1-5]. In <strong>the</strong>se studies, dose calculations have generally been
performed using MIRD-type anthropomorphic phantoms or o<strong>the</strong>r simpli ed phantoms.
While <strong>the</strong> MIRD-type phantoms have been widely used, voxel phantoms derived from image data
have been developed and used for dose analysis[6-8]. Veit et al. developed 8 week old baby and 7 year
old child voxel phantom[6], and organ doses and SAF were evaluated[7,8]. The voxel phantoms were
based on CT scans <strong>of</strong> real persons, while MIRD-type phantoms describe <strong>the</strong> geometry <strong>of</strong> human body
and its organs by simple ma<strong>the</strong>matical equations based on anatomical data <strong>of</strong> a reference man. By
using <strong>the</strong> voxel phantom construction technique developed by Zankl et al., Saito et al. has recently
developed a Japanese male voxel phantom [9]. Hunt et al. have also developed a voxel phantom called
NORMAN from a whole-body magnetic resonance image (MRI). [10]
We have developed an EGS4 user code (<strong>the</strong> UCPIXEL code) which can treat voxel geometry in
order to make precise dose analysis and evaluate dose di erence between races and individuals byusing
<strong>the</strong> voxel phantoms. Also, electron dose conversion coe cients for <strong>the</strong> Japanese male voxel phantom
have been calculated by <strong>the</strong> UCPIXEL code. In this paper, preliminary results <strong>of</strong> <strong>the</strong> calculation are
presented and compared with <strong>the</strong> previous results for MIRD-type phantoms[3].
1

Figure 6 to 8 show organ doses at <strong>the</strong> electron energy <strong>of</strong> 10 MeV and 10 GeV respectively for
AP, PA, ISO. The results are also compared with those given by Ferrari et al. [3]. At <strong>the</strong> energy
<strong>of</strong> 10 GeV, <strong>the</strong> agreement <strong>of</strong> both results are good since at such a high energy, electrons are highly
relativistic and energy is almost uniformly deposited in <strong>the</strong> phantoms. On <strong>the</strong> o<strong>the</strong>r hand, at <strong>the</strong>
energy <strong>of</strong> 10 MeV, some organ doses for <strong>the</strong> Japanese male phantom are signi cantly di erent from
those for <strong>the</strong> MIRD-type phantom. This is mainly due to <strong>the</strong> di erence in <strong>the</strong> positions and structures
<strong>of</strong> <strong>the</strong> organs and tissues.
From <strong>the</strong> results described above, we con rmed that <strong>the</strong> UCPIXEL code works well and that voxel
phantoms are indispensable in precise dose estimation for irradiation <strong>of</strong> electrons with relatively low
energies like internal exposure analysis and dose evaluation for environmental electron radiation.
4 The Voxel Phantom Generation System
A prototype <strong>of</strong> an intelligent system which automatically constructs a voxel phantom from CT
data has been developed. To formavoxel phantom from a given CT images, we readeach image in,
colorize <strong>the</strong> grey CT value, identify and segment <strong>the</strong> organs/tissues, and enumerate <strong>the</strong> segments. It
is very laborious work to this procedures manually. The voxel phantom generation system reduces
this labor and makes human body modeling e cient.
4.1 Outline <strong>of</strong> <strong>the</strong> system
The system reads normalized CT data and constucts a voxel phantom which consists <strong>of</strong> 4 regions:
skin, lung, bone, and <strong>the</strong> o<strong>the</strong>r region inside <strong>the</strong> body (we call this remainder region \s<strong>of</strong>t tissure" here).
The input CT data must be normalized as 0 < CT value < 4095. The outline <strong>of</strong> this system is shown
in Figure 9. This system consists <strong>of</strong> a master module and 4 submodules: skin, lung, bone, s<strong>of</strong>t tissue
indenti ers. Each submodule is optimized to identify one speci c part <strong>of</strong> a human body assigned
by <strong>the</strong> master (for instance, skin identi er identi es only skin ) and sends back <strong>the</strong> identi cation
results to <strong>the</strong> master. The master combines <strong>the</strong> results to fom <strong>the</strong> corresponding voxel phantom.
The optimization is done by giving <strong>the</strong> following knowledge and rules about human anatomy toeach
indenti er.
1. CT values:
Skin, lung, and bone have characteristic CT values.
Skin has CT values greater than 500.
Lungs have CTvalues between 80 and 839.
Bone has CT values greater than 1139.
2. Volume <strong>of</strong> regions:
Small regions are removed as noise.
3. Postion in a image:
4. Distribution:
5. Symmetry:
The center <strong>of</strong> mass, maximum and minimum coordinates <strong>of</strong> <strong>the</strong> organ/tissue.
Standard deviation <strong>of</strong> <strong>the</strong> organ/tissue distribution
A Left and right lung
3

4.2 Results and discussion
The function <strong>of</strong> <strong>the</strong> voxel phantom generation system was examined using CT data from which
<strong>the</strong> Japanese male phantom was developed by Saito et al.[9]. Figure 10 shows some slices thorough
<strong>the</strong> Japanese voxel phantom manually developed by Saito et al.[9] and <strong>the</strong> corresponding phantom
automatically constructed by <strong>the</strong>voxel phantom generation system. Automatically constructed voxel
phantom is quite simple compared with that developed by Saito et al because it consists <strong>of</strong> only 4
regions, but <strong>the</strong> voxel phantom generation system worked quite well and succeed to identify human
body, lungs, bones, s<strong>of</strong>t tissues. We examined that this system works well in <strong>the</strong> region containing
lungs.
5 Summary and Future Work
An EGS4 user code with voxel geometry (UCPIXEL code) has been developed. Using <strong>the</strong>
UCPIXEL code, e ective dose for electrons <strong>of</strong> <strong>the</strong> Japanese male voxel phantom was evaluated. Voxel
phantom exhibited quite di erent organ dose characteristics for low-energy electrons in comparison
with MIRD-type phantoms. Detailed dose analysis using <strong>the</strong> Japanese male and female voxel phantom
is still underway.
A prototype <strong>of</strong> an intelligent system which automatically constructs a voxel phantom from CT
images has also been developed. Given a set <strong>of</strong> CT data, <strong>the</strong> prototype system generates voxel
phantoms de ned by skin, lungs, bones, and s<strong>of</strong>t tissues. We have examined that <strong>the</strong> system works
well in indentifying organs and tissues, although <strong>the</strong> generality <strong>of</strong> <strong>the</strong> knowledge and rules <strong>of</strong> <strong>the</strong>
identi ers has to be examined thoroughly by using more data sets. In addition, identi ers for o<strong>the</strong>r
organs may also be incorporated to <strong>the</strong> system
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69(2)(1996)97-104.
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4

[8] N. Petoussi-Hen , M. Zankl, and K. Henrichs, \Tomographic Anthropomorphic Models: Part
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[10] J. G. Hunt, I. Malatova, andS.Foltanova, \Calculation and Mesurement <strong>of</strong> Calibration Factors
for Bone Surface Seeking Low Energy Gamma Emitters and Determination <strong>of</strong> 241Am Acitivity in
a Real Case <strong>of</strong> Internal Contamination", Radiat. Protec. Dosim. 82(3)(1999)215.
Figure 1: The Japanese male phantom developed by Saito et al.[9]
Figure 2: Original CT images (<strong>the</strong> left) and <strong>the</strong> corresponding Japanese male phantom (<strong>the</strong> right) in 4 slices.
5

6

BoneSurface
Skin
Thyroid
Oesoph.
Liver
Breast
Bladder
Stomach
Lung
Colon
BoneMarrow
Gonads
Thiswork
Ferrarietal.
electron,10MeV,AP
1 10 100 1000
OrganDose[pGycm 2 ]
BoneSurface
Skin
Thyroid
Oesoph.
Liver
Breast
Bladder
Stomach
Lung
Colon
BoneMarrow
Gonads
Thiswork
Ferrarietal.
electron,10GeV,AP
1 10 100 1000
OrganDose[pGycm 2 ]
Figure 6: Organ dose for AP irradiation geometry at <strong>the</strong> electron energy <strong>of</strong> 10 MeV on <strong>the</strong> left side and 10 GeV
on <strong>the</strong> right side <strong>of</strong> <strong>the</strong> Japanese mail phantom
BoneSurface
Skin
Thyroid
Oesoph.
Liver
Breast
Bladder
Stomach
Lung
Colon
BoneMarrow
Gonads
Thiswork
Ferrarietal.
electron,10MeV,PA
0 50 100 150 200
OrganDose[pGycm 2 ]
BoneSurface
Skin
Thyroid
Oesoph.
Liver
Breast
Bladder
Stomach
Lung
Colon
BoneMarrow
Gonads
Thiswork
Ferrarietal.
electron,10GeV,PA
1 10 100 1000
OrganDose[pGycm 2 ]
Figure 7: Organ dose for PA irradiation geometry at <strong>the</strong> electron energy <strong>of</strong> 10 MeV on <strong>the</strong> left side and 10 GeV
on <strong>the</strong> right side <strong>of</strong> <strong>the</strong> Japanese mail phantom
BoneSurface
Skin
Thyroid
Oesoph.
Liver
Breast
Bladder
Stomach
Lung
Colon
BoneMarrow
Gonads
Thiswork
Ferrarietal.
electron,10MeV,ISO
1 10 100 1000
OrganDose[pGycm 2 ]
BoneSurface
Skin
Thyroid
Oesoph.
Liver
Breast
Bladder
Stomach
Lung
Colon
BoneMarrow
Gonads
Thiswork
Ferrarietal.
electron,10GeV,ISO
0 200 400 600 800 1000
OrganDose[pGycm 2 ]
Figure 8: Organ dose for ISO irradiation geometry at <strong>the</strong> electron energy <strong>of</strong> 10 MeV on <strong>the</strong> left side and 10
GeV on <strong>the</strong> right side <strong>of</strong> <strong>the</strong> Japanese mail phantom
7

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.64-73
Applications <strong>of</strong> EGS4 on Leksell Gamma Unit
Joel YC Cheung 12 , KN Yu 2 , Robert TK Ho 1 and CP Yu 1
1 Gamma Knife Centre (HK), Canossa Hospital, No. 1 Old Peak Road, Hong Kong.
2 Department <strong>of</strong> Physics and Materials Science, City University <strong>of</strong> Hong Kong,
Tat Chee Avenue, Kowloon, Hong Kong.
Abstract
The Monte Carlo modelling <strong>of</strong> particle transport problems in medical radiation physics o ers signi
cant advantages over o<strong>the</strong>r techniques. Experiments can be performed without actually setting
up <strong>the</strong> physical situation. Reliable results can be obtained without any unavoidable perturbations.
In <strong>the</strong> present study, <strong>the</strong> EGS4 Monte Carlo code was applied to simulate <strong>the</strong> Leksell Gamma
Knife - model B. The Leksell Gamma Knife is a surgical tool for brain lesions. It directs beams
<strong>of</strong> Cobalt-60 radiation to a speci c region to treat patients whose brain tumours or lesions are so
deeply buried that conventional surgery is not possible.
The PRESTA (Parameter Reduced Electron-Step Transport Algorithm) version <strong>of</strong> <strong>the</strong> EGS4
(Electron Gamma Shower) computer code was employed. The EGS4 Monte Carlo code allows a
more exible geometrical simulation than o<strong>the</strong>r Monte Carlo code. The purpose <strong>of</strong> this report is to
demonstrate how to apply <strong>the</strong> EGS4 Monte Carlo code in radiosurgical tool, <strong>the</strong> Leksell Gamma
Knife, in order to calculate <strong>the</strong> radiation output factors and <strong>the</strong> dose distributions. The EGS4 user
code allowed all <strong>the</strong> 201 Cobalt-60 sources to be simulated in a single session.
1 Methodology
1.1 Simulation <strong>of</strong> <strong>the</strong> Single-Beam Channel
The 201 radiation beams <strong>of</strong> <strong>the</strong> Gamma Knife unit were con ned by <strong>the</strong> collimator system.
Therefore, simulation <strong>of</strong> <strong>the</strong> collimator system de ned <strong>the</strong> physics <strong>of</strong> <strong>the</strong> radiation beams. Primary
photons exited from <strong>the</strong> Co-60 sources through <strong>the</strong> collimator system and interacted with <strong>the</strong> spherical
water phantom.
The source body consists <strong>of</strong> <strong>the</strong> pre-collimator, <strong>the</strong> lead collimator, <strong>the</strong> exchangeable nal collimator
and <strong>the</strong> spherical water phantom. There are two available strategies in simulating <strong>the</strong> Co-60
source. First, as in <strong>the</strong> gure we simulated <strong>the</strong> whole single beam channel, including <strong>the</strong> cylindrical
double encapsulated stainless steel source, pre-collimator, lead collimator and <strong>the</strong> interchangeable nal
collimator.
<strong>Second</strong>, each source was modelled by a cylinder without any source and capsule ltration. The
beam was collimated by <strong>the</strong>internal diameters <strong>of</strong> <strong>the</strong> interchangeable nal collimator ma<strong>the</strong>matically.
Radiation scattering due to <strong>the</strong> collimator system was ignored. Single beam dose pro les were generated
by <strong>the</strong>se two strategies. Because <strong>of</strong> larger source to target distance when compared with <strong>the</strong>
source dimensions, no observable di erence was obtained in <strong>the</strong> single-beam pro les. For simplicity,
we employed <strong>the</strong> second strategy in simulating <strong>the</strong> 201 Co-60 sources.
1.2 EGS4 Monte Carlo Code
In <strong>the</strong> present work, PRESTA (Parameter Reduced Electron-Step Transport Algorithm) [1, 2]
version <strong>of</strong> EGS4 (Electron Gamma Shower) Monte Carlo code was employed to calculate <strong>the</strong> dose
outputs <strong>of</strong> <strong>the</strong> Leksell Gamma Knife - model B in a spherical water phantoms. The employment <strong>of</strong>
1

PRESTA in <strong>the</strong> simulation made <strong>the</strong> EGS4 Monte Carlo code select a suitable step length dynamically,
which enables fast simulation while still providing accurate physics. Detailed descriptions on <strong>the</strong>
structure <strong>of</strong> <strong>the</strong> EGS4 code can be found from Jenkins et al 1988[3]. The EGS4 code allows users
to de ne a more exible geometrical simulation than o<strong>the</strong>r Monte Carlo computer code. Leksell
Gamma Knife involves a complicated geometrical layout and that is <strong>the</strong> reason why was <strong>the</strong> EGS4
code employed.
For <strong>the</strong> simulation, <strong>the</strong> patient's head was modelled by a water phantom 160 mm in diameter.
Each one <strong>of</strong> <strong>the</strong> 201 sources located in <strong>the</strong> radiation unit is composed <strong>of</strong> 20 Co-60 pellets 1 mm in
diameter and 1 mm in length. A total <strong>of</strong> 201 gamma beams exiting from <strong>the</strong> 201 Cobalt-60 sources
were simulated. Each source was <strong>the</strong>refore modelled by a cylinder 1 mm in diameter and 20 mm in
length.
The Co-60 sources are arranged in a sector <strong>of</strong> a hemispherical surface with a radius <strong>of</strong> 400 mm.
They are distributed along ve parallel circles separated from each o<strong>the</strong>r by an angle <strong>of</strong> 7.5 [4].
The 201 radiation beams passed through <strong>the</strong> opening <strong>of</strong> <strong>the</strong> collimators to <strong>the</strong> target point. The
diameters <strong>of</strong> <strong>the</strong> radiation beams at <strong>the</strong> focus were con ned by <strong>the</strong> size <strong>of</strong> collimators which are 4, 8,
14 and 18 mm. The measured internal diameters <strong>of</strong> <strong>the</strong> 4 mm collimator were 2.14 mm and 2.66 mm.
For <strong>the</strong> 8 mm collimator, <strong>the</strong>y were 3.92 mm and 5.00 mm. For <strong>the</strong> 14 mm collimator, <strong>the</strong>y were 6.52
mm and 8.56 mm. For <strong>the</strong> 18 mm collimator, <strong>the</strong>y were 8.26 mm and 10.88 mm.
1.3 Coordinates <strong>of</strong> <strong>the</strong> 201 Co-60 sources
For simplicity in calculations, we needed to treat <strong>the</strong> unit centre point as (0,0,0) instead <strong>of</strong>
(100,100,100). In Fig. 1, <strong>the</strong> angle was de ned on every rows <strong>of</strong> collimators inclined to <strong>the</strong> z-plane.
The values are given in Table 1.
By considering <strong>the</strong> spacing between collimators on each row in Figure 2, we can calculate an angle
between collimators on each row. The values <strong>of</strong> spacing S between collimators on each row were
obtained based on physical measurement on <strong>the</strong> collimator helmets. The values S are given in Table
2.
Therefore, <strong>the</strong> values <strong>of</strong> angle can be obtained using <strong>the</strong> following equation.
=
S
225 cos
The coordinates in mm (x, y, z) <strong>of</strong> collimators on <strong>the</strong> surface <strong>of</strong> <strong>the</strong> helmet are obtained by <strong>the</strong>
following equations. 8
>< x = 225 cos sin
y = 225 cos
>:
z = ;225 sin
cos
Consider <strong>the</strong> source to focus distance to be 400 mm. The coordinates in mm (x, y, z) <strong>of</strong> <strong>the</strong> 201
Co-60 sources can be obtained by <strong>the</strong> following equations.
8
><
1.3.1 Calculation <strong>of</strong> <strong>the</strong> target points
>:
x = 400 cos sin
y = 400 cos cos
z = ;400 sin
Consider a point P(x1,y1,z1) at <strong>the</strong> central axis <strong>of</strong> <strong>the</strong> cylindrical Co-60 source. A photon exits
from <strong>the</strong> source and targets to <strong>the</strong> spherical water phantom. The direction cosine <strong>of</strong> <strong>the</strong> line joining
<strong>the</strong> point P and <strong>the</strong> unit centre point (0, 0, 0) is
0
1
@
x 1
q
x 2
1 + y2
1
+ z2
1
y 1
q
x 2
1 + y2
1
2
+ z2
1
z 1
q
x 2
1 + y2
1
+ z2
1
A :

De ne an arbitrary point M(x,y,z) on <strong>the</strong> plane perpendicular to <strong>the</strong> incident ray. Then, <strong>the</strong>
equation <strong>of</strong> <strong>the</strong> plane is
0
1
Or,
(x y z)
@
x 1
q
x 2
1 + y2
1
+ z2
1
y 1
q
x 2
1 + y2
1
+ z2
1
z 1
q
x 2
1 + y2
1
+ z2
1
A =0:
(xx 1 + yy 1 + zz 1)=0: (1)
The equation <strong>of</strong> <strong>the</strong> target sphere with radius R is: x 2 + y 2 + z 2 = R 2 .
The equation becomes
x 2 + y 2 + z 2 R 2 (2)
if any point (x,y,z) is inside <strong>the</strong> volume <strong>of</strong> <strong>the</strong> target sphere.
From <strong>the</strong> equation [1], we write:
and substitute z into <strong>the</strong> equation [2].
Now, <strong>the</strong> equation [2] becomes:
Then,
x 2
z = ; xx 1 + yy 1
z 1
x 2 + y 2 + xx 1 + yy 1
z 1
1+ x2
1
z 2
!
+ y
1
2
1+ y2
1
z 2
!
1
We choose random numbers x and y in mm, so that
(
;R x R
and z can be determined by using <strong>the</strong> equation [3].
;R y R
2
R 2 :
+ 2xyx 1y 1
z 2
1
1.4 Determination <strong>of</strong> <strong>the</strong> radius R <strong>of</strong> <strong>the</strong> target sphere
The maximum radius R(mm) should include <strong>the</strong> region <strong>of</strong> geometrical penumbra. Therefore, by
considering a photon exiting from <strong>the</strong> circumference and <strong>the</strong> bottom <strong>of</strong> <strong>the</strong> cylindrical source, <strong>the</strong>
value <strong>of</strong> R can be found (Figure 3).
In trigonometry, <strong>the</strong> addition formula <strong>of</strong> <strong>the</strong> function tangent is:
tan( ; )=
In Figure 3, <strong>the</strong> value <strong>of</strong> and are given below,
Therefore,
= tan ;1
rout +0:5
390 ; 165 = tan;1 0:5
390
R = p
0:52 + 3902 2
4
tan ; tan
1 + tan tan
rout+0:5
390;165
1+ rout+0:5
390;165
R 2 :
and tan ( ; )=
; 0:5
390
0:5
390
where Rout is <strong>the</strong> internal radius <strong>of</strong> <strong>the</strong> collimator at <strong>the</strong> exiting end.
3
3
5
R
p
0:52 :
+3902 (3)

1.5 Con ning a photon passing through <strong>the</strong> collimator
In Figure 4, de ne a point A at <strong>the</strong> central axis and at <strong>the</strong> exiting end <strong>of</strong> collimator, ano<strong>the</strong>r point
B at <strong>the</strong> central axis and at <strong>the</strong> incident end <strong>of</strong> collimator. Then, any points exiting from within <strong>the</strong>
cylindrical source try to point at <strong>the</strong> target (xtytzt) and pass through <strong>the</strong> collimator. At <strong>the</strong> incident
end and exiting end <strong>of</strong> <strong>the</strong> collimator, we de ne a point C and a point D at <strong>the</strong> interfaces. Therefore,
if <strong>the</strong> distance BC is less than <strong>the</strong> radius <strong>of</strong> <strong>the</strong> incident end <strong>of</strong> <strong>the</strong> collimator and <strong>the</strong> distance AD
is less than <strong>the</strong> radius <strong>of</strong> <strong>the</strong> exiting end <strong>of</strong> <strong>the</strong> collimator, <strong>the</strong>n <strong>the</strong> emerging photon is able to pass
through <strong>the</strong> whole collimator. The coordinate <strong>of</strong> point C and point D can be found as follow.
Direction cosine <strong>of</strong> OP is:
0
1
@
x 1
q
x 2
1 + y2
1
+ z2
1
y 1
q
x 2
1 + y2
1
Then, <strong>the</strong> equation <strong>of</strong> <strong>the</strong> plane containing point B is:
0
and
(x ; xBy; yBz ; zB)
Then, we have
@
x 1
q
x 2
1 + y2
1
+ z2
1
+ z2
1
z 1
q
x 2
1 + y2
1
y 1
q
x 2
1 + y2
1
+ z2
1
+ z2
1
A :
z 1
q
x 2
1 + y2
1
+ z2
1
1
A =0:
(x ; xB) x 1 +(y ; yB) y 1 +(z ; ZB) z 1 =0: (4)
Consider <strong>the</strong> equation <strong>of</strong> <strong>the</strong> photon exiting from Q to <strong>the</strong> target (xtytzt):
Therefore,
x ; xin
xin ; xt
x =
z =
= y ; yin
y ; yin
ym ; yt
y ; yin
ym ; yt
yin ; yt
= z ; zin
:
zin ; zt
(xin ; x)+xin (5)
(zin ; z)+zin (6)
Substitute <strong>the</strong> equations [5] and [6] into [4]. We get <strong>the</strong> result <strong>of</strong> y as follow.
y = (zB ; zin)+(xB ; xin) x 1 + yBy 1 + yin
x 1
x in;xt
y in;yt
+ z 1
x 1
z in;zt
y in;yt
x in;xt
y in;yt
+ y 1
+ z 1
z in;zt
y in;yt
Therefore, <strong>the</strong> point C can be found. The point D can also be found in a similar way.
1.6 Obtaining <strong>the</strong> coordinates <strong>of</strong> <strong>the</strong> point A and B
In Figure 5, consider <strong>the</strong> equation <strong>of</strong> line OP:
and <strong>the</strong> equation <strong>of</strong> sphere A:
Substitute <strong>the</strong> equations [7] into [8].
We obtain <strong>the</strong> coordinate <strong>of</strong> point A.
x 1
xA
= y 1
yA
= z 1
zA
x 2 + y 2 + z 2 =165 2 (8)
zA ; r
x2 1
z2 1
4
;165
+ y2 1
z 2 1
+1
(7)

and
xA = zAx1
yA = zAy1
z1
With <strong>the</strong> equation <strong>of</strong> sphere B:x 2 + y 2 + z 2 = 225 2 . The coordinate <strong>of</strong> point B can be found in a
similar way.
1.7 Select points within <strong>the</strong> cylindrical source
We needed to randomly select a point Q within <strong>the</strong> cylindrical source (Figure 6). At rst, a
randomly selected point Rwas found based on <strong>the</strong> distance ratio OR and OP.
That is,
With <strong>the</strong> direction cosine <strong>of</strong> OR:
0
@
R(x2y2z2) = jORj
x2 q
2
x2 + y 2 2 + z2
2
equation <strong>of</strong> <strong>the</strong> plane containing R becomes:
Or,
(x ; x2y; y2z ; z2)
0
@
jOP j
y2 q
2
x2 + y 2 2 + z2
2
x2 q
2
x2 + y 2 2 + z2
2
z1
P (x1y1z1):
z2 q
2
x2 + y 2 2 + z2 2
y2 q
2
x2 + y 2 2 + z2
2
1
A
z2 q
2
x2 + y 2 2 + z2 2
1
A =0
(x ; x2) x2 +(y ; y2) y2 +(z ; z2) z2 =0: (9)
Consider <strong>the</strong> equation <strong>of</strong> solid sphere with <strong>the</strong> point Rasacentre:
(x ; x2) 2 +(y ; y2) 2 +(z ; z2) 2
where 0.5 is <strong>the</strong> radius <strong>of</strong> <strong>the</strong> cylindrical source.
Solve <strong>the</strong> equations [9] and [10]. We have,
z = (x2 ; x) x2 +(y2 ; y) y2
z2
0:5 2 (10)
+ z2
and <strong>the</strong> values<strong>of</strong>xandywere selected from random numbers as follow.
( ;0:5 y ; y2 0:5
;0:5 x ; x2 0:5
The coordinate <strong>of</strong> point Q can be found. Therefore, any photons exiting within <strong>the</strong> cylindrical
source can nd a target coordinate on <strong>the</strong> plane perpendicular to <strong>the</strong> direction <strong>of</strong> incident photon.
2 Discussion and Conclusions
Experimental determination <strong>of</strong> <strong>the</strong> output factors are di cult due to <strong>the</strong> extremely narrow beams
for which <strong>the</strong> dose is determined. In <strong>the</strong> simulation, a spherical probe with a radius <strong>of</strong> 1 mm was
utilized at <strong>the</strong> centre <strong>of</strong> <strong>the</strong> spherical water phantom, 160 mm in diameter. Our simulation con rmed
<strong>the</strong> new 4 mm output factor[5, 6] provided by ELEKTA (Manufacturer <strong>of</strong> Leksell Gamma Knife).
EGS4 Monte Carlo technique was also employed to calculate <strong>the</strong> dose distribution along <strong>the</strong> x, y and
z axes when a single shot with <strong>the</strong> opening <strong>of</strong> all 201 sources was delivered at <strong>the</strong> centre <strong>of</strong> a simulated
water phantom. Di erent collimator helmets <strong>of</strong> 4, 8, 14 and 18 mm were studied. Good agreements
were obtained between <strong>the</strong> results <strong>of</strong> <strong>the</strong> planning system and <strong>the</strong> Monte Carlo. Small discrepancies
5

were observed along <strong>the</strong> z-axis <strong>of</strong> <strong>the</strong> 8 mm collimator helmet[7]. Fur<strong>the</strong>rmore, <strong>the</strong> change in dose
distributions can also be predicted after applying some plugged patterns at <strong>the</strong> collimator helmets[8].
Owning to <strong>the</strong> energy dependency <strong>of</strong> radiographic lms, accurate measurement results may not be
obtained easily[9]. Therefore, <strong>the</strong> applications <strong>of</strong> EGS4 Monte Carlo technique is important and should
be included as a part <strong>of</strong> quality assurance program for <strong>the</strong> Gamma Knife radiosurgery.
Table 1 Row A to E inclined to <strong>the</strong> z-plane by anangle .
Row
A 6.0
B 13.5
C 21.0
D 28.5
E 36.0
Table 2 The spacing S between collimators within <strong>the</strong> row from A to E.
Row S(mm)
A 30.00
B 30.55
C 33.00
D 31.06
E 31.77
6

References
[1] Bielajew A. F. and Rogers D. W. O., \Electron Step-size Artefacts and PRESTA, In Monte Carlo
Transport <strong>of</strong> Electrons and Photons", p115, edited by Jenkins T.M., Nelson W. R. and Rindi A.,
Plenum Publishing Corporation, 1988.
[2] Bielajew A. F. and Rogers D. W. O., \PRESTA: The Parameter Reduced Electron-Step Transport
Algorithm for Electron Monte Carlo Transport", NRC-CNRC, 1988.
[3] Jenkins, T. M., Nelson, W. R., Rindi, \A. Monte Carlo Transport <strong>of</strong> Electrons and Photons".
New York: Plenum Publishing Corporation, 1988.
[4] Elekta, \Leksell Gamma Unit: User's Manual 1", 1992.
[5] Elekta, \New 4-mm Helmet Output Factor, Bulletin Leksell Gamma Knife Public", 02/17/98,
1998.
[6] Joel Y C Cheung, K N Yu, Robert T K Ho and C P Yu, \Monte Carlo calculated output factors
<strong>of</strong> a Leksell Gamma Knife unit", Physics in Medicine and Biology, Volume 44, Number 12
(1999)N247-N249.
[7] Joel Y. C. Cheung, K. N. Yu, C. P. Yu, and Robert T. K. Ho, \Monte Carlo calculation <strong>of</strong> singlebeam
dose pro les used in a gamma knife treatment planning system", Med. Phys., Volume 25,
Issue 9 (1998)1673-1675.
[8] Joel Y. C. Cheung, K. N. Yu, Robert T. K. Ho and C. P. Yu, \Monte Carlo calculations and
GafChromic lm measurements for plugged collimator helmets <strong>of</strong> Leksell Gamma Knife unit",
Med. Phys., Volume 26, Issue 7(1999)1252-1256.
[9] Joel Y.C. Cheung, K.N. Yu, R.T.K. Ho and C.P. Yu, \Stereotactic dose planning system used
in Leksell Gamma Knife model-B: EGS4 Monte Carlo versus GafChromic lms MD-55", Appl.
Radiat. Isot., Vol 53, Issue 3(2000)427-430.
7

Figure1Anangleθinclinedto<strong>the</strong>z-plane<strong>of</strong><strong>the</strong>
collimatorhelmet.
Figure2Anangleδinclinedtox-plane<strong>of</strong><strong>the</strong>
collimatorhelmet
8

390
165 60
Co-60Source
R
α
R out
0.5
β
(0,0,0)
90 o
20
Collimator
Figure3Thecalculation<strong>of</strong>amaximumradiusRat
<strong>the</strong>targetplane.
P(x 1,y 1,z 1)
D
target(x t ,y t ,z t )
C
B
A
Q(x in,y in,z in)
O(0,0,0)
Collimator
Figure4Thecalculation<strong>of</strong>coordinates<strong>of</strong><strong>the</strong>points
CandDinteracting<strong>the</strong>collimator.
9

A
O(0,0,0)
B
Source
Collimator
P(x 1 ,y 1 ,z 1 )
Figure5Thecalculation<strong>of</strong>coordinates<strong>of</strong>pointsA
andBat<strong>the</strong>centralaxis<strong>of</strong><strong>the</strong>collimator.
R(x 2,y 2,z 2)
O(0,0,0)
P(x 1,y 1,z 1)
Q(x,y,z)
Figure6Thecalculation<strong>of</strong>randomselected
pointswithin<strong>the</strong>volume<strong>of</strong><strong>the</strong>cylindrical
10

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.74-91
Dosimetric Characterization <strong>of</strong>
Low Energy Brachy<strong>the</strong>rapy Sources:
An EGS4 Monte Carlo Study
E. Mainegra and R. Capote
Departamento de Fisica,
Centro de Estudios Aplicados al Desarrollo Nuclear,
Calle 30 #502, e/ 5ta y 7ma, Miramar, La Habana, Cuba
Abstract
An exhaustive revision <strong>of</strong> dosimetry data for low energy interstitial brachy<strong>the</strong>rapy sources has
been performed by means <strong>of</strong> <strong>the</strong> EGS4 Simulation System. DLC-136/PHOTX cross section library,
water molecular form factors, bound Compton scattering and Doppler broadening <strong>of</strong> <strong>the</strong> Comptonscattered
photon energy were considered in <strong>the</strong> calculations. Two-dimensional dose rate distributions
in water and air-kerma strength around 103 Pd model 200 and 125 I models 6702 and 6711
were calculated, allowing dose rate constants (DRC) , radial dose functions g(r) and anisotropy
functions F (r ) to be estimated. In uence <strong>of</strong> calibration procedure on source strength for lowenergy
brachy<strong>the</strong>rapy seeds is discussed. A <strong>the</strong>oretical estimate <strong>of</strong> <strong>the</strong> DRC for 103 Pd model 200
seed equal to 0.669 0.002 cGyh ;1 U ;1 was obtained. Radial dose functions g(r) were extensively
compared with experimental as well as with <strong>the</strong>oretical results. Binding corrections for Compton
scattering have a negligible e ect on radial dose function for 103 Pd seeds under 5.0 cm from source
center and for 125 I seed model 6702 under 8.0 cm. Solid water results underestimate radial dose
function for low-energy sources by asmuch as 6 % for 103 Pd and 2.5 % for 125 I already at 2 cm
from source center. Anisotropy functions F (r )were compared against a limited set <strong>of</strong> measured
data selected from <strong>the</strong> literature and o<strong>the</strong>r Monte Carlo results. Binding corrections and phantom
material selection have been found to have no in uence on <strong>the</strong> anisotropy function. A right cylindrical
model <strong>of</strong> <strong>the</strong> titanium container seems to overestimate <strong>the</strong> anisotropy for angles below 20-30
degrees.
1 Introduction
Accurate knowledge <strong>of</strong> two-dimensional dose distribution around radioactive sources employed in
interstitial brachy<strong>the</strong>rapy implants is necessary in order to provide a solider basis when developing a
clinical strategy. In <strong>the</strong> past fteen years experimental and <strong>the</strong>oretical studies on <strong>the</strong> dosimetry <strong>of</strong>
brachy<strong>the</strong>rapy sources have been undertaken intensively. Nath et al [1] reviewed studies for 125 I seed
models 6711 and 6702, and 103 Pd seed model 200. A great amount <strong>of</strong> data both, experimental [2-12] ,
and <strong>the</strong>oretical [13-25] are available to be used directly in clinical treatment planning. However, some
practical as well as <strong>the</strong>oretical problems remain still open.
The numerical value <strong>of</strong> <strong>the</strong> dose rate constant depends strongly on <strong>the</strong> standardization measurements
to which <strong>the</strong> air-kerma strength calibration <strong>of</strong> <strong>the</strong> source is traceable. The recent history <strong>of</strong>
125 I sources illustrates that not even existence <strong>of</strong> NIST air-kerma strength standard is a guarantee <strong>of</strong>
accuracy <strong>of</strong> Monte Carlo calculated absolute dose rates. Only by careful simulation <strong>of</strong> <strong>the</strong> original
NIST free-air chamber measurements, so as to model <strong>the</strong> e ect <strong>of</strong> low-energy contaminant x-rays on
<strong>the</strong> standard, can experimental and Monte Carlo dosimetry be reconciled [19, 20]. Measurement <strong>of</strong>
<strong>the</strong> dose distribution is usually performed in "water equivalent" solid plastic phantoms. Williamson
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[20] showed that solid water does not reproduce <strong>the</strong> scattering and absorption cross sections <strong>of</strong> liquid
water in <strong>the</strong> low energy range ( 125 I and 103 Pd sources), thus resulting in an underestimation <strong>of</strong> <strong>the</strong>
radiation penetrability inwater. Interstitial brachy<strong>the</strong>rapy treatment planning systems <strong>of</strong>ten use <strong>the</strong>
one-dimensional point source approximation for dose rate distribution calculations. This is a fair assumption
in implants with large number <strong>of</strong> sources randomly distributed. However, anisotropy e ects
cannot be neglected when small number <strong>of</strong> sources regularly arranged is used, i.e., in temporary brain
implants and ophthalmic plaque applications. Single seeds, especially those with average emission
energy below 80keV, present amarked anisotropy in dose distribution around <strong>the</strong> longitudinal source
axis.
In this study we review <strong>the</strong> state <strong>of</strong> <strong>the</strong> art dosimetry <strong>of</strong> iodine and palladium brachy<strong>the</strong>rapy seeds.
Comparison with experimental and <strong>the</strong>oretical results reported in <strong>the</strong> literature will be presented
to validate our calculations. In uence <strong>of</strong> calibration procedure on source strength for low-energy
brachy<strong>the</strong>rapy seeds is discussed. The in uence <strong>of</strong> phantom material and Compton binding corrections
on <strong>the</strong> radial dose and anisotropy function is studied. Limitations and advantages <strong>of</strong> Monte Carlo
simulation <strong>of</strong> photon transport in predicting 2-D anisotropy functions is discussed.
2 Materials and Methods
2.1 Dose calculation formalism
We follow <strong>the</strong> dose calculation formalism proposed originally by <strong>the</strong> Interstitial Brachy<strong>the</strong>rapy
Collaborative Working Group [10] to predict two-dimensional dose distributions around cylindrically
symmetric sources and expanded to all brachy<strong>the</strong>rapy sources by <strong>the</strong> AAPM Radiation Therapy
Committee Task Group No.43 [1]. The dose rate at a point (r ) relative to <strong>the</strong> geometric source
center is given by
_D (r )=Sk G (r ) =G (r0 0) g (r) F (r ) (1)
In this formalism, <strong>the</strong> air-kerma strength Sk, a measure <strong>of</strong> source strength, is speci ed in terms
<strong>of</strong> air kerma rate at a point along <strong>the</strong> transverse axis <strong>of</strong> <strong>the</strong> source in free space. It is de ned as
<strong>the</strong> product <strong>of</strong> air kerma rate at a calibration distance, d, in free space Kr(d), measured along <strong>the</strong>
transverse bisector <strong>of</strong> <strong>the</strong> source, and <strong>the</strong> square <strong>of</strong> <strong>the</strong> distance, d. The dose rate constant, , is <strong>the</strong>
dose rate per unit source strength at a reference point taken here to be 1 cm from <strong>the</strong> source center on
its transverse bisector. The geometry distribution G(r ) accounts for <strong>the</strong> variation <strong>of</strong> relative dose due
to <strong>the</strong> spatial distribution <strong>of</strong> radioactivity in <strong>the</strong> source. Because <strong>the</strong> three-dimensional distribution <strong>of</strong>
radioactivity within <strong>the</strong> source core is uncertain for many sources, and because <strong>the</strong> choice <strong>of</strong> geometrical
factor G(r ) in uences mainly <strong>the</strong> accuracy <strong>of</strong> interpolation, we have adopted <strong>the</strong> line source model
(see Ref.[1]). The radial dose function g(r) accounts for radial dependence <strong>of</strong> photon absorption and
scatter in <strong>the</strong> medium along <strong>the</strong> transverse axis ( = =2). The anisotropy function F (r ) accounts
for <strong>the</strong> angular dependence <strong>of</strong> photon absorption and scatter in <strong>the</strong> encapsulation and <strong>the</strong> medium.
For a de nition or more detailed description <strong>of</strong> <strong>the</strong> formalism and <strong>the</strong> quantities used, <strong>the</strong> reader is
referred to <strong>the</strong> Task Group 43 report [1] or <strong>the</strong> paper by Williamson and Nath [26].
2.2 Brachy<strong>the</strong>rapy sources and phantoms
For <strong>the</strong> sources studied <strong>the</strong> basic sizes and materials <strong>of</strong> <strong>the</strong> core and capsules (cladding) used in
<strong>the</strong> calculations were taken as follows: 125 I seeds as described by Williamson [20] and 103 Pd seed model
200 as described by Chiu-Tsao and Anderson [12]. Energy spectra <strong>of</strong> source photons were taken from
<strong>the</strong> NUDAT database [27]. In this study a cylindrical phantom was used. A brachy<strong>the</strong>rapy source
was located in <strong>the</strong> center <strong>of</strong> <strong>the</strong> phantom with its long axis coincident with<strong>the</strong>phantom central axis.
Phantom materials included air, water and solid water. The composition by weight <strong>of</strong> solid water
is stated to be hydrogen 8.0%, carbon 67.22%, nitrogen 2.4%, oxygen 19.84%, calcium 2.32%, and
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chlorine 0.13% [28]. Its density was taken as 1.015 g/cm 3 . An additional calculation with liquid water
thin ring detector embedded in solid water phantom was done to obtain solid water-to-water correction
factor. The dose calculation grid was so dimensioned that on <strong>the</strong> transverse and longitudinal axes a
width <strong>of</strong> 0.02 cm under 0.1 cm, between 0.1 cm and 2.0 cm a width <strong>of</strong> 0.1 cm and beyond 2 cm a
width <strong>of</strong> 0.5 cm were used.
2.3 Monte Carlo calculations
Monte Carlo calculations were performed using <strong>the</strong> EGS4 code system [29,30]. The most recent
photon cross section compilation, DLC-136/PHOTX cross section library [31] contributed by <strong>the</strong>
National Institute <strong>of</strong> Standards and Technology (NIST) and implemented for EGS4 use by Sakamoto
[32] was employed in <strong>the</strong> calculations. This library uses <strong>the</strong> <strong>the</strong>oretical photo-e ect cross section <strong>of</strong>
Sco eld [33], but without renormalization for low atomic number elements. This di erence between
DLC-136 and its predecessors (DLC-7F, DLC-99) is very important for low-energy sources, since
mean emission energy <strong>of</strong> <strong>the</strong>se sources falls in <strong>the</strong> photoe ect dominated region. Bound Compton
scattering and Doppler broadening <strong>of</strong> <strong>the</strong> Compton-scattered photon energy were considered in <strong>the</strong>
calculations by including <strong>the</strong> Low-Energy Photon-Scattering (LSCAT) expansion for <strong>the</strong> EGS4 Code
[34]. Molecular form factors from Morin [35] for coherent scattering in water as implemented by
Leliveld [36] were also included. Cylindrically symmetric brachy<strong>the</strong>rapy sources were modeled with
a modi ed version <strong>of</strong> <strong>the</strong> EGS4 user code DOSRZ [37] that allows simulation <strong>of</strong> particle transport
through a mesh composed by cylindrical shells and scores deposited energy in any desired shell. In
addition, our Monte Carlo EGS4 user code was used to calculate <strong>the</strong> air kerma strength per unit
activity for each seed model allowing clinically relevant absolute absorbed dose rates in water to be
estimated.
An analog dose estimator was employed, since we adopted <strong>the</strong> original scheme <strong>of</strong> scoring deposited
energy in each shell and averaging it over <strong>the</strong> mass <strong>of</strong> <strong>the</strong> cylindrical shell. Electrons were not transported
and <strong>the</strong> cuto energy for photon transport in all calculations was 1 keV (PCUT=0.001MeV).
A variance reduction technique was used in which photons were not allowed to undergo photoelectric
absorption, but were forced to scatter at each interaction site. The resulting bias in <strong>the</strong>
dose estimator was removed by reducing <strong>the</strong> weight <strong>of</strong> <strong>the</strong> scattered photon by <strong>the</strong> branching ratio
( Compton + pair)=( Compton + pair + photo) (coherent scattering in EGS4 system is treated in an
independent way as a correction) and scoring a deposited energy equal to <strong>the</strong> photon energy times
<strong>the</strong> initial photon weight reduced by <strong>the</strong> ratio photo=( Compton + pair + photo). For air kerma calculations
in vacuum, particles heading to detector were split into 100 daughter particles with weight
1/100 in any o<strong>the</strong>r case, particles emerging from <strong>the</strong> source were discarded. The ring detector region
for vacuum simulations was located 100 cm away from <strong>the</strong> source in <strong>the</strong> transverse axis direction.
Inner and outer radiuses <strong>of</strong> <strong>the</strong> ring were 99.5 and 100.5 cm respectively and height <strong>of</strong> <strong>the</strong> ring was
equal to 1 cm. The outer diameter <strong>of</strong> <strong>the</strong> simulation geometry is 40 cm for liquid / solid water.
Air kerma strength Sk for 125 I model 6711 and 6702 seeds was calculated by simulating <strong>the</strong> free-air
chamber calibration measurements performed at NIST [38]. The air-kerma strength Sk for 103 Pd was
evaluated in a vacuum simulation (excluding all source spectrum radiation below 10keV and Ti x-ray
uorescence emission). All quoted calculation errors are only statistical within 1 standard deviation.
3 Results and discussion
3.1 Dose rate constant
3.1.1 125 I seeds
Table 1 compares our <strong>the</strong>oretically calculated DRC [24] with previously published results. Statistical
uncertainty in all regions <strong>of</strong> interest for DRC calculations was below 0.5% for water and solid water
medium and below 1% for air medium. DRC values obtained by us using <strong>the</strong> original photon cross
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section compilation (DLC-15) supplied with EGS4 and those by Williamson [19] using photon cross
section compilation (DLC-7F), are also reported. They show excellent agreement and reinforce <strong>the</strong>
need to use up-to-date photon cross section libraries, since <strong>the</strong>y can a ect DRC values. As mentioned
before, air-kerma strength was calculated by simulating free-air chamber calibration measurements
performed at NIST by L<strong>of</strong>tus [38]. From those computed values <strong>of</strong> Sk, correction factors for attenuation
in air <strong>of</strong> 0.001490 cm ;1 and 0.001486 cm ;1 were obtained for <strong>the</strong> seed models 6702 and 6711
respectively in excellent agreement with <strong>the</strong> 0.0015 cm ;1 value measured by L<strong>of</strong>tus [38] and <strong>the</strong> value
<strong>of</strong> 0.0014 cm ;1 calculated by Williamson [20]. Applying air attenuation correction factors and averaging
over all distances we obtained DRC values showed in table 1. Calculated DRC values for solid
water medium agree with <strong>the</strong> average <strong>of</strong> <strong>the</strong> ICWG measurements [10] within 1.5% and 1.4% and with
Williamson [20] calculations within 1.2% and 0.01% for <strong>the</strong> model 6711 and 6702 seeds respectively.
In addition, our calculations are in agreement within 1.0% with Luxton [22] corrected DRC value
obtained from lucite-medium measurement for <strong>the</strong> 6711 seed .
Using air-kerma strength calculated in vacuum we obtained a DRC value <strong>of</strong> 0.83 cGyh ;1 U ;1 for
<strong>the</strong> 125 I model 6702 seed. This value is in excellent agreement within 0.4% with <strong>the</strong> one obtained by
Mason et al [39] and should be considered a <strong>the</strong>oretical constant based on a fundamental geometry
with vacuum between <strong>the</strong> source and detector, and fully consistent with <strong>the</strong> AAPM de nition [26].
This result suggests that NIST correction for air attenuation does not properly yield <strong>the</strong> air-kerma rate
in free space. It is worth noticing that Ti K-edge characteristic x-rays were included in our vacuum
calculations as well as in Mason et al work [39].
On January 1, 1999 NIST implemented its revised air-kerma strength standard for low-energy
interstitial brachy<strong>the</strong>rapy seeds. This calibrations are based upon measurements using Loevingers
wide-angle free-air chamber (WAFAC) with a thin absorber to eliminate <strong>the</strong> Ti x rays [40]. The
revised DRC value for model 6702 is equal 1.040 cGyh ;1 U ;1 : In a previous work we reported airkerma
strength calculations for this model in vacuum, neglecting characteristic x-ray production [24].
The obtained DRC value <strong>of</strong> 1.009 cGyh ;1 U ;1 is 3% lower than <strong>the</strong> one <strong>of</strong> <strong>the</strong> 1999 NIST standard .
3.1.2 103 Pd seed model 200
Chiu-Tsao and Anderson [12] published absolute dose rate distributions measured in solid water
phantom for this seed. Their data are presented as <strong>the</strong> product <strong>of</strong> distance squared and dose rate
per unit source strength in units <strong>of</strong> cm 2 cGy h ;1 mCi ;1 . This product has <strong>the</strong> value 0.680 cm 2 cGy
h ;1 U ;1 at a distance <strong>of</strong> 1 cm on <strong>the</strong> transverse axis. By de nition this value is <strong>the</strong> measured DRC for
103 Pd seed model 200 in solid water. Meigooni et al [11] reported a value <strong>of</strong> DRC for 103 Pd equal to
0.735 0.03 cGy h ;1 U ;1 . The AAPM in TG-43 report recommended to average <strong>the</strong>se measurements
and applied a multiplicative correction factor (1.048) to convert from solid water measurement medium
to a liquid water reference phantom obtaining a DRC value <strong>of</strong> 0.74 cGy h ;1 U ;1 for <strong>the</strong> model 200
seed. Both TLD measurements were normalized by an air-kerma strength derived from <strong>the</strong> vendor's
contained activity speci cation and deviate by 7.5%. The most likely explanation <strong>of</strong> this di erence is
poor reproducibility and systematic error <strong>of</strong> <strong>the</strong> vendor's activity measurement procedures. Ano<strong>the</strong>r
possible explanation for this discrepancy might be that Chiu-Tsao and Anderson [12] used homemade
solid water, which may have had a slightly di erent composition than <strong>the</strong> commercial material used
in <strong>the</strong> work <strong>of</strong> Meigooni et al [11].
We computed absorbed dose in a liquid water detector embedded in a solid water phantom and
calculated Sk in vacuum, considering photon emission above 10keV and without Ti x-ray uorescence
emission. A DRC value in solid water <strong>of</strong> 0.639 0.002 cGy h ;1 U ;1 was obtained, being 6% smaller
than Chiu-Tsao's experimental value. Our above mentioned solid water result assumes a detector
calibrated for dose to water. A calculation in a solid water phantom which does not consider such
calibration yielded a DRC value <strong>of</strong> 0.677 0.002 cGy h ;1 U ;1 , agreeing with Chiu-Tsao and Anderson
[12] experimental value within 0.4%. Calculations in liquid water medium produced a DRC value <strong>of</strong>
0.669 0.002 cGy h ;1 U ;1 [24].
An air kerma standard for 103 Pd model 200 seed was introduced by NIST only in January 1999
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and in 2000 new AAPM recommendations on 103 Pd dosimetry were published [41]. In this report
<strong>the</strong> authors recommend to average a measured DRC value using TLD dosimeters in solid water by
Nath et al. [42] <strong>of</strong> 0.650 0.050 cGy h ;1 U ;1 with <strong>the</strong> Monte Carlo calculated DRC value performed
by Williamson [43] <strong>of</strong> 0.680 0.020 cGy h ;1 U ;1 . Averaging <strong>the</strong>se two estimates a DRC value <strong>of</strong>
0.665 0.030 cGy h ;1 U ;1 was recommended in <strong>the</strong> AAPM 69 report. This average value is in excellent
agreement with our Monte Carlo predicted value <strong>of</strong> 0.669 0.002 cGy h ;1 U ;1 in a previous work [24].
However, in our opinion, it is inconsistent toaverage DRC values obtained in di erent media. To
account for di erences between solid and liquid water results, conversion factors have been reported
in <strong>the</strong> literature [20], [22], [24]. A more realistic choice can be obtained applying a correction factor
to <strong>the</strong> most recent measurements by Nath et al. [41] as done in TG43. In this way a DRC value <strong>of</strong>
0.681 0.050 cGy h ;1 U ;1 is obtained in excellent agreement with <strong>the</strong> latest Monte Carlo calculation
by Williamson [43]. This value can be considered <strong>the</strong> best selection for <strong>the</strong> DRC <strong>of</strong> 103 Pd seed model
200.
3.2 Radial dose functions
3.2.1 125 I seeds
Radial dose functions g(r) for 125 I seed models 6702 and 6711 have been calculated in liquid and
solid water phantoms [25]. Statistical errors are smaller than 1% within one standard deviation for
distances under 10 cm. From gure 1 can be seen that results are divided in two well de ned trends.
Values <strong>of</strong> g(r) in solid water are consistently smaller than those in liquid water giving rise to di erences
<strong>of</strong> 4.19 % for model 6702 and 5.62 % for model 6711 already at 2.5 cm and 12.26 % for model 6702
and 14.31 % for model 6711 at 5 cm from source center. We compared our liquid water calculations
with <strong>the</strong> Monte Carlo data <strong>of</strong> Burns and Raeside [17] and those <strong>of</strong> Williamson [20] nding excellent
agreement. Solid water results are in good agreement with experimental measurements <strong>of</strong> Nath [7]
with discrepancies smaller than 5 % (mean relative di erence is 2.73 %) for model 6702 and 3.5 %
(mean relative di erence is 1.80 %) for model 6711 under 7 cm. We also included in <strong>the</strong> comparison
<strong>the</strong> fth order polynomial t proposed by <strong>the</strong> ICWG [10], nding an excellent agreement under 6 cm
(1.11 % mean relative error) for model 6702. The di erence is progressively larger over this distance
and a somewhat worse agreement is obtained for model 6711 with 6 % relative di erence at 5cm (4.5 %
mean relative error under 5 cm). For tabulated values <strong>of</strong> radial dose functions <strong>the</strong> reader can consult
[25].
3.2.2 103 Pd seed model 200
103 Pd sources are less studied than 125 I sources. Meigooni et al [11] and, Chiu-Tsao and Anderson
[12] performed dose measurements using LiF TLD in a solid water phantom. Both results were in good
agreement (within 5 %) for distances greater than 2 cm. Calculated radial dose functions [25] in liquid
and solid water were compared with values obtained from <strong>the</strong> experimental results reported in [12] and
<strong>the</strong> compromise chosen by <strong>the</strong> AAPM Task Group No.43 [1] <strong>of</strong> averaging <strong>the</strong> above mentioned data
sets. We can see in Figure 1 (lower panel) that our results in liquid and solid water show discrepancies
<strong>of</strong> 6% already at 2 cm from source center and <strong>of</strong> 10% at 3 cm. Interesting is <strong>the</strong> fact that Chiu-Tsao's
results match much better our liquid water results than those in solid water. There is an excellent
agreement between our results in solid water with <strong>the</strong> averaged results <strong>of</strong> <strong>the</strong>se two data sets. As
reported in <strong>the</strong> Task Group 43 report [1], a homemade solid water phantom was used in [12], which
may have had a slightly di erent composition than <strong>the</strong> commercial material used in [11]. For <strong>the</strong>
tabulated values <strong>of</strong> radial dose function for 103 Pd model 200 seed <strong>the</strong> reader can consult [25].
3.2.3 E ect <strong>of</strong> Compton binding corrections on radial dose functions
The in uence <strong>of</strong> Compton binding corrections on radial dose function for all sources was investigated.
As reported by Williamson [14], binding e ects become non-negligible for a seed with average
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emission energy below 100 keV. We will refer to <strong>the</strong> bound case when considering binding corrections
and to <strong>the</strong> free case when we do not consider <strong>the</strong>m. Comparing <strong>the</strong> bound case with <strong>the</strong> free approach
for 103 Pd sources (Figure 2, upper panel) we see that up to 2.5 cm di erences are under 1% between
both cases, reaching 2% at 5 cm. Beyond 5 cm an increasingly larger bound to free ratio is observed.
A similar behavior is observed for 125 I seed model 6702 (Figure 2, lower panel). Under 4.5 cm <strong>the</strong>
bound to free ratio is almost 1 with di erences under 1% beginning a slowly increase beyond 4.5 cm.
Beyond 8 cm di erences become larger than 2%. Wang and Slovoda [23] explored <strong>the</strong> in uence <strong>of</strong>
binding e ects <strong>of</strong> Compton scattering on deposited dose along <strong>the</strong> transverse axis for 125 I seed model
6711. They reported bound and free results to be nearly identical (less than or equal to 1%) under
7 cm from source center and an increasingly larger bound to free ratio beyond this distance. Since
we calculate <strong>the</strong> ratio between radial dose functions (see de nition) our results will di er by a factor
given by <strong>the</strong> ratio between dose rate at 1cm in <strong>the</strong> free case to that <strong>of</strong> <strong>the</strong> bound case. From our MC
calculations we computed this factor to be 1.0102. Dividing by this factor our results <strong>of</strong> <strong>the</strong> bound to
free ratio is lowered by about 1% achieving excellent agreement with [23].
3.3 Anisotropy functions
Monte Carlo calculations were performed in liquid and solid water phantoms to obtain anisotropy
function for all three low-energy brachy<strong>the</strong>rapy sources [44]. No in uence <strong>of</strong> phantom material selection
nor <strong>of</strong> <strong>the</strong> binding corrections on <strong>the</strong> anisotropy function was observed.
3.3.1 103 Pd model 200 seed
Liquid and solid water medium : With its lower average photon energy, 103 Pd seed exhibits
stronger anisotropy e ects and a faster dose fallo with distance than 125 I sources. Therefore, it is
<strong>of</strong> interest to determine <strong>the</strong> anisotropy function at very close distances from <strong>the</strong> source. Anisotropy
function values calculated from <strong>the</strong> Monte Carlo simulations in liquid and solid water phantoms are
shown in gure 3 as a function <strong>of</strong> distance. As can be observed from <strong>the</strong> similar results in both
media, <strong>the</strong>re is practically no in uence <strong>of</strong> phantom material on <strong>the</strong> anisotropy function for 103 Pd
photon energies. Although not graphically shown, calculations with and without binding corrections
have been also performed nding not signi cant in uence on <strong>the</strong> anisotropy function. An analysis at
50 o and 80 o , where statistical uncertainties are under 0.5%, showed mean relative di erences between
results with and without binding corrections <strong>of</strong> 0.18% and 0.11% respectively.
A strong anisotropy and a marked dependence with distance on <strong>the</strong> longitudinal axis can be
observed. This dependence with distance decreases considerably already at 10 o . It can be observed
that <strong>the</strong> anisotropy function along <strong>the</strong> longitudinal axis for r = 0.3 cm is equal 1.0793, i.e., 7.93 % higher
than on <strong>the</strong> transverse axis at <strong>the</strong> same distance, what may be attributed to <strong>the</strong> greater proximity
to one <strong>of</strong> <strong>the</strong> two active pellets in <strong>the</strong> seed [12]. Anisotropy function uncertainties due to statistical
uctuations in computed dose distributions are under 1% elsewhere excluding <strong>the</strong> longitudinal axis.
Along this axis uncertainties are somewhat higher, being under 1% below 1cm,under 3% up to 3cm
and around 5% over this distance.
Signi cant di erences <strong>of</strong> our results with <strong>the</strong> experimental values [12,45] are observed below 2.5 cm
from <strong>the</strong> seed. However, we are able to reproduce <strong>the</strong> physical fact that <strong>the</strong> dose on <strong>the</strong> longitudinal
axis near <strong>the</strong> source is higher than that on <strong>the</strong> transverse axis, as was measured by Chiu- Tsao and
Anderson [12]. The drastic increase <strong>of</strong> <strong>the</strong> anisotropy function near <strong>the</strong> source on <strong>the</strong> longitudinal
axis is not observed in <strong>the</strong> experimental data reported by Nath [45], which are limited to 1 cm from
<strong>the</strong> source.
Recently, Weaver [6] reported anisotropy functions for 103 Pd-source model 200 and for 125 I-source
models 6702 and 6711. Data were generated through a two-step process, determining rst <strong>the</strong> source
intrinsic radiation emission pattern from in-air measurements at 100 cm from source center and <strong>the</strong>n
using <strong>the</strong>se data as input to Monte Carlo calculations <strong>of</strong> <strong>the</strong> uence distribution in water. This
approach was developed in an e ort to design a fast, e cient source model that would produce
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accurate results, without having to propagate photons through detailed source geometry [46]. Data
from this work were also included in gure 3 for comparison. The largest discrepancy with our values
is found along <strong>the</strong> longitudinal source axis where Weaver's values are lower than ours and do not
reproduce <strong>the</strong> physical fact that <strong>the</strong> dose on <strong>the</strong> longitudinal axis near <strong>the</strong> source is higher than that
on <strong>the</strong> transverse axis. At 10 o agreement is excellent between both data sets except near <strong>the</strong> source.
At higher angles Weaver's values become systematically slightly higher than ours.
Air medium : In order to understand <strong>the</strong> discrepancies observed with <strong>the</strong> results <strong>of</strong> Weaver [6] we
modeled his experimental setup and simulated <strong>the</strong> procedure used to measure <strong>the</strong> angular emission
distribution in air. The idea was to compare directly with measured experimental data, avoiding
e ects, which could be introduced by <strong>the</strong> Weaver Monte Carlo simulation. We found it necessary to
model <strong>the</strong> 103 Pd electroplated on graphite cylinders as a 0.3 mm layer. The layer thickness was deduced
by tting Weaver's experimental results. Calculations performed in air and in vacuum produced <strong>the</strong>
same result showing that contributions to <strong>the</strong> uence by scattered radiation in air is negligible. Figure
4 shows a comparison <strong>of</strong> our Monte Carlo simulation with values from <strong>the</strong> best representation curve
<strong>of</strong> <strong>the</strong> experimental uence. Although <strong>the</strong> minimum in both data sets is located almost at <strong>the</strong> same
position, our values are somewhat lower than Weaver's data. Experimental maximum is observed at
80 o and in our calculation at 87 o . Our right cylindrical model could produce <strong>the</strong> underestimation <strong>of</strong>
experimental data between 20 and 40 degrees. Irregularities in source design reported by Weaver [6]
and <strong>the</strong> lack <strong>of</strong> an accurate source description are likely to be <strong>the</strong> reasons for remaining discrepancies
and set <strong>the</strong> limits for <strong>the</strong> prediction capability <strong>of</strong> Monte Carlo generated data for Pd-103 seed model
200.
3.3.2 125 I model 6702 seed.
In this model <strong>the</strong> radioactive material is adsorbed onto three resin spheres, which canmove freely
inside <strong>the</strong> titanium capsule. This movement is responsible for variability in measured values even <strong>of</strong> <strong>the</strong>
same source before and after movement <strong>of</strong> <strong>the</strong> source [6], making reproducibility <strong>of</strong>any measurement
hard to achieve. We simulated <strong>the</strong> three active resin spheres as small xed cylinders and assumed
<strong>the</strong>m to be spaced, center-to-center, at intervals <strong>of</strong> 1.1 mm. However, photon emission was modeled
from a spherical surface located inside each resin cylinder. Statistical uncertainties are under 1% for
any angle excluding <strong>the</strong> longitudinal axis where uncertainties are under 2.5 % for distances up to 5
cm getting up to 5 % beyond this distance.
In gure 5 we plotted anisotropy values as function <strong>of</strong> distance obtained in liquid water at four
angles for distances between 0.5 cm and 9.0 cm. As for 103 Pd sources, <strong>the</strong>re is no in uence <strong>of</strong> phantom
material nor <strong>of</strong> <strong>the</strong> binding corrections on <strong>the</strong> anisotropy function. We compared our results with
values measured by Nath [45] in a solid water phantom and recommended as reference data by <strong>the</strong>
AAPM Radiation Therapy Committee Task Group 43 [1], those <strong>of</strong> Weaver [6] combining experimental
measurements <strong>of</strong> angular emission distribution with Monte Carlo simulation as mentioned before and
with Monte Carlo calculated values by Williamson (private communication, 1997) using MCPT code,
who simulated a 6702 seed with elliptical end welds (0.5 mm thick) and three resin balls spaced
center-to-center at intervals <strong>of</strong> 1.1 mm.
Nath values appear scattered around <strong>the</strong> o<strong>the</strong>r data sets making it di cult to assess whe<strong>the</strong>r our
right cylinder model or <strong>the</strong> elliptical end welds model used by Williamson are a closer representation
<strong>of</strong> <strong>the</strong> real geometrical structure <strong>of</strong> <strong>the</strong> seed. Our results are about 12 % more anisotropic than those
<strong>of</strong> Williamson for angles close to <strong>the</strong> longitudinal axis. These di erences progressively diminish with
increasing angle. This behavior is in correspondence with <strong>the</strong> geometrical models assumed since a
right cylinder would a ect <strong>the</strong> emitted radiation in a stronger way than a source with elliptical end
welds in <strong>the</strong> region near <strong>the</strong> longitudinal axis. Values reported by Weaver are more anisotropic than
ours at 0 o within 7 %, but at larger angles di erences tend to vanish.
7

3.3.3 125 I model 6711 seed.
Liquid and solid water medium : Several structural details <strong>of</strong> this model, including geometrical
con guration <strong>of</strong> <strong>the</strong> capsule end welds and <strong>the</strong> shape <strong>of</strong> <strong>the</strong> axial surfaces <strong>of</strong> <strong>the</strong> silver rod, are not
known precisely and <strong>the</strong> 2D dose distribution is sensitive to <strong>the</strong>se factors [47]. We have used two
geometrical source models with <strong>the</strong> common feature that <strong>the</strong> radioactive silver core is a right cylinder
centered inside <strong>the</strong> titanium encapsulation, but photons can be emitted from <strong>the</strong> cylindrical surface
disregarding source ends (partial emission) or from its whole surface (total emission). In gure 6
anisotropy function values as function <strong>of</strong> angle at three di erent distances are compared with values
measured by Nath [45] in a solid water phantom using TLD dosimeters, with <strong>the</strong> data obtained by
Weaver [6] as described earlier and with Monte Carlo calculated values tted to a truncated Fourier
series by Williamson and Quintero [47]. The latter workers assumed <strong>the</strong> silver rod to be ellipsoidal in
shape and coated with a 4mmthicklayer <strong>of</strong> AgH with 125 I uniformly distributed over an ellipsoidal
surface embedded 1 mm below its surface. We have also included <strong>the</strong> matrix t to diode and TLD
measured data <strong>of</strong> Ling [2] and <strong>the</strong> Monte Carlo calculation <strong>of</strong> Chiu-Tsao with <strong>the</strong> code MORSE [8].
The later authors modeled <strong>the</strong> silver wire as a right circular cylinder emitting photons from a uniform
layer 1 mm thick, with a 1 mm stando , over <strong>the</strong> entire surface including <strong>the</strong> cylindrical portion and
<strong>the</strong> two end points.
In <strong>the</strong> results obtained using a partial emitting source no values over unity are observed. A
good agreement with Williamson calculations [47] is found very close to <strong>the</strong> source excluding <strong>the</strong>
region on <strong>the</strong> longitudinal axis, where our right cylinder model predicts more anisotropic values than
<strong>the</strong> geometrical model used by this author <strong>of</strong> an elongated ellipsoid. Weaver data [6] show a less
anisotropic dose distribution close to <strong>the</strong> source at angles near <strong>the</strong> longitudinal axis and <strong>the</strong>y do not
present values greater than unity. The data <strong>of</strong> Ling is limited up to 30 o and lie within <strong>the</strong> limits
de ned by <strong>the</strong> <strong>the</strong>oretical results[43]. In general, di erences between all data sets tend to disappear
at large distances. This result strongly favors <strong>the</strong> full emitting source model, <strong>the</strong>refore we selected it
to produce <strong>the</strong> nal results. EGS4 calculated values <strong>of</strong> <strong>the</strong> anisotropy function for <strong>the</strong> total emitting
source model are presented in table 2 from 0 o to 80 o in 10 o steps and for distances between 0.5 cm
and 9 cm. Statistical uncertainties are under 1% for any angle excluding <strong>the</strong> longitudinal axis where
uncertainties are under 3% for distances up to 5 cm reaching 5 % below 9 cm.
Air medium : Experimental measurements <strong>of</strong> <strong>the</strong> angular emission distribution performed by
Weaver [6] were simulated and <strong>the</strong> resulting in-air relative uence is compared with <strong>the</strong> curve best
representing <strong>the</strong> experimental values in gure 7. There is an excellent agreement between <strong>the</strong> experimental
and <strong>the</strong> Monte Carlo calculated data. Only near <strong>the</strong> longitudinal axis between 5 o and 10 o is
our data slightly lower than <strong>the</strong> experimental values. This is probable a consequence <strong>of</strong> <strong>the</strong> assumed
geometrical model in our Monte Carlo calculations, although variations in source encapsulation are
also possible. Weaver reported less variability inmeasurements performed for this seed model than
for <strong>the</strong> o<strong>the</strong>r low energy seeds suggesting less movement in <strong>the</strong> active material. Considering <strong>the</strong> excellent
agreement for <strong>the</strong> in-air relative uence at 100 cm shown in Figure 7, we can conclude that
di erences observed in our calculated anisotropy function values in water with Weaver calculations
near <strong>the</strong> source are mainly due to <strong>the</strong> use <strong>of</strong> an angular emission distribution measured at 100 cm.
This angular distribution misses signi cant geometrical information about <strong>the</strong> source. This could be
considered a limitation <strong>of</strong> <strong>the</strong> Weaver approach.
4 Conclusions
An exhaustive and consistent evaluation <strong>of</strong> dosimetric characteristic <strong>of</strong> commercially available 125 I
seed models 6711 and 6702 and 103 Pd seed model 200 has been performed [24,25,44]. The accuracy <strong>of</strong>
a Monte Carlo EGS4 simulation in <strong>the</strong> energy range from 20 to 40 keV was validated by comparing
its predictions with a large set <strong>of</strong> experimental data and <strong>the</strong>oretical calculations <strong>of</strong> well characterized
8

125 I seeds. The agreement <strong>of</strong> our Monte Carlo calculations with experimental measurements, as well
as with o<strong>the</strong>r Monte Carlo simulations, within 1.5% for DRC <strong>of</strong> 125 I seeds, enhances con dence in
<strong>the</strong> reliability <strong>of</strong> Monte Carlo simulation as a dose-computation tool, allowing us to study o<strong>the</strong>r, less
measured, brachy<strong>the</strong>rapy sources. When a new NIST standard for 125 I seeds, correcting <strong>the</strong> in uence
<strong>of</strong> low-energy contaminant radiation is released, excellent agreement between experimental results in
air, corrected for attenuation in air, and in vacuum calculations should be expected.
A DRC value for 103 Pd seed model 200 in liquid water medium <strong>of</strong> 0.669 0.002 cGy h ;1 U ;1 was
obtained in 1998 [24] in excellent agreement with 0.665 0.02 cGy h ;1 U ;1 value recently recommended
in AAPM Report 69 [41].
Monte Carlo calculated radial dose functions for 125 I seeds in liquid and solid water phantoms
were validated against experiment and o<strong>the</strong>r calculations nding excellent agreement. The fth order
polynomial t obtained by <strong>the</strong> ICWG [10] and recommended by <strong>the</strong> AAPM Task Group No.43 [1]
reproduces very good our solid water calculations for both 125 I seed models under 5 cm.
We have studied <strong>the</strong> in uence <strong>of</strong> binding corrections on <strong>the</strong> radial dose function for low-energy
brachy<strong>the</strong>rapy seeds. Neglecting binding e ects does introduce a maximal error in radial dose function
<strong>of</strong> about 2% under 5 cm for 103 Pd and under 8 cm for 125 I seeds.
Anisotropy functions near low energy sources re ect <strong>the</strong>ir geometrical internal details. At large
distances those geometrical details become less visible. Only through detailed knowledge <strong>of</strong> seed structure
can Monte Carlo calculations accurately reproduce measured relative in-air uence. On <strong>the</strong> o<strong>the</strong>r
side, measurements performed on several seeds for <strong>the</strong> same model can produce di erent outputs,
introducing certain ambiguity in <strong>the</strong> experimental determination <strong>of</strong> angular dose distributions. Averaged
values should be taken for clinical practice. No appreciable in uence <strong>of</strong> binding e ects and
phantom material selection (liquid water or water-equivalent material) on <strong>the</strong> anisotropy function has
been found.
Anisotropy function values for <strong>the</strong> 103 Pd seed model 200 obtained from our calculations and experimental
values reported by Chiu-Tsao reproduce <strong>the</strong> physical fact <strong>of</strong> an increase in <strong>the</strong> anisotropy
function on <strong>the</strong> longitudinal axis towards <strong>the</strong> source. AAPM TG 43 [1] recommended anisotropy
values for this source are limited down to 1 cm from <strong>the</strong> source and do not reproduce <strong>the</strong> above mentioned
anisotropy increase. At larger angles <strong>the</strong> latter values appear more scattered making it di cult
to extract any useful conclusion. Therefore, Chiu-Tsao two-dimensional data could be considered a
closer representation <strong>of</strong> <strong>the</strong> reality than <strong>the</strong> currently recommended data.
It was found necessary to model <strong>the</strong> 103 Pd seed model 200 in greater detail, i.e. including a 0.3 mm
103Pd layer around <strong>the</strong> graphite pellets in order to reproduce experimental measurements <strong>of</strong> angular
radiation distribution in air. Lack <strong>of</strong> a detailed source design information is probably <strong>the</strong> cause for
remaining discrepancies. Although scattering in water tend to smooth out geometrical source features,
such e ects are not completely removed and are actually observed in <strong>the</strong> anisotropy function.
Experimental measurements and Monte Carlo calculations <strong>of</strong> dose rate distributions around 125 I
seed model 6711 demonstrate that dose rate values at angles over 50 o are greater than on <strong>the</strong> transverse
axis for all distances. With increasing distance this e ect is shifted towards <strong>the</strong> transversal axis. When
modeling <strong>the</strong> source without photon emission from <strong>the</strong> source ends such e ect is not observed. A better
agreement with experimental values is obtained when <strong>the</strong> source model <strong>of</strong> photon emission from <strong>the</strong>
whole silver rod surface is used. It is remarkable <strong>the</strong> quality <strong>of</strong> agreement between Monte Carlo
simulation and experimental data achieved for 125 I seed model 6711. In this case simplicity and a
better knowledge <strong>of</strong> <strong>the</strong> internal geometrical details <strong>of</strong> <strong>the</strong> seed allows for precise computation <strong>of</strong> <strong>the</strong>
two-dimensional dose distribution around <strong>the</strong> source in air as well as in water medium, con rming
reliability <strong>of</strong> Monte Carlo simulations.
Use <strong>of</strong> algorithms for fast dose estimation in clinical practice based on previously measured angular
pro les in air should be carefully examined and <strong>the</strong>ir validity tested. Sources are "seen" with di erent
grades <strong>of</strong> detail at di erent distances. The angular distribution at 100 cm contains less information
about <strong>the</strong> geometrical design <strong>of</strong> <strong>the</strong> source than at shorter distances. When using <strong>the</strong> angular distribution
at 100 cm from <strong>the</strong> source as starting angular distribution from an emitting source <strong>the</strong> information
9

is incomplete and an underestimation <strong>of</strong> <strong>the</strong> anisotropy near <strong>the</strong> source is observed. Anisotropy functions
in water based on angular distributions measured in air at 100 cm from <strong>the</strong> source for 103 Pd
seed model 200 and 125 I seed model 6711 fail to reproduce geometrical e ects observed in our Monte
Carlo data and previous published experimental results.
Insu cient knowledge about source structure is responsible for discrepancies observed in Monte
Carlo generated data by di erent authors. A limited amount <strong>of</strong> experimental data can be used to
validate or optimize <strong>the</strong> assumed models because <strong>of</strong> <strong>the</strong> large experimental errors. Therefore more
accurate measurements will be welcome. Accuracy in Monte Carlo calculation <strong>of</strong> dose rate distributions
is limited only by <strong>the</strong> extent to which <strong>the</strong> Monte Carlo program can model <strong>the</strong> physical structures,
<strong>the</strong> physics <strong>of</strong> <strong>the</strong> radiation transport through <strong>the</strong>se materials, and <strong>the</strong> statistical uncertainty <strong>of</strong> <strong>the</strong>
random process simulated. In order to have a realistic information about <strong>the</strong> geometric structure,
imaging techniques, such as pinhole autoradiography and contact transmission micro-radiography
should be used. Statistical uctuations can be computationally drastically reduced, making a Monte
Carlo method an e cient alternative to measured data, once complete and accurate geometrical
information is available.
Acknowledgments
We are deeply indebted to Pr<strong>of</strong>. Dr. J. F. Williamson, Pr<strong>of</strong>. Dr. A. Piermattei, Dr. A. S.
Meigooni, Dr. A. Bielajew and Dr. R. Wang for useful comments and discussion <strong>of</strong> relevant problems.
Special thanks to Dr. D.W.O. Rogers and Dr. M. C. Schell for <strong>the</strong> considerable support in accessing
key information for <strong>the</strong> successful conclusion <strong>of</strong> this work. We also express our gratitude to Dr. Y.
Namito who kindly provided us with <strong>the</strong> LSCAT extension to <strong>the</strong> EGS4 system and to <strong>the</strong> whole
Organizing Committee for providing nancial support, allowing one <strong>of</strong> us (EM) to present this work.
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12

Table 1 Dose rate constants for 125 I seeds.
Author
(Cross section library)
Air-kerma
strength
Phantom
Material
Λ [cGy h -1 U -1 ]
model 6702
Λ [cGy h -1 U -1 ]
model 6711
Williamson 1988, Ref.45 (DLC-7F) Sk in air Atomic water 0.962 0.909
This study 1998, Ref.24 (DLC-15) Sk in air Atomic water 0.96 ± 0.04 0.89 ± 0.01
Sk in vacuum Atomic water 0.83 ± 0.02 0.73 ± 0.01
Mason 1992, Ref.39, (DLC-99) Sk in vacuum Atomic water 0.82 ± 0.04 ---
Sk in air Atomic water 0.93 ± 0.04 ---
Wang et al 1996, Ref.23 (DLC-99) Sk in air atomic water --- 0.895 ± 0.004
Williamson 1991, Ref.20 (DLC-99) Sk in air liquid water 0.932 0.877
solid water 0.899 0.841
This study, Ref.24 (DLC-136) Sk in air liquid water 0.933 ± 0.002 0.888 ± 0.002
solid water 0.908 ± 0.004 0.858 ± 0.004
Piermattei et al 1988, Ref.4 Measurements MS11(water) --- 0.890
Luxton et al 1990, Ref.9 Measurements PMMA --- 0.984
Luxton 1994 (correction), Ref.24 --- liquid water --- 0.879
NCI contract group
Nath et al 1990, Ref.7 Measurements solid water 0.903 0.855
Weaver et al 1989, Ref.5 Measurements solid water 0.923 0.832
Chiu-Tsao et al 1990, Ref.8 Measurements solid water 0.932 0.853
ICWG average 1990, Ref.10 --- solid water 0.919 0.847
Table 2. Anisotropy Function for a 125 I seed model 6711.
R[cm]/θ[deg] 0 10 20 30 40 50 60 70 80
0.50 0.2307 0.3770 0.6246 0.8239 0.9435 1.0009 1.0338 1.0460 0.9897
1.0 0.3130 0.4820 0.7006 0.8396 0.9279 0.9893 1.0247 1.0394 1.0417
1.5 0.3762 0.5359 0.7345 0.8495 0.9284 0.9832 1.0196 1.0334 1.0383
2.0 0.4230 0.5741 0.7532 0.8573 0.9285 0.9808 1.0143 1.0307 1.0357
2.5 0.4403 0.5967 0.7546 0.8412 0.9074 0.9549 0.9925 1.0175 1.0302
3.0 0.4753 0.6204 0.7743 0.8614 0.9170 0.9652 0.9996 1.0173 1.0281
3.5 0.4938 0.6389 0.7836 0.8668 0.9244 0.9663 1.0008 1.0166 1.0264
4.0 0.5137 0.6531 0.7906 0.8693 0.9245 0.9681 0.9993 1.0168 1.0242
4.5 0.5417 0.6649 0.7971 0.8736 0.9284 0.9690 0.9987 1.0166 1.0235
5.0 0.5652 0.6753 0.8020 0.8740 0.9289 0.9688 0.9976 1.0140 1.0232
5.5 0.5672 0.6859 0.8057 0.8776 0.9290 0.9686 0.9942 1.0133 1.0205
6.0 0.5828 0.6945 0.8107 0.8807 0.9332 0.9698 0.9978 1.0145 1.0208
6.5 0.5760 0.6996 0.8126 0.8830 0.9322 0.9688 0.9944 1.0104 1.0193
7.0 0.5776 0.7066 0.8150 0.8832 0.9324 0.9690 0.9951 1.0103 1.0168
7.5 0.6439 0.7147 0.8154 0.8846 0.9325 0.9677 0.9929 1.0079 1.0160
8.0 0.6439 0.7150 0.8183 0.8837 0.9317 0.9672 0.9928 1.0052 1.0134
8.5 0.6594 0.7238 0.8230 0.8876 0.9337 0.9703 0.9934 1.0089 1.0165
9.0 0.6041 0.7312 0.8250 0.8895 0.9374 0.9714 0.9955 1.0102 1.0171
13

adialdosefunctiong(r)
1
0,1
1
0,1
1
0,1
Polynomialfit,solidwater,ICWG1990,[10]
TLDmeasurementsinsolidwater,Na<strong>the</strong>tal1993,[7]
SolidwaterMCcalculations[25]
LiquidwaterMCcalculations,BurnsandRaeside1992,[17]
LiquidwaterMCcalculations,Williamson1991,[20]
LiquidwaterMCcalculations[25]
Polynomialfit,solidwater,ICWG1990[10]
TLDmeasurementsinsolidwater,Na<strong>the</strong>tal1993[7]
SolidwaterMCcalculations[25]
LiquidwaterMCcalculations,BurnsandRaeside1988,[17]
LiquidwaterMCcalculations,Williamson1991,[20]
LiquidwaterMCcalculations[25]
0 1 2 3 4 5 6 7 8 9 10
compared with experimental measurements in solid water phantoms.
125 Iseedmodel6711
125 Iseedmodel6702
103 Pdseedmodel200
TLDmeasurementsinsolidwater,Chiu-Tsaoetal1991,[12]
TLDmeasurementsinsolidwater,Na<strong>the</strong>tal1995,[1]
SolidwaterMCcalculations[25]
LiquidwaterMCcalculations[25]
distancefromsourcer[cm]
Figure 1: Calculated radial dose functions g(r) for low-energy brachy<strong>the</strong>rapy seeds in liquid and solid water
14

atiobounded/freeelectronapproach
1,08
1,06
1,04
1,02
1,00
0,98
1,10
1,08
1,06
1,04
1,02
1,00
0,98
0 1 2 3 4 5 6 7 8
1,08
103 Pdseedmodel200
125
Iseedmodel6702
0 2 4 6 8 10 12 14
distancefromsourcecenterr[cm]
Figure 2: In uence <strong>of</strong> Compton binding corrections on radial dose function for low energy brachy<strong>the</strong>rapy seeds.
The ratio <strong>of</strong> radial dose functions with and without <strong>the</strong> corrections is plotted as a function <strong>of</strong> distance on
transverse axis.
15
1,06
1,04
1,02
1,00
0,98
1,10
1,08
1,06
1,04
1,02
1,00
0,98

anisotropyfunctionF(r,θθθθ)
1.2
1.0
0.8
0.6
0.4
1.2
1.0
0.8
0.6
0.4
0 1 2 3 4 5
θ = 0 o
0 1 2 3 4 5
θ = 50 o
0 1 2 3 4 5
103 Pdseedmodel200
distancefromsourcecenterr[cm]
TLDmeasureddatainsolidwater
(Na<strong>the</strong>tal,1993)
TLDmeasureddatainsolidwater
(Chiu-Tsaoetal,1991)
θ = 10 o
Exp+EGS4calculateddatainliquidwater
(Weaver,1998)
EGS4calculateddatainsolidwater
(this study,1999)
EGS4calculateddatainliquidwater
(this study,1999)
0 1 2 3 4 5
Figure 3: Anisotropy function for a 103 Pd seed model 200 as function <strong>of</strong> distance.
relativeairfluence
1,0
0,8
0,6
0,4
103 Pdseedmodel200
0,2
0 10 20 30 40 50 60 70 80 90
EGS4calculationwith0.3µm 103 Pdlayer[42]
NaI(Tl)Measurement(Weaver1998,[6])
angleθ[degrees]
θ = 80 o
Figure 4: Comparison <strong>of</strong> relative in air uence for 103 Pd seed model 200 obtained from our EGS4 calculations
with measurements <strong>of</strong> Weaver [6].
16
1.2
1.0
0.8
0.6
0.4
1.2
1.0
0.8
0.6
0.4

anisotropyfunctionF(r,θ)
1,0
0,8
0,6
0,4
1,0
0,8
0,6
0,4
1,0
0,8
0,6
0,4
0 10 20 30 40 50 60 70 80 90
r=0.5cm
r=1.0cm
r=2.0cm
0 10 20 30 40 50 60 70 80 90
angleθ[degrees]
125 Iseedmodel6702
Capote2000,[42]
Chiu-Tsaoetal.1990,[8]
Williamson,1997,Priv.Comm.
Weaver,1998,[6]
Na<strong>the</strong>tal.,1993,[7]
Schelletal.,1987,[3]
Figure 5: Anisotropy Function for a 125 I seed model 6702 as function <strong>of</strong> angle. Diode measurements in liquid
water are represented with a star, TLD measurements in solid water with an open square, EGS4 calculations
based on experimental determined angular emission distributions with an open triangle, calculations using
MORSE code with a solid triangle, MCPT calculations with dotted line and full EGS4 calculations with a solid
line.
anisotropyfunctionF(r,θ)
1.0
0.8
0.6
0.4
0.2
1.0
0.8
0.6
0.4
0.2
1.0
0.8
0.6
0.4
0 10 20 30 40 50 60 70 80 90
r=0.5cm
r=1.0cm
r=5.0cm
Williamsonetal.,1988 Chiu-Tsaoetal.,1990
thisstudy,1999 thisstudy,2000
Na<strong>the</strong>tal.,1993 Lingetal.,1985
Weaver,1998
0.2
0 10 20 30 40 50 60 70 80 90
polarangleθ [degrees]
125 Iseedmodel6711
Figure 6: Anisotropy Function for a 125 I seed model 6711 as function <strong>of</strong> angle. Diode measurements in liquid
water are represented with a cross, TLD measurements in solid water with an open square, EGS4 calculations
based on experimental determined angular emission distributions with an open circle, MCPT calculations with
an open triangle and full EGS4 calculations for a partially and a whole emitting source with a dashed and a
solid line respectively.
17
1,0
0,8
0,6
0,4
1,0
0,8
0,6
0,4
1,0
0,8
0,6
0,4

elativeairfluence
1,1
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0 20 40 60 80
125 Iseedmodel6711
0 20 40 60 80
Fittoexperimentaldata
(Weaveretal.,1998),[6]
EGS4simulation,Capoteetal2000,[42]
angleθ[degrees]
Figure 7: Relative air uence at 100 cm for a 125 I seed model 6711.
18
1,1
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.92-99
Optimization <strong>of</strong> PET Scanner Geometry
Lars-Eric Adam and J. S. Karp
Department <strong>of</strong> Radiology, University <strong>of</strong> Pennsylvania
3400 Spruce Street, Philadelphia, PA 19104, U.S.A.
Abstract
Modern positron emission tomographs (PET), when used for 3D imaging, have a wide open
gantry without intra plane septa and only little shielding. In order to reduce <strong>the</strong> scatter contamination
from activity inside and outside <strong>the</strong> eld-<strong>of</strong>-view (FOV), and to block radiation originating
from activity outside-<strong>the</strong>-FOV, we have investigated <strong>the</strong> implementation <strong>of</strong> septa and additional
patient shielding on our existing whole body PET scanner. A series <strong>of</strong> Monte Carlo simulations,
based on EGS4, were performed to predict <strong>the</strong> potential bene ts. Our simulations include point
and line sources at various radial and axial positions in <strong>the</strong> FOV <strong>of</strong> <strong>the</strong> scanner, and di erent sized
uniform cylinders (up to 100 cm long and 50 cm in diameter). The scanner itself is based on 6 continuous
NaI(Tl) crystals, an axial FOV <strong>of</strong> 25.6 cm, a ring diameter <strong>of</strong> 90 cm, and a transaxial FOV
<strong>of</strong> 56 cm. The results show that septa can reduce <strong>the</strong> relative scatter fraction and e ectively block
radiation from outside-<strong>the</strong>-FOV, but <strong>the</strong>y also reduce <strong>the</strong> sensitivity for true events, leading to a
decrease <strong>of</strong> <strong>the</strong> trues-to-singles ratio that is not desirable. The use <strong>of</strong> septa is only advantageous
for large objects, if <strong>the</strong> loss <strong>of</strong> true events is compensated for by increasing <strong>the</strong> injected activity.
Patient shields that are mounted outside-<strong>the</strong>-FOV reduce <strong>the</strong> contamination from scattered and
single events without interfering with true events. They are more e ective for objects with a small
diameter and less e ective for objects with a large diameter.
1 Introduction
The strength <strong>of</strong> positron emission tomography (PET) is <strong>the</strong> ability toquantify <strong>the</strong> activity distribution
<strong>of</strong> radionuclides in <strong>the</strong> human body. During <strong>the</strong> data acquisition, a considerable amount <strong>of</strong>
<strong>the</strong> emission photons are scattered and/or attenuated within <strong>the</strong> patient body, which leads to an error
<strong>of</strong> <strong>the</strong> measurement that requires correction methods. With <strong>the</strong> new generation <strong>of</strong> 3D PET scanners,
<strong>the</strong> scatter problem becomes even more prominent, and also activity located outside <strong>the</strong> FOV contributes
signi cantly to <strong>the</strong> deadtime <strong>of</strong> <strong>the</strong> scanner. This is due to <strong>the</strong> lack <strong>of</strong>adequate shielding in
3D whole-body imaging compared to 2D imaging. Fur<strong>the</strong>rmore, <strong>the</strong> correction <strong>of</strong> <strong>the</strong> data is more
complicated. Many <strong>of</strong> <strong>the</strong> simple 2D correction algorithms like <strong>the</strong> convolution subtraction algorithm
do not work for 3D [1].
In 2D PET, <strong>the</strong> shielding between rings restricts <strong>the</strong> solid angle for scattered events and <strong>the</strong>refore
leads to a signi cant geometrical suppression <strong>of</strong> scattered events. However, 3D PET is generally septaless
with a large axial FOV. The focus <strong>of</strong> our study is <strong>the</strong>refore to investigate <strong>the</strong> bene ts <strong>of</strong> septa
and additional patient shields outside <strong>the</strong> scanner on our current 3D whole-body PET scanner.
A powerful and widely accepted tool for such examinations are Monte-Carlo (MC) simulations
that allow <strong>the</strong> simulation <strong>of</strong> real experiments on <strong>the</strong> computer. In contrast to actual experiments,
it is possible to distinguish between scattered and unscattered radiation with MC simulations, and
<strong>the</strong>refore between di erent count rate contributions. Fur<strong>the</strong>rmore, MC simulations are more exible
than experiments, and <strong>the</strong>y help to to reduce <strong>the</strong> number <strong>of</strong> experiments, which can be restricted to
those that are needed to verify <strong>the</strong> code.
Additional information on PET and scattered radiation in PET can be found in <strong>the</strong> proceedings
<strong>of</strong> <strong>the</strong> First <strong>International</strong> <strong>Workshop</strong> on EGS4 [2, 3].
1

crystal (NaI)
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cylinder phantom
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y−axis
z−axis
ring diameter: 900 mm
160 mm
side
shielding
(lead)
patient shielding (lead)
crystal (NaI)
septa (tungsten)
x−axis z−axis
water−filled cylinder phantom
Figure 1: PET scanner geometry. Left) Frontal view, right) axial cross section. The use <strong>of</strong> <strong>the</strong> patient shields
and <strong>the</strong> septa are optional.
2 Material and methods
2.1 PET System
The simulated PET scanner was a CPET from ADAC/UGM. It uses 6 curved NaI(Tl) detectors
(45 30 cm 2 , 2.54 cm thick) with a ring diameter <strong>of</strong> 90 cm. The axial FOV is 25.6 cm and <strong>the</strong> transverse
FOV is 57.6 cm. The side shielding is 16 cm long and <strong>the</strong>re are no septa. The default energy window
for <strong>the</strong> scanner is currently set at 435 - 665 keV. A detailed description <strong>of</strong> <strong>the</strong> scanner can be found
in [4, 5].
2.2 Monte-Carlo simulations
Our MC simulations are based on EGS4 [6]. The basic geometric elements which are used to
setup <strong>the</strong> scanner geometry are planes and spheres. These elements are used to model <strong>the</strong> gantry, NaI
detectors and tungsten septa. Figure 1 shows a sketch <strong>of</strong> <strong>the</strong> coded geometry.
A complete physical description <strong>of</strong> <strong>the</strong> scatter process is very complex and would require too much
CPU time to calculate <strong>the</strong> desired number <strong>of</strong> histories (typically 10 7 - 10 9 ). It is <strong>the</strong>refore necessary
to make some simplifying approximations, while still describing <strong>the</strong> scatter process in a su ciently
accurate way. The approximations give up some accuracy, but reduce <strong>the</strong> statistical error. The + -
decay is simulated by two back-to-back photons, each with 511 keV, neglecting <strong>the</strong> positron range
(1-2 mm) and <strong>the</strong> small non-collinearity <strong>of</strong> <strong>the</strong> photon pairs ( 0:5 ). Moreover, we restricted <strong>the</strong>
simulations to Rayleigh and Compton scattering, <strong>the</strong> latter being <strong>the</strong> predominant interaction <strong>the</strong>
photons undergo at <strong>the</strong> considered energy. To speed up <strong>the</strong> simulations we did not simulate <strong>the</strong>
detection process, instead we determined <strong>the</strong> detection probability <strong>of</strong> <strong>the</strong> photon for <strong>the</strong> undisturbed
trajectory in <strong>the</strong> crystal and counted <strong>the</strong> photon with this detection probability. We applied several
(lower) energy thresholds, from 200 keV to 510 keV in steps <strong>of</strong> 10 keV. It should be noted that energy
smearing <strong>of</strong> <strong>the</strong> detected events is available in our code, but was not used for <strong>the</strong> present study.
Events can be rebinned into <strong>the</strong> sinogram format which is used by our PET scanners. This allows
us to process <strong>the</strong> simulated data like measured data. An event is considered as `true' or unscattered
when nei<strong>the</strong>r <strong>of</strong> <strong>the</strong> two photons is de ected, and is considered as `scatter' when one or both photons
are scattered.
The cross sections for <strong>the</strong> di erent media were generated for an energy range from 50 - 550
keV using PEGS4. Available media are water, lead, tungsten, aluminum, and di erent scintillator
materials, including NaI. Interaction in air was neglected and <strong>the</strong> vacuum cross section was taken
2
y
x

instead. MC data were obtained by simulating water- lled cylindrical phantoms with diameters up
to 50 cm and di erent lengths. The phantoms contained a point source or a homogeneous activity
distribution. The simulations were mainly performed on a SUN Ultra 60 and a SUN ULTRA 10. The
simulation <strong>of</strong> 10 8 histories required approximately 4 hours CPU time, depending on <strong>the</strong> object and
activity distribution.
2.3 Simulated Geometries
2.3.1 Patient Shield: Point source in water- lled cylinders
To investigate <strong>the</strong> bene ts <strong>of</strong> additional patient
shielding, we simulated a point source in a waterlled
cylinder (30 cm diameter and 100 cm long) as
depicted in Fig. 2. A thickness <strong>of</strong> 20 mm and a
length <strong>of</strong> 37.2 cm was chosen to achieve <strong>the</strong> maximum
bene ts from <strong>the</strong> shield (<strong>the</strong> shield completely
covers <strong>the</strong> phantom outside <strong>the</strong> FOV and 20 mm is
thick enough to practically stop all photons in <strong>the</strong>
shield). For each setup, 10 8 histories were simulated.
2.3.2 Patient Shield: Uniform activity distributions
In a very simple approximation, <strong>the</strong> activity distribution
in a patient can be described as an extended
uniform activity distribution. This is justi
ed as long as we consider only global contributions
to <strong>the</strong> scanner countrates. We simulated a
uniform activity distribution in 100 cm long waterlled
cylinders with diameters ranging from 10 to
50 cm, such that <strong>the</strong> activity concentration was <strong>the</strong>
same in all phantoms. The length <strong>of</strong> <strong>the</strong> patient
patient shield
37.2 cm long
detector crystal
y−axis
water−filled cylinder
−50 −12.8 0 12.8
50 z−axis
detector crystal
stepped point source
(not drawn to scale)
Figure 2: Stepped pointsourceinawater- lled cylinder.
The full circles indicate <strong>the</strong> di erent axial positions
<strong>of</strong> <strong>the</strong> point source. The distance between
<strong>the</strong> patient shield and <strong>the</strong> cylinder was 10 mm, independently
<strong>of</strong> <strong>the</strong> cylinder diameter. The simulations
were performed without and with patient shield (20
mm thick).
shield was again 37.2 cm, which completely covers <strong>the</strong> part <strong>of</strong> <strong>the</strong> cylinders that is outside <strong>the</strong> FOV.
In order to compare <strong>the</strong> simulated patient shield to <strong>the</strong> best possible shield, we also simulated cylinders
with <strong>the</strong> length <strong>of</strong> <strong>the</strong> axial FOV (i.e.where <strong>the</strong>re was no activity outside <strong>the</strong> FOV).
2.3.3 Length and thickness <strong>of</strong> <strong>the</strong> patient shield
In order to determine <strong>the</strong> minimum length and thickness <strong>of</strong> <strong>the</strong> patient shield that are required for
an e ective shield, we simulated water- lled phantoms ( = 20 cm) with di erent lengths (l =25:6,
51.2, 76.8 cm) and shielding thicknesses (d =0:32, 0.64, 0.96, 1.32 mm). The 25.6 cm long phantom
was centered in FOV, while for <strong>the</strong> longer phantoms, one end <strong>of</strong> <strong>the</strong> phantom was ush with <strong>the</strong> edge
<strong>of</strong> <strong>the</strong> FOV, and <strong>the</strong> o<strong>the</strong>r end extended through <strong>the</strong> scanner and outside <strong>the</strong> FOV. The length <strong>of</strong> <strong>the</strong>
patient shield was 25.6 cm which corresponds with <strong>the</strong> length <strong>of</strong> <strong>the</strong> axial FOV. The energy threshold
was set to 250 keV.
2.3.4 Septa: Point source in water- lled cylinders
In <strong>the</strong> current CPET con guration, <strong>the</strong> rotation mechanism for <strong>the</strong> 137 Cs transmission source
uses <strong>the</strong> 9 cm directly in front <strong>of</strong> <strong>the</strong> detector crystal. Therefore, <strong>the</strong> septa length is limited to 70 mm
(see Fig. 1). In <strong>the</strong> simulations presented below, we used 31 septa, each 60 mm long and 1 mm thick,
and <strong>the</strong>y were equally spaced across <strong>the</strong> axial FOV. The phantom was again <strong>the</strong> stepped point source
in a water- lled cylinder ( = 30 cm, length = 100 cm, see 2.3.1) and <strong>the</strong> energy threshold was set to
450 keV.
3

singles [a.u.]
scatter [a.u.]
x 10
1800
1600
A B
1400
1200
1000
800
600
400
200
0
3
250 keV
without patient shield
with patient shield
50000
45000
40000
end FOV
35000
without and with
350 keV
30000
patient shield
450 keV
25000
20000
(all curves overlap)
15000
10000
end FOV
5000
0 10 20 30 40
0
0 10 20 30 40
axial source position [cm]
axial source position [cm]
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
250 keV
350 keV
450 keV
C
end FOV
without patient shield
with patient shield
0 10 20 30 40
axial source position [cm]
2.3.5 Uniform activity distributions
trues [a.u.]
250 keV 350 keV
450 keV
Figure 3: Stepped point source in a 100-cm long
water- lled cylinder ( = 30 cm), without and
with patient shield. A) Singles, B) trues, and C)
scatter.
To investigate <strong>the</strong> impact <strong>of</strong> septa on a uniform activity distribution, we simulated a water- lled
cylinder (length = 76.8 cm) with di erent diameter d = 20, 30, 40, 50 cm and an energy threshold <strong>of</strong>
450 keV. The same septa as in 2.3.4 were used. In addition, <strong>the</strong> simulations were repeated with <strong>the</strong>
patient shields described above.
3 Results and discussion
3.1 Patient Shield
3.1.1 Point source in water- lled cylinders
Independently <strong>of</strong> <strong>the</strong> energy threshold, <strong>the</strong>re is a signi cant singles contribution from activity
outside <strong>the</strong> FOV (see Fig. 3 A). For example, at a distance <strong>of</strong> 7.2 cm beyond <strong>the</strong> edge <strong>of</strong> <strong>the</strong> FOV
(z=20 cm), a point source has a singles countrate <strong>of</strong> 60.6 % <strong>of</strong> a point source in <strong>the</strong> center <strong>of</strong> <strong>the</strong> FOV
(z=0 cm, LLD=450 keV). At 17.2 cm from <strong>the</strong> edge <strong>of</strong> <strong>the</strong> FOV (z=30 cm), <strong>the</strong> singles countrate
is 28.5 %. If a patient shield is used, <strong>the</strong> contribution decreases to 32.0 % and 0.8 %, respectively.
This leads to <strong>the</strong> conclusion that patient shields signi cantly reduce <strong>the</strong> singles from activity outside
<strong>the</strong> FOV, reducing detector deadtime and randoms. The trues events are not a ected by <strong>the</strong> patient
shield and are also independent <strong>of</strong> <strong>the</strong> energy threshold, since no energy smearing was applied (see
Fig. 3 B). Figure 3 C shows that <strong>the</strong> e ect <strong>of</strong> <strong>the</strong> shields on scattered events is nearly negligible for an
energy threshold <strong>of</strong> 450 keV, but increases with decreasing energy threshold. The data for a threshold
<strong>of</strong> 250 keV shows that <strong>the</strong> patient shield is even e ective for source positions inside <strong>the</strong> FOV, blocking
<strong>the</strong> trajectories for photons reentering <strong>the</strong> FOV after being scattered outside <strong>the</strong> FOV.
The results show also that PET scanners like <strong>the</strong> NaI based CPET with good energy resolution
(but limited countrate capability) and a high energy threshold, su er from outside-<strong>the</strong>-FOV activity
mainly due to single events. PET scanners with poor energy resolution (typically BGO block detector
based) and a low energy threshold, but high countrate capability, su er from outside-<strong>the</strong>-FOV activity
also due to scattered events.
4

singles [a.u.]
trues-to-single ratio
x 10 2
A B
100 cm, without patient shield
100 cm, with patient shield
2500
25.6 cm, without shield
2000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
10 20 30 40 50
phantom diameter [cm]
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
C
100 cm, without patient shield
100 cm, with patient shield
25.6 cm
10 20 30 40 50
phantom diameter [cm]
3.1.2 Uniform activity distributions
scatter [a.u.]
1500
(curves partially overlap)
1000
100 cm, without patient shield
500
100 cm, with patient shield
25.6 cm
0
10 20 30 40 50
phantom diameter [cm]
Figure 4: A) Single and B) scattered events for a
uniform cylinder phantoms with di erent diameters
(r = 10, 20, 30, 40, and 50 cm) and an energy
threshold <strong>of</strong> 450 keV. The true events depend only
on <strong>the</strong> cylinder diameter, but not on <strong>the</strong> length
(25.6 cm or 100 cm) or <strong>the</strong> patient shield. C)
Trues-to-singles ratio.
Figure 4 A shows that <strong>the</strong> patient shield reduces <strong>the</strong> singles contribution by approximately 45 %
for a 10-cm diameter phantom and is nearly as good as <strong>the</strong> optimum shield (25.6 cm long phantom),
which has a singles rate approximately 50 % <strong>of</strong> that with <strong>the</strong> 100-cm long phantom. The result is
an improvement in <strong>the</strong> trues-to-singles ratio <strong>of</strong> more than 80 % due to <strong>the</strong> patient shield (see Fig.
4 C). The patient shield is most e ective for a small phantom diameter and its e ciency decreases
with increasing diameter. For a 50 cm diameter phantom, <strong>the</strong> improvement in <strong>the</strong> singles rates is only
10 %, while <strong>the</strong> singles rate for <strong>the</strong> 25.6 cm long phantom shows a reduction <strong>of</strong> 30 %. We can also
conclude from <strong>the</strong>se data that for <strong>the</strong> 10-cm diameter phantom (length = 100 cm), 50 % <strong>of</strong> <strong>the</strong> singles
rate comes from <strong>the</strong> activity outside <strong>the</strong> FOV, while for <strong>the</strong> 50-cm diameter phantom (length = 100
cm) only 30 % <strong>of</strong> <strong>the</strong> singles rate comes from outside <strong>the</strong> FOV. Consequently, <strong>the</strong> relative contribution
from activity outside <strong>the</strong> FOV becomes less important with increasing object diameter. This is an
e ect <strong>of</strong> <strong>the</strong> change in <strong>the</strong> scan geometry and <strong>the</strong> self-attenuation <strong>of</strong> <strong>the</strong> object.
As we already learned from <strong>the</strong> point source simulations above, <strong>the</strong>re is no signi cant scatter
contribution from outside <strong>the</strong> FOV for an energy threshold <strong>of</strong> 450 keV. The scatter contributions are
very comparable for all three phantom con gurations for a given phantom diameter (see Fig. 4 B).
Note, this is not true if <strong>the</strong> threshold is lowered, as it is <strong>the</strong> case for most BGO based PET scanner.
3.1.3 Length and thickness <strong>of</strong> <strong>the</strong> patient shield
Figure 5 shows that <strong>the</strong> singles contribution and <strong>the</strong> resulting trues-to-singles ratio are nearly
identical for <strong>the</strong> 51.2-cm and 76.8-cm long phantom, independently <strong>of</strong> <strong>the</strong> shielding thickness. From
this we conclude that a shielding length <strong>of</strong> 25.6 cm is su cient. The number<strong>of</strong>singleevents decreases
with increasing shielding thickness, and consequently <strong>the</strong> trues-to-singles improves with increasing
shielding thickness, showing an asymptotic behavior. The improvement from a thickness <strong>of</strong> 0.96 mm
to 1.32 mm is only marginal and de nes <strong>the</strong> optimum shielding thickness. As was shown above in <strong>the</strong>
simulations <strong>of</strong> <strong>the</strong> point source, increasing <strong>the</strong> energy threshold only improves <strong>the</strong> situation and <strong>the</strong>
results can be applied to any higher threshold than 250 keV, in particular 450 keV.
5

singles [a.u.]
x 10 2
10000
8000
6000
A B
0.04
4000
76.8 cm long phantom
51.2 cm long phantom
2000
25.6 cm long phantom
(curves partially overlap)
0
0 0.2 0.4 0.6 0.8 1 1.2
thickness <strong>of</strong> patient shield [mm]
trues-to-singles ratio [a.u.]
0.035
0.03
0.025
0.02
0.015
0.01
0.005
76.8 cm long phantom
51.2 cm long phantom
25.6 cm long phantom
(curves partially overlap)
0
0 0.2 0.4 0.6 0.8 1 1.2
thickness <strong>of</strong> patient shield [mm]
Figure 5: A) Singles contributions and B) trues-to-singles ratio for uniform activity distributions in a water- lled
cylinder ( = 20 cm) as function <strong>of</strong> <strong>the</strong> shielding thickness.
3.2 Septa
3.2.1 Point source in water- lled cylinders
Figure 6 shows that septa signi cantly reduce <strong>the</strong> singles contribution. For example, <strong>the</strong> reduction
for <strong>the</strong> center position is 66 %. At <strong>the</strong> same time, septa also reduce <strong>the</strong> trues contribution, and <strong>the</strong>
resulting trues-to-singles ratio for septa is lower in <strong>the</strong> center <strong>of</strong> <strong>the</strong> FOV than without septa, but is
higher at <strong>the</strong> edge <strong>of</strong> <strong>the</strong> FOV. Overall, septa lead to an axially more uniform trues-to-singles ratio.
The biggest impact <strong>of</strong> <strong>the</strong> septa is on scattered events for example, <strong>the</strong>y are reduced by 86 % for <strong>the</strong>
central source position. The scatter fraction (SF), which isde nedas
SF =
scattered events
total events
is signi cantly lower with septa than without septa across <strong>the</strong> FOV. This leads to <strong>the</strong> conclusion that
septa are helpful to reject scattered events, but it is unclear from <strong>the</strong> point source simulation, if <strong>the</strong>
e ect on <strong>the</strong> trues-to-singles ratio is bene cial, neutral, or negative.
3.2.2 Uniform activity distributions
While it was unclear from <strong>the</strong> point source simulations if <strong>the</strong> septa are bene cial for <strong>the</strong> truesto-singles
ratio or not, Fig. 7 A clearly shows that septa lower <strong>the</strong> trues-to-singles ratio. This is true
for all simulated phantom diameters. The best results for <strong>the</strong> trues-to-singles ratio can be achieved,
if patient shields without septa are used. As expected from <strong>the</strong> point source simulations, septa help
to reduce <strong>the</strong> scatter fraction and <strong>the</strong> e ect increases with increasing diameter.
4 Conclusions
The use <strong>of</strong> external patient shields is advantageous, particularly for small objects. Patient shields
have no impact on true events and help to reduce scatter contamination from activity inside and
outside <strong>the</strong> FOV. But this only relevant if a low energy threshold is used (e.g. 250 keV). For a high
energy threshold (e.g. 450 keV), <strong>the</strong> simulations showed that <strong>the</strong> scatter contamination is already
suppressed even without <strong>the</strong> external patient shields. The singles contribution can be reduced up to
25 %, which corresponds to a reduction <strong>of</strong> random events <strong>of</strong> 44 % and a reduction <strong>of</strong> <strong>the</strong> scanner
deadtime by 40 % for a typical clinical countrate.
The use <strong>of</strong> septa can be advantageous for large objects, if <strong>the</strong> main objective is to reduce scatter
and if <strong>the</strong> loss <strong>of</strong> true events is compensated for by an increase <strong>of</strong> <strong>the</strong> injected activity. The investigated
septa reduce <strong>the</strong> true countrate by 75 %, but <strong>the</strong>y also reduce <strong>the</strong> trues-to-singles ratio, particularly
for small objects. The reduction <strong>of</strong> scattered events leads to a decrease <strong>of</strong> <strong>the</strong> scatter fraction by 15%
(for small objects) - 30 % (for large objects). It should be noted that septa cause axial inhomogeneities
6
(1)

singles [a.u.]
scatter [a.u.]
scatter fraction
x 10
9000
8000
7000
6000
A B
5000
4000
3000
2000
1000
0
2
end FOV
without septa
with septa
with patient shield
50000
45000
40000
35000
30000
end FOV
without septa
with septa
25000
20000
15000
10000
5000
0 10 20 30 40
0
0 10 20 30 40
axial source position [cm]
axial source position [cm]
22500
20000
17500
15000
12500
10000
7500
5000
2500
0
1
0.8
0.6
0.4
C D
end FOV
0.05
end FOV
without septa
with septa
with patient shield
0 10 20 30 40
axial source position [cm]
E
without septa
with septa
0.2
0
0 10
end FOV
20 30 40
axial source position [cm]
trues [a.u.]
trues-to-singles ratio
0.04
0.03
0.02
0.01
without septa
with septa
0
0 10 20 30 40
axial source position [cm]
Figure 6: Stepped point source in a water- lled
cylinder ( = 30 cm, length = 100 cm) for an energy
threshold <strong>of</strong> 450 keV. A) Singles, B) trues,
C) scatter, D) trues-to-singles ratio, and E) scatter
fraction.
in <strong>the</strong> sensitivity that are a potential problem for data corrections. Fur<strong>the</strong>r MC simulations are
necessary to investigate <strong>the</strong> e ectiveness <strong>of</strong> septa <strong>of</strong> varying number, length and thickness.
Acknowledgments
The authors would like to thank Dr. Margaret E. Daube-Wi<strong>the</strong>rspoon for her help and suggestions.
This work was supported by a grant from <strong>the</strong> Department <strong>of</strong> Energy (DE-FG02-88ER60642). Dr. L.
E. Adam was supported in part by a Benedict Cassen Postdoctoral Fellowship from <strong>the</strong> Education
and Research Foundation <strong>of</strong> <strong>the</strong> Society <strong>of</strong> Nuclear Medicine.
References
[1] L.-E. Adam, J. S. Karp, and G. Brix, \Investigation <strong>of</strong> scattered radiation in 3D whole-body
positron tmission tomography using Monte Carlo simulations," Phys. Med. Biol. 44 (1999)2879{
2895.
[2] Y. Narita, M. Shidara, T. Nakumara, T. Fujiwara, and M. Itoh, \Simulation <strong>of</strong> Compton scatter
in 3-dimensional pet," in <strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> First <strong>International</strong> <strong>Workshop</strong> on EGS4.
7

trues-to-singles ratio
0.05
0.045
0.04
0.035
0.03
0.025
A
without septa,
with patient shield
without septa,
without patient shield
0.4
0.35
0.3
0.25
0.2
B
(curves partially overlap)
0.02
0.015
0.01
0.005
0
20
with septa, with patient shield
with septa, without patient shield
30 40 50
0.15
0.1
0.05
0
20
without septa, with patient shield
without septa, without patient shield
with septa, with patient shield
with septa, without patient shield
30 40 50
phantom diameter [cm]
phantom diameter [cm]
Figure 7: A) Trues-to-singles ratio and B) scatter fraction for uniform, cylindrical phantoms with di erent
diameters (r = 20, 30, 40, and 50 cm) and an energy threshold <strong>of</strong> 450 keV.
[3] M. Shidara, Y. Narita, T. Nakamura, M. Miyake, T. Fujiwara, and M. Itoh, \A preliminary study
<strong>of</strong> Compton scattering correction in 3D-PET study based on <strong>the</strong> unfolding method," in <strong>Proceedings</strong>
<strong>of</strong> <strong>the</strong> First <strong>International</strong> <strong>Workshop</strong> on EGS4.
[4] L.-E. Adam, J. S. Karp, and R. J. Smith, \PET camera performance measurements: a comparison
between three PET cameras," J. Nucl. Med. 40(1999)76.
[5] L.-E. Adam, J. S. Karp, M. E. Daube-Wi<strong>the</strong>rspoon, and R. J. Smith, \Performance <strong>of</strong> a wholebody
PET scanner using curve-plate NaI(Tl) detectors," (submitted).
[6] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, The EGS4 code system. SLAC-Report-265,
Stanford University, Stanford, 1985.
8
scatter fraction

in <strong>the</strong> case <strong>of</strong> lung cancer, a thorax is composed several tissues and it is di cult to determinate <strong>the</strong>
absorbed dose distribution. In <strong>the</strong> lung, <strong>the</strong> recoil electron travels longer distance and arrives <strong>the</strong>
outside <strong>of</strong> <strong>the</strong> eld. Fur<strong>the</strong>rmore <strong>the</strong> numbers <strong>of</strong> recoil election per unit volume is smaller than <strong>the</strong>
s<strong>of</strong>t tissue. Consequently, <strong>the</strong> second electrons equilibrium dose not exists and it makes determination
<strong>of</strong> <strong>the</strong> absorbed dose to be di cult. In this study, <strong>the</strong> absorbed dose distribution <strong>of</strong> thorax was
calculated using <strong>the</strong> EGS4 Monte Carlo simulation. The variation <strong>of</strong> <strong>the</strong> absorbed dose distribution
as a function <strong>of</strong> eld size, incident x-ray energy and optimal incident energy were investigated.
3 Methods and Materials
3.1 The geometrical arrangement
Figure 1 shows <strong>the</strong> geometrical arrangement <strong>of</strong>
simulations for <strong>the</strong> absorbed dose calculation. The
diameter <strong>of</strong> <strong>the</strong> thorax model was 40 cm and <strong>the</strong>
thickness was 23 cm. This thorax model was composed
<strong>of</strong> 3 layers. These are <strong>the</strong> front chest wall, <strong>the</strong>
lung layer and <strong>the</strong> back chest wall. The density <strong>of</strong>
Frontchestwall
<strong>the</strong> front chest wall and <strong>the</strong> back chest wall were 1.0
g/cm
Lunglayer
Backchestwall
Figure 1. Geometrical arrangement <strong>of</strong> Monte Carlo
simulation
3 . The thickness <strong>of</strong> <strong>the</strong> front chest wall was 3.0
cm and <strong>the</strong> back chest wall was 5.0 cm. The thickness
<strong>of</strong> lung layer was 15 cm, and <strong>the</strong> density was
0.3 g/cm3 . There was a tumor volume embedded in
lung at a 10 cm depth. Its diameter and thickness
were 2.0 cm. In this model, imaginary planes were
arranged perpendicular to <strong>the</strong> beam axis at an interval
<strong>of</strong> 0.5 cm. Fur<strong>the</strong>rmore, <strong>the</strong> model was divided
into concentric cylinders at an interval <strong>of</strong> 0.1 cm.
The absorbed dose <strong>of</strong> each volume was calculated. In <strong>the</strong> case <strong>of</strong> homogeneous model, <strong>the</strong> lung layer
was replaced with water equivalent material. And <strong>the</strong> results <strong>of</strong> lm method were compared. This
experiment was performed for 6 MV and 10 MV X-ray with MEVATRON KD2/65 linear accelerator
at <strong>the</strong> Cancer Institute Hospital. The thorax phantom was similar with <strong>the</strong> geometrical arrangement
<strong>of</strong> simulation. And <strong>the</strong> absorbed dose distribution <strong>of</strong> thorax model and homogeneous model were
compared.
3.2 Condition <strong>of</strong> simulation
The absorbed dose distribution was calculated using <strong>the</strong> EGS4 Monte Carlo simulation. An EGS4
user code, which recorded <strong>the</strong> absorbed dose at arbitrary depth for an arbitrary eld size, was coded
for this study. The incident beams were parallel beam <strong>of</strong> photons. Field shape was circular eld.
Those Spectra data was quoted from Mohan's data[4]. A set <strong>of</strong> 5,000,000 photons was generated per
batch and ten batches were performed for eld diameters <strong>of</strong> 2.8, 3.0 and 3.2 cm respectively. The
simulation was performed for a 4, 6, 10 and 15 MV X-ray.
2

4 Results and Discussion
4.1 Variation in OCR
OCR
1.2
1.0
0.8
0.6
0.4
0.2
fieldsize
tumorsize
Thoraxmodel
Homogeneousmodel
0.0
0.0 0.5 1.0 1.5 2.0
distance[cm]
Figure2.Comparison<strong>of</strong>OCRforthoraxmodelandhomogeneousmodel<strong>of</strong>4
MVat9cmdepth.
OCR
1.2
1.0
0.8
fieldsize
tumorsize
0.6
4 MV
0.4
6 MV
0.2
0.0
10MV
15MV
0.0 0.5 1.0 1.5 2.0
Distance[cm]
Figure3.Variation<strong>of</strong>OCRasafunction<strong>of</strong>X-rayenergy.
The o -center ratio (OCR), which is <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> dose at a point o <strong>the</strong>central ray to <strong>the</strong> dose
at <strong>the</strong> same depth on <strong>the</strong> central ray, represents one-dimensional dose distribution for perpendicular
direction to beam axis. Figure 2 shows <strong>the</strong> OCR in <strong>the</strong> thorax and homogeneous model at a 9 cm
depth for a 3.0 cm eld <strong>of</strong> 4 MV X-ray. The standard deviation was about 3.5 % near <strong>the</strong> beam axis
and less than 1.0% at 1.0 cm from <strong>the</strong> axis. In a region between <strong>the</strong> center and 1.5 cm from <strong>the</strong> center,
<strong>the</strong> OCR curve <strong>of</strong> <strong>the</strong> thorax model declined more steeply than <strong>the</strong> one <strong>of</strong> <strong>the</strong> homogeneous model.
But outside <strong>of</strong> <strong>the</strong> eld, <strong>the</strong> OCR in thorax model was greater than <strong>the</strong> OCR <strong>of</strong> <strong>the</strong> homogeneous
model. Figure 3 shows <strong>the</strong> variation <strong>of</strong> OCR as a function <strong>of</strong> X-ray energy. The OCR curve became
to be more steeply as <strong>the</strong> X-ray energy increased. In <strong>the</strong> case <strong>of</strong> 4 MV, <strong>the</strong> di erence <strong>of</strong> OCR at <strong>the</strong>
center and at 1.0 cm was 7.3 %. In <strong>the</strong> case <strong>of</strong> 15 MV, <strong>the</strong> di erence <strong>of</strong> OCR at <strong>the</strong> center and at 1.0
cm was 15.0 %. The at range <strong>of</strong> OCR in <strong>the</strong> tumor decreased as <strong>the</strong> X-ray energy increased. And in
<strong>the</strong> lung area, <strong>the</strong> OCR increased as <strong>the</strong> X-ray energy increased.
Offcenterratio
1.2
1.0
0.8
0.6
0.4
0.2
0.0
fieldsize
tumorsize
0 5 10 15 20
Distancefromcenter(mm)
Figure4.Thedifference<strong>of</strong>OCRbetween6MVand10MV
withfilmmethod
10 MV
3
OCRlung/OCRwater
2.5
2.0
1.5
fieldsize
tumorsize
1.0
9-9.5
9.5-10.0
0.5
0.0
10.0-10.5
10.5-11.0
0.0 0.5 1.0 1.5 2.0
distance[cm]
Figure 5. The change <strong>of</strong> ratio <strong>of</strong> <strong>the</strong> OCR <strong>of</strong> thorax model for <strong>the</strong> OCR <strong>of</strong>
homogeneousmodelfora3.0cmφfield<strong>of</strong>4MVX-ray.

The range <strong>of</strong> <strong>the</strong> 0.2-0.8 and 0.8-0.8 <strong>of</strong> OCR are 1.2
summarized in Table1. The range <strong>of</strong> <strong>the</strong> 0.2-0.8 <strong>of</strong>
OCR is <strong>the</strong> distance between <strong>the</strong> points at 20% and
1.0
80% <strong>of</strong> <strong>the</strong> central-axis dose value[5]. The 0.8-0.8 0.8 tumorsize
<strong>of</strong> OCR is <strong>the</strong> width that receives at least 80% <strong>of</strong>
<strong>the</strong> dose on <strong>the</strong> central axis. The range <strong>of</strong> <strong>the</strong> 0.2-
0.8 <strong>of</strong> OCR increased as <strong>the</strong> X-ray energy increased.
0.6
0.4
30cmf
32cmf
The 0.8-0.8 <strong>of</strong> OCR decreased as <strong>the</strong> X-ray energy
increased. Thus, with higher energy a greater mar-
0.2
28cmf
gin must be maintained around a lung tumor. Fig- 0.0
ure 4 shows <strong>the</strong> di erence <strong>of</strong> OCR between 6 MV
0.0 0.5 1.0 1.5 2.0
and 10 MV with lm method. The at range <strong>of</strong>
distance[cm]
OCR in <strong>the</strong> tumor decreased as <strong>the</strong> X-ray energy
increased. By comparing this result and <strong>the</strong> prior
result, it was found that <strong>the</strong>ir results behave similarly.
Figure 5 shows <strong>the</strong> change <strong>of</strong> ratio <strong>of</strong> <strong>the</strong> OCR
Figure6.Thechange<strong>of</strong>OCRasafunction<strong>of</strong>fieldsizefor4MVX-ray.
<strong>of</strong> thorax model to <strong>the</strong> OCR <strong>of</strong> homogeneous model for a 3.0 cm eld <strong>of</strong> 4 MV X-ray. The y-axis
shows <strong>the</strong> ratio <strong>of</strong> OCR in <strong>the</strong> thorax model to homogeneous model. In <strong>the</strong> region between 1.0 cm
and 1.5 cm distance from <strong>the</strong> center, <strong>the</strong> ratio decreased. And in <strong>the</strong> region from 1.5cm to 2.0 cm
from <strong>the</strong> center, <strong>the</strong> ratio increased. At a 1.5 cm, <strong>the</strong> OCR <strong>of</strong> lower energy almost corresponded with
<strong>the</strong> one <strong>of</strong> higher energy. But in <strong>the</strong> tumor, <strong>the</strong> OCR ratio increased as <strong>the</strong> X-ray energy decreased.
Figure 6 shows <strong>the</strong> change <strong>of</strong> OCR as a function <strong>of</strong> eld size. As <strong>the</strong> result, it was found that <strong>the</strong> at
range increased as <strong>the</strong> eld size increased but <strong>the</strong> OCR increased outside <strong>of</strong> <strong>the</strong> tumor.
4.2 Summary <strong>of</strong> OCR
Table 1 <strong>the</strong> range <strong>of</strong> <strong>the</strong> 0.2-0.8 and 0.8-0.8 <strong>of</strong> OCR
Energy 0.2-0.8 <strong>of</strong> OCR [cm] 0.8-0.8 <strong>of</strong> OCR [cm]
4MV 0.5 2.4
6MV 0.6 2.2
10 MV 0.8 2.0
15 MV 0.8 2.0
It was found that <strong>the</strong> at range decreased as X-ray energy increased. From <strong>the</strong> variation <strong>of</strong> OCR
as function <strong>of</strong> eld size, <strong>the</strong> at range increased as <strong>the</strong> eld size was extended but a greater amount
<strong>of</strong> normal tissue must be irradiated.
4.3 Variation in percentage depth dose
The Percent Depth Dose (PDD) is <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> dose to <strong>the</strong> dose at standard depth. PDD
represents one-dimensional dose distribution on beam axis. Figure 7 shows <strong>the</strong> comparison <strong>of</strong> PDD
between thorax and homogenous model at acenter for 3.0 cm eld <strong>of</strong> 4MVX-ray. The graph was
normalized at a peak depth. At a 3.0 cm depth, <strong>the</strong> build-down exists re-buildup and build-down
exist at <strong>the</strong> interface <strong>of</strong> lung and tumor. Figure 8 shows <strong>the</strong> change <strong>of</strong> PDD as a function <strong>of</strong> X-ray
energy. The PDD curve became more steeply at <strong>the</strong> interface <strong>of</strong> lung and tumor as <strong>the</strong> X-ray energy
increased. And <strong>the</strong> at range in <strong>the</strong> tumor decreased. Figure 9 shows <strong>the</strong> di erence <strong>of</strong> PDD between
EGS4 and RTAR at <strong>the</strong> center for a 3.0 cm <strong>of</strong> 4 MV X-ray. RTAR is <strong>the</strong> inhomogeneous correction
without scatter correction. It is used generally in clinical. The PDD <strong>of</strong> EGS4 was less than <strong>the</strong> one <strong>of</strong>
RTAR. The di erence between EGS4 and RTAR was summarized Table 2. In <strong>the</strong> tumor, <strong>the</strong> di erence
between EGS4 and RTAR for 4 MV and 6 MV was about 5 %. Figure 10 shows <strong>the</strong> di erence <strong>of</strong>
PDD between 6 MV and 10 MV with lm method. X-axis shows depth from <strong>the</strong> surface in mm. The
4
OCR

PDD
PDD
100
80
60
40
20
0
chest
wall
lung tumor lung
0 10 20
Depth[cm]
Thorax
Homogeneous
chest
wall
Figure7.Thecomparison<strong>of</strong>PDDbetweenthoraxandhomogenousmodelata
120
100
80
60
40
centerfor3.0cmφfield<strong>of</strong>4MVX-ray.
Depth[cm]
4MV(RTAR)
4MV(EGS4)
20
0
chest
wall
lung tumor lung
chest
wall
0 5 10 15 20
Figure9.Thedifference<strong>of</strong>PDDbetweenEGS4andRTARat<strong>the</strong>
centerfora3.0cmφ<strong>of</strong>4MVX-ray.
PDD
Depthdosenormalizedatpeakdepth
100
80
60
40
20
0
chest
wall
lung tumor lung
0 5 10 15 20
Depth[cm]
4MV
6MV
10MV
15MV
chest
wall
Figure8.Thechange<strong>of</strong>PDDasafunction<strong>of</strong>X-rayenergy
1.2
1.0
0.8
0.6
0.4
0.2
0.0
tumor
0 50 100 150 200 250
Depthinthoraxphantom(mm)
Figure10.Thedifference<strong>of</strong>PDDbetween6MVand10
MV with film method. In this case,
absorbed dose distribution was measured
withsphericaltumorphantom.
build-up and build-down exist at <strong>the</strong> interface between lung and tumor. And in <strong>the</strong> tumor, <strong>the</strong> at
range <strong>of</strong> PDD increased as <strong>the</strong> X-ray energy decreased. By comparing <strong>the</strong> results <strong>of</strong> lm method and
simulation, it was found that <strong>the</strong>ir results behave similarly.
Table 2. The di erence [%] between <strong>the</strong> result <strong>of</strong> EGS4 and RTAR
4MV 6MV 10 MV 15 MV
In <strong>the</strong> tumor 5.4 5.3 7.0 9.8
In <strong>the</strong> lung 10.1 13.5 20.1 23.9
The coe cient <strong>of</strong> variance <strong>of</strong> <strong>the</strong> absorbed dose in tumor as a function <strong>of</strong> X-ray energy was
examined. The change <strong>of</strong> <strong>the</strong> coe cient <strong>of</strong> variance was show in Figure 11. In <strong>the</strong> tumor, <strong>the</strong>
coe cient <strong>of</strong>variance increased as <strong>the</strong> X-ray energy increased.
5
10 MV
6 MV

Coefficient<strong>of</strong>Variance%
4.4 Summary <strong>of</strong> PDD
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
4 6 8 10 12 14
Energy[MV]
Figure11.Coefficient<strong>of</strong>variancein<strong>the</strong>tumor
As <strong>the</strong> result, <strong>the</strong> build-up and <strong>the</strong> build-down caused by decrease <strong>of</strong> <strong>the</strong> number <strong>of</strong> secondly
electrons in <strong>the</strong> lung existed at <strong>the</strong> interface <strong>of</strong> <strong>the</strong> front chest wall and lung, and <strong>the</strong> interface <strong>of</strong> lung
and tumor. The PDD curve became more steeply at <strong>the</strong> interface <strong>of</strong> lung and tumor as X-ray energy
increased. And <strong>the</strong> di erence between <strong>the</strong> result <strong>of</strong> EGS4 and <strong>the</strong> one <strong>of</strong> RTAR is about 5 % for 4
MV X-ray. But <strong>the</strong> di erences increase as <strong>the</strong> X-ray energy increase.
5 Conclusion
In this study, <strong>the</strong> absorbed dose distribution <strong>of</strong> tumor in <strong>the</strong> lung could be calculated using <strong>the</strong>
EGS4 Monte Carlo simulation. As <strong>the</strong> result, it was found that a lower energy could irradiate with
better <strong>the</strong> absorbed dose distribution ra<strong>the</strong>r than a higher energy, because <strong>the</strong> at range <strong>of</strong> OCR and
PDD in <strong>the</strong> tumor increased as <strong>the</strong> X-ray energy decreased. In stereotactic irradiation for lung cancer,
it is required that high equality <strong>of</strong> absorbed dose in <strong>the</strong> tumor and decreasing radically out side <strong>of</strong> <strong>the</strong>
tumor[6]. Consequently, alower energy was recommended ra<strong>the</strong>r than a higher energy.
References
[1] L. Wang, M. Lovelock, C-S. Chui, \Experimental veri cation <strong>of</strong> a CT-based Monte Carlo dosecalculation
method in heterogeneous phantoms", Med. Phys. 26 (1999)2626-2634.
[2] M. Uematsu, A. Shioda, K. Tahara, et al., \Focal, high dose, and fractionated modi ed stereotactic
radiation <strong>the</strong>rapy for lung carcinoma patients", Cancer 82(1998)1062-1070.
[3] H. Saitoh, T. Fujisaki, M. Fukushi, et al., \A study on eld size and depth dependence <strong>of</strong> energy
spectrum", J. Jpn. Soc. Ther. Radiol. Oncol. 11(1999)279-285.
[4] M. Mohan, C. Chui, L. Lid<strong>of</strong>aky, \Energy and angular distributions <strong>of</strong> photons from medical
linear accelerators", Med. Phys. 12(1985)592-597.
[5] K. E. Ekstrand, W. H. Barnes, \Pitfalls in <strong>the</strong> use <strong>of</strong> high-energy X rays to treat tumors in <strong>the</strong>
lung", Int. J. Radiat. Oncol. Biol. Phys. 18(1990)249-252.
6

[6] H. Kato, M. Nakamura and S. Tsuki, \Physical characteristics for high energy X-ray narrow
beams", Jpn. J. Radiol. Technol. 48(1992)991-996 (in Japanese).
7

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.107-115
The Caluculation <strong>of</strong> 3D Saptial Dose Distribution
Around a Shielded Vaginal Cylinder with Iridium-192 Source
Calculated by using Monte Carlo Code EGS4
I. J. Chen 1 , R. D. Sheu 2 , B. J. Chang 1 ,
Y. M. Liu 3 , L. S. Chao 3 , S. H. Yen 3
1 Institute <strong>of</strong> Nuclear Energy Research, Lungtan, Taiwan
2 National Tsing Hua University, Hsin Chu, Taiwan
3 Cancer Therapy Center, Taipei Veterans General Hospital, Taipei Taiwan
Abstract
According to our previous study on <strong>the</strong> dose distribution around a shielded vaginal cylinder
with a high-intensity 192 Ir source by using EGS4 code, <strong>the</strong> more detailed 3D-simulation model was
established in this work. The results obtained by <strong>the</strong> 3D-simulation model were compared with
those measured by ionchamber in previous work and evaluated by <strong>the</strong> existing treatment planning
system. These results show good agreement. Fur<strong>the</strong>rmore, <strong>the</strong> 3D spatial dose distribution around
aunitintensity 192 Ir source was calculated at each probable position in <strong>the</strong> vaginal cylinder with
90 ,180, 270 tungsten shield and no shield cases. Those results save as a database which could
be accessed through <strong>the</strong> graphical user interface developed by IDL TM to display dose distributions
in 1D, 2D, and 3D plot under any combination <strong>of</strong> source intensity ateach position, and shielding
situation. It demonstrates a prototype <strong>of</strong> <strong>the</strong> brachy<strong>the</strong>rapy treatment planning system based on
<strong>the</strong> Monte Carlo EGS4 code.
1 Introduction
192 Ir is a widely used source in brachy<strong>the</strong>rapy to treat localized malignancies in nearly every body
site and a variety <strong>of</strong>such source are commercially available. Both <strong>the</strong>oretical and experimental methods
have been widely used to characterize <strong>the</strong> dose distributions around an isolated source in water
medium[1-7] and <strong>the</strong> heterogeneity correction factors for such a source near localized heterogeneity[8].
An intracavitary source consisting <strong>of</strong> encapsulated high-intensity (1Ci) 192 Ir is available for using in
high dose rate (HDR) single-stepping source remote afterloaders to treat vaginal and cervix malignancy.
The vaginal cylinder is one typical set <strong>of</strong> applicator applied in <strong>the</strong> treatment <strong>of</strong> <strong>the</strong> vaginal
lesion. Due to <strong>the</strong> radiosensitivity <strong>of</strong> <strong>the</strong> adjacent organs, e.g. bladder and rectum, severe complication
<strong>of</strong> rectal bleeding may develop for some <strong>of</strong> <strong>the</strong> patients. For <strong>the</strong>se patients, a shielded vaginal cylinder
(Applicator 084.320 Nucletron Corporation, Columbia MD, USA) was developed to reduce excess
dose to <strong>the</strong> rectum. The previously available commercial brachy<strong>the</strong>rapy treatment planning programs
did not take <strong>the</strong> perturbation into consideration when <strong>the</strong> presence <strong>of</strong> high-density material such as
tungsten shield. Waterman had measured <strong>the</strong> planar dose distributions around a high-activity 192 Ir
and proposed a way toevaluate <strong>the</strong> dose distributions under <strong>the</strong> presence <strong>of</strong> tungsten shield[9]. In our
previous study[10], <strong>the</strong> dose distribution around a shielded vaginal cylinder with an 192 Ir source could
also be calculated by applying EGS4 Monte Carlo code. The relative isodose distribution calculated
by EGS4 on <strong>the</strong> transverse plane at source location shows good agreement with <strong>the</strong> measurements obtained
by ion chamber and diode detector in water phantom. It demonstrates <strong>the</strong> reliable and accurate
modality toapply EGS4 code for <strong>the</strong> simulation <strong>of</strong> this kind <strong>of</strong> problem. One might take advantage
1

<strong>of</strong> using EGS4 to calculate <strong>the</strong> dose distribution in heterogeneous media owing to <strong>the</strong> capability <strong>of</strong>
Monte Carlo method dealing with three-dimension problem and <strong>the</strong> exibility <strong>of</strong> EGS4 code describing
arbitrary 3D geometry models. Hence, <strong>the</strong> purpose <strong>of</strong> this work is to apply EGS4 code to calculate <strong>the</strong>
3D spatial dose distribution around a shielded vaginal cylinder and propose a way to use <strong>the</strong>se results
in practical applications. However, it is di cult to implement a real time Monte Carlo calculation
for clinical applications because <strong>of</strong> its time consuming. Therefore, it is more realistic to establish a
database which includes <strong>the</strong> data pre-calculated by EGS4 for <strong>the</strong> 3D spatial dose distribution around
an unit intensity 192 Ir source at several positions in <strong>the</strong> vaginal cylinder with 90 ,180 , 270 tungsten
shield and without shield. Fur<strong>the</strong>rmore, a visualized user interface was developed by using Interactive
Data Language (IDL TM ) for accessing this database. Through <strong>the</strong> interactive graphical user interface,
it provides a convenient way to display <strong>the</strong> 3D spatial dose distribution obtained by EGS4 calculations
for any probable combination <strong>of</strong> source and shielded situations. This work indicates that <strong>the</strong> database
<strong>of</strong> 3D spatial dose distributions around a shielded vaginal cylinder pre-calculated by EGS4 could be
applied to develop a practical treatment planning system. The treatment planning system based on
Monte Carlo method could provide some more detailed and accurate dose distribution for <strong>the</strong> shielded
case.
2 Materials and Methods
The EGS4 computer code was used to simulate <strong>the</strong> 3D-dose distribution around a shielded vaginal
cylinder with an 192 Ir source. The simulation could be divided into two main components: <strong>the</strong> 192 Ir
source, and <strong>the</strong> shielded vaginal cylinder. The details <strong>of</strong> each component, including <strong>the</strong> encapsulation
material, <strong>the</strong> composition and thickness <strong>of</strong> <strong>the</strong> applicator wall, and <strong>the</strong> composition and geometry <strong>of</strong>
shielded vaginal cylinder are described as closely as possible.
The source simulated in this work is <strong>the</strong> HDR 192 Ir source (designed by Nucletron-Oldelft <strong>International</strong>
B. V. and manufactured by Mallinckrodt Diagnostica) is shown schematically in Fig. 1[11].
The cylindrical active 192 Ir pellet has a length <strong>of</strong> 3.5 mm and 0.6 mm in diameter. It is encapsulated
in AISI 316L stainless steel sheath with an outer length <strong>of</strong> 5 mm and 1.1 mm in diameter. One end
<strong>of</strong> <strong>the</strong> source has a round shape, and <strong>the</strong> distance form <strong>the</strong> distal face <strong>of</strong> <strong>the</strong> active source core to <strong>the</strong>
physical source tip was 0.55 mm. The energy <strong>of</strong> <strong>the</strong> emitted photons from <strong>the</strong> unencapsulated 192 Ir
source simulated in this work was listed in table 1[12].
The internal construction and dimensions <strong>of</strong> <strong>the</strong> shielded vaginal cylinder (Applicator 084.320,
Nucletron Corporation, Columbia MD, USA) <strong>of</strong> 3.0 cm in diameter upon our simulation are based,
are illustrated by Fig. 2. The applicator consists <strong>of</strong> 15-cm long cylinder plastic shell with an outer
diameter <strong>of</strong> 3.0 cm and 0.5 cm thick wall. It centered on a thin-wall stainless steel tube (0.4 cm o.d.)
which serves as pathway for <strong>the</strong> 192 Ir source. There is an air gap between <strong>the</strong> steel tube and <strong>the</strong> inner
wall <strong>of</strong> <strong>the</strong> cylinder. This gap could be lled with 0.8 cm thick tungsten 90 , 180 ,or270 shield. All
<strong>of</strong> <strong>the</strong>se components are held in place along with <strong>the</strong> central tube by <strong>the</strong> plastic end cap.
The geometry model <strong>of</strong> EGS4 simulation was shown in Fig. 3. As it shown, <strong>the</strong> detailed geometry
<strong>of</strong> <strong>the</strong> components that were near <strong>the</strong> tip <strong>of</strong> cylinder was also taken into consideration. In <strong>the</strong> EGS4
simulation, <strong>the</strong> scoring volume for recording spatial dose distribution was divided into two regions,
semi-spherical region (10 cm in radius) and <strong>the</strong> cylindrical region (10 cm in radius and 10 cm height).
The space <strong>of</strong> <strong>the</strong> semi-spherical region was divided into 50 36 144 scoring volumes, respectively in
radial direction, polar angle, and azimuthal angle. The space <strong>of</strong> <strong>the</strong> cylindrical region was divided into
50 40 144 scoring volumes, respectively in radial direction, axial direction, and azimuthal angle.
The number <strong>of</strong> particles tracked in EGS4 simulation was chosen to keep <strong>the</strong> statistic deviation <strong>of</strong> all
<strong>the</strong> results under 5% level.
2

3 Results and Discussions
3.1 The veri cation <strong>of</strong> <strong>the</strong> 3D simulation model
In our previous study, <strong>the</strong> dose distribution around a shielded vaginal cylinder was concerned
only on <strong>the</strong> plane where <strong>the</strong> 192 Ir source was. The detail geometry <strong>of</strong> two ends was simpli ed in our
previous simulation model. In order to evaluate <strong>the</strong> 3D spatial dose distribution, <strong>the</strong> 3D-simulation
model was established in this work. Hence, this 3D model was veri ed with <strong>the</strong> previous results at
rst. Fig. 4 and Fig. 5 show <strong>the</strong> relative dose fall-o in <strong>the</strong> radial direction and <strong>the</strong> isodose curve
on a transverse plane containing <strong>the</strong> 192 Ir source for <strong>the</strong> unshielded vaginal cylinder respectively. The
relative dose was normalized to 0.3 cm away from <strong>the</strong> cylinder wall. The results evaluated by <strong>the</strong>
3D-simulation model show good agreement with those measured by ion chamber in our previous work.
3.2 The comparison with <strong>the</strong> commercial treatment planning system
The 3D-simulation model was compared with <strong>the</strong> commercial brachy<strong>the</strong>rapy treatment planning
system that was adopted by <strong>the</strong> cancer center <strong>of</strong> <strong>the</strong> Veterans General Hospital-Taipei[13]. Fig. 6
shows <strong>the</strong> dwell time <strong>of</strong> <strong>the</strong> 192 Ir source at each position for a clinical case, in order to meet <strong>the</strong>
prescribed dose, 500 cGy at 2 cm o set from <strong>the</strong> center point in radial direction and 3 cm o set
from <strong>the</strong> center point in axial direction. The isodose curve evaluated and plotted by <strong>the</strong> treatment
planning system is also shown in Fig. 6. According to <strong>the</strong> dwell time <strong>of</strong> <strong>the</strong> source at each position, <strong>the</strong>
spatial dose distribution around <strong>the</strong> vaginal cylinder was also calculated by <strong>the</strong> 3D-simulation model
<strong>of</strong> this work. The results evaluated by commercial treatment planning system and EGS4 were shown
in Fig. 7. These results show good agreement in prescribed dose position in radial direction, but some
discrepancy close to <strong>the</strong> source axis. The discrepancy is due to <strong>the</strong> existing treatment planning system
neglected heterogeneity e ect, such as <strong>the</strong> encapsulated material <strong>of</strong> source and <strong>the</strong> guide tube. The
e ect <strong>of</strong> heterogeneity and oblique ltration could be taken into consideration by EGS4 simulation
without any extra e ort.
3.3 The prototype <strong>of</strong> treatment planning system based on EGS4
One important bene t <strong>of</strong> using EGS4 simulation is its capability <strong>of</strong> dealing with three-dimension
problems, especially <strong>the</strong> presence <strong>of</strong> heterogeneity. However it is di cult to implement a real time
Monte Carlo calculation for clinical applications because <strong>of</strong> its time consuming. It is more realistic to
establish a database that includes <strong>the</strong> data pre-calculated by EGS4 for <strong>the</strong> 3D spatial dose distribution
around an 192 Ir source under all probable combination <strong>of</strong> source position, intensity and shielding
situations. As it shown in Fig. 8, each source position and stepping size in <strong>the</strong> applicator is xed
for <strong>the</strong> HDR system. Hence, <strong>the</strong> spatial dose distributions around <strong>the</strong> cylinder with an unit intensity
192 Ir source were calculated by <strong>the</strong> 3D simulation model <strong>of</strong> this work at each probable position in <strong>the</strong>
vaginal cylinder with 90 , 180 , 270 tungsten shield and no shield cases. These results were save as
a database and could be accessed by <strong>the</strong> graphical user interface developed by using Interactive Data
Language (IDL TM )[14]. Through this interface, it provided an interactive graphical user interface to
display 1D, 2D, and 3D spatial dose distribution obtained by EGS4 calculations for any probable
combination <strong>of</strong> source and shielded situations. Fig. 9 shows <strong>the</strong> interactive dialog for setting up <strong>the</strong>
source positions, intensity and shielding situation. The dwell time and positions mentioned in above
paragraph with 180 tungsten shield were input, <strong>the</strong> 1D radial dose distribution and 2D isodose curve
on transverse and vertical plane could be shown by this interface as it shown in Fig. 10. Fur<strong>the</strong>rmore,
The 3D-isodose volume could be also displayed. Fig. 11 shows <strong>the</strong> isodose volume (100 cGy) <strong>of</strong> a
single source in <strong>the</strong> vaginal cylinder with 90 shield. Through this interactive graphical user interface,
users can generate and display <strong>the</strong> results pre-calculated by EGS4 in a few seconds. It seems to be a
prototype <strong>of</strong> our treatment planning system based on Monte Carlo code EGS4 for <strong>the</strong> shielded vaginal
cylinder.
3

References
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41(1996)955-1006.
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primary and scatter dose seperation technique", Phys. Med. Biol. 41(1996)1007-1024.
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[8] J. F. Wallisamson, H. Perera, and Z. Li, \Comparison <strong>of</strong> calculated and measured heterogeneity
correction factors for I-125, Cs-137, and Ir-192 brachy<strong>the</strong>rapy sources near localized heterogeneities",
Med. Phys. 20(1)(1993)1975-1984.
[9] F. M. Waterman and D. E. Holcomb, \Dose diatributions produced by a shielded vaginal cylinder
using a high-activity irdium-192 source", Med. Phys. 21(1)(1994).
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\Monte Carlo simulation <strong>of</strong> <strong>the</strong> dose distribution <strong>of</strong> a shielded vaginal cylinder using a highactivity
iridum-192 source", <strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> First <strong>International</strong> <strong>Workshop</strong> on EGS, KEK
Tsukuba Japan (1997).
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Iridium-192 Brachy<strong>the</strong>rapy Source", Nucletron-Oldelft Activity Report No.7-1, 43-47(1995).
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Table 1 The energy distribution <strong>of</strong> 192Ir assumed by our EGS4 simulation
Energy (MeV) yield Energy (MeV) yield Energy (MeV) yield
0.06683 0.10380 0.30850 0.29300 0.48906 0.00476
0.07563 0.02869 0.31650 0.83000 0.58860 0.04470
0.20138 0.00707 0.41647 0.01456 0.60440 0.08230
0.20580 0.03180 0.46810 0.47700 0.61250 0.05340
0.29600 0.28300 0.48460 0.03130 0.88454 0.00345
4

1.10 mm
0.60 mm
5.00 mm
0.55 mm 3.50 mm
0.95 mm
Active Ir-192 Core
3 mm Steel
Cable/Stem
AISI 316L Steel Capsule Steel capsule
Figure 1: Geometric models <strong>of</strong> <strong>the</strong> MircoSelectron HDR 192 Ir source.
air gap
plasic
cylinder
thin-wall stainless
steel tube
metal ring for xray
visualization
metal end plate
plastic end cap
180 deg.
tungsten shield
Figure 2: Geometric models <strong>of</strong> <strong>the</strong> shielded vaginal cylinder (Applicator 084.320 Nucletron Corporations).
33
32
31
15
16
19
20
30
7
8
22
7
6
9
10 12 11 12 10
6
8
2
1 4
14
17
1
24
3 12 3 4 5 6
10 12 13 12 10
31
18
21
2
32
26
3
33
7 8
12 3 4 5 6
7 8 9
Figure 3: The geometric model <strong>of</strong> <strong>the</strong> 3D spatial dose distribution assumed by our EGS4 simulation.
5
30
4
23
28
5
25
27
5
4
3
11
9
2
6
1
8
7

RelativeDose(%)
100
90
80
70
60
50
40
30
20
10
For<strong>the</strong>unshieldedvaginalcylinder
(sourceposition=-3.00cm)
EGS4
IonChamber
0
1 2 3 4 5 6 7 8 9 10
RadiusDistance(cm)
Figure 4: Relative dose fall-o along <strong>the</strong> radial direction on a transverse plane containing <strong>the</strong> 192 Ir source for
<strong>the</strong> unshielded vaginal cylinder.
Figure 5: Isodose curve on <strong>the</strong> transverse plane containing <strong>the</strong> 192 Ir source for <strong>the</strong> unshielded vaginal cylinder
(solid lines are <strong>the</strong> results obtained by 3D model, dot lines are those measured by ion chamber).
Figure 6: The dwell time and position <strong>of</strong> 192 Ir source in <strong>the</strong> vaginal cylinder meet <strong>the</strong> prescribed dose for a
clinical case. The isodose curve was evaluated by existing treatment planning system.
6

Figure 7: The comparison <strong>of</strong> isodose curve obtained by 3D simulation model and existing treatment planning
system.
1.50
-0.40 1
-0.65 2
-0.90 3
-1.15 4
-1.40 5
-1.65 6
-1.90 7
-2.15 8
-2.40 9
-2.65 10
-2.90 11
-3.15 12
-3.40 13
-3.65 14
-3.90 15
-4.15 16
-4.40 17
-4.65 18
0.20
1.00
1.50
1.10
First Source
Position
Figure 8: The probable source dwelling positions in <strong>the</strong> shielded vaginal cylinder for <strong>the</strong> HDR system.
Figure 9: The interactive dialog for setting up <strong>the</strong> source intensity at each position in <strong>the</strong> shielded vaginal
cylinder and shielding situation.
7

Figure 10: The 1D radial dose distribution and 2D isodose curve on <strong>the</strong> transverse and vertical plane under a
given source arrangement with 180 tungsten shield.
Figure 11: The 3D-isodose volume under a given source arrangement with90 tungsten shield.
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.115-123
Polarization Study for NLC Positron Source Using EGS4 1
J. C. Liu, T. Kotseroglou, W. R. Nelson, and D. Schultz
Stanford Linear Accelerator Center,
MS 48, P. O. Box 4349, Stanford, CA 94309, USA
Abstract
SLAC is exploring a polarized positron source to study new physics for <strong>the</strong> NLC project. The
positron source envisioned in this paper consists <strong>of</strong> a polarized electron source, a 50-MeV electron
accelerator, a thin target (= 0.2 radiation length) for positron production, and a capture system
for high-energy, small angular divergence positrons. The EGS4 code was used to study <strong>the</strong> yield,
energy spectra, emission-angle distribution, and <strong>the</strong> mean polarization <strong>of</strong> <strong>the</strong> positrons emanating
from W-Re and Ti targets hit by longitudinally polarized electron and photon beams. To account
for polarization within <strong>the</strong> EGS4 code a method devised by Flotmann was used, which takes into
account polarization transfer for pair production, bremsstrahlung, and Compton interactions. A
mean polarization <strong>of</strong> 0.85 for positrons with energies greater than 25 MeV was obtained. Most <strong>of</strong>
<strong>the</strong> high-energy positrons were emitted within a forward angle <strong>of</strong> 20 degrees. The yield <strong>of</strong> positrons
above 25 MeV per incident photon was 0.034, which was about 70 times higher than that obtained
with an electron beam.
1 Introduction
SLAC is exploring a polarized positron source to study new physics for <strong>the</strong> Next Linear Collider
(NLC) project. The positron source envisioned[1] consists <strong>of</strong> a polarized electron source, a 50-MeV
electron accelerator, a thin target for positron production, and a capture system for high-energy, small
angular divergence positrons. In <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> study, <strong>the</strong> positron yield and its spectral and
angular distributions for W-Re targets (0.5 to 5 mm thick) struck by 30-MeV electrons were rst
calculated with EGS4[2] and FLUKA99[3]. To check <strong>the</strong> validity <strong>of</strong> our polarization calculations,
<strong>the</strong> polarization <strong>of</strong> positrons from a tungsten target hit by backward-Compton scattered photons
calculated by Omori[4] were also compared with our calculated values. In <strong>the</strong> main work, <strong>the</strong> EGS4
code was used to study <strong>the</strong> yield, energy spectra, emission-angle distribution, and <strong>the</strong> polarization
<strong>of</strong> <strong>the</strong> positrons emanating from thin targets hit by longitudinally polarized, 50 MeV electron and
photon beams.
2 Methods
A generalized cylinder-slab EGS4 user code, called ucRTZ.mortran, has been designed to run with
<strong>the</strong> EGS4 Code System that was o cially released by <strong>the</strong> National Research Council <strong>of</strong> Canada in
Canada in January 1997. This version <strong>of</strong> EGS4 contains all <strong>of</strong> <strong>the</strong> latest features, such as <strong>the</strong> PRESTA-
I algorithm for low-energy electron transport and proper sampling <strong>of</strong> angles following bremsstrahlung
and pair-production processes. With <strong>the</strong> ucRTZ.mortran user code, geometry implementation was
facilitated by means <strong>of</strong> an input le (e.g., ucRTZ.data) that allows <strong>the</strong> user to specify, among o<strong>the</strong>r
things, cylindrical shells (concentric with <strong>the</strong> Z-axis), planes (normal to <strong>the</strong> Z-axis), and azimuthal
1 Work supported by <strong>the</strong> US Department <strong>of</strong> Energy under contract DE-AC-03-76SF00515
1

planes (parallel to <strong>the</strong> Z-axis, and rotated at an angle relative to X-axis). The azimuthal-plane feature
was not required in <strong>the</strong> present study.
All materials were prepared with AE=0.521 MeV, UE=100.511 MeV, AP=0.001 MeV, and
UP=100 MeV. The material <strong>of</strong> W-Re has 75% tungsten and 25% rhenium (by weight fraction), a
density <strong>of</strong> 19.65 gcm ;3 . Unless o<strong>the</strong>rwise speci ed, <strong>the</strong> ECUT and PCUT for all regions were set at
1.511 and 1 MeV, respectively.
Flottmann[5] introduced mean polarization calculations into <strong>the</strong> AUSGAB subroutine <strong>of</strong> <strong>the</strong> EGS4
user code. His method, acceptable in high-energy region, considered polarization transfer process only
in <strong>the</strong> bremsstrahlung, pair production and Compton reactions. The depolarization processes in
o<strong>the</strong>r reactions, e.g., Bhabha and Rayleigh scattering, were not considered. Thus, <strong>the</strong> polarization
calculated using this scheme should represent a higher estimation <strong>of</strong> <strong>the</strong> actual polarization. Since we
are interested in only high-energy positrons (> a few MeV), <strong>the</strong> Flottmann's approach is suitable. In
this work Flottmann's routines were incorporated into our EGS4 user code.
Only <strong>the</strong> longitudinal polarization, <strong>the</strong> fourth Stokes parameter 3[5], has a long-term stabilityinan
electromagnetic shower development. In <strong>the</strong> NLC source polarization study, longitudinal polarization
is <strong>the</strong> parameter studied. Positrons from <strong>the</strong> W-Re and titanium targets (0.2-radiation-length thick)
hit by an electron beam (50-MeV kinetic energy and a longitudinal polarization 3=1) were scored as
a function <strong>of</strong> yield, energy-angle distribution, and <strong>the</strong> polarization. The case <strong>of</strong> a 50-MeV, polarized
photon beam incident on <strong>the</strong> W-Re target was also studied for comparison.
3 Results
3.1 Spectra and Yield Comparison
Energy spectra <strong>of</strong> positrons, emanating from <strong>the</strong> downbeam side <strong>of</strong> W-Re targets having thicknesses
<strong>of</strong> 0.5, 1, 2 and 5 mm, are given in Figures 1a through 1d for an incident electron with <strong>the</strong>
kinetic energy <strong>of</strong> 30 MeV (ECUT=0.611 MeV and PCUT=0.1 MeV). The solid histograms are EGS4
calculations (100,000 cases) and <strong>the</strong> points are <strong>the</strong> FLUKA99 results (500,000 cases). A special EGS4
run (15,000,000 cases) was also made using cuto s <strong>of</strong> 19.9 MeV, and <strong>the</strong> results are shown as dotted
histograms. The agreement is quite good.
In Figure 2 we presents <strong>the</strong> positron yield (within energy range <strong>of</strong> 0.1 ;; 30 MeV) as a function
<strong>of</strong> polar angle emitted from <strong>the</strong> back plane <strong>of</strong> <strong>the</strong> W-Re target at four thicknesses. In Table 1 we
compared <strong>the</strong> positron yields (integrated over all angles) calculated by EGS4 and FLUKA99.
3.2 Comparison <strong>of</strong> Polarization Calculations
Omori <strong>of</strong> KEK has proposed a polarized positron source design[4] based on electron-positron
pair creation from backward-Compton scattered laser photons (maximum energy 60 MeV) hitting
a 1.5-mm-thick tungsten target. Omori calculated <strong>the</strong> positron production and polarization using
<strong>the</strong> EGS4/GRACE codes. To check <strong>the</strong> validity <strong>of</strong> our approach, we performed a corresponding
calculation. Table 2 shows that <strong>the</strong> positron yields between Omori's and our results are in good
agreement, while <strong>the</strong> positron polarization values calculated in this work are higher than those <strong>of</strong>
Omori.
3.3 Polarization for NLC Positron Source
The NLC decided to explore in detail <strong>the</strong> positron yield and polarization from thin W-Re and
titanium targets hit by monoenergetic, longitudinally polarized electron and photon beam at 50 MeV.
The target thickness was 0.2-radiation-length, i.e., 0.06866 cm for W-Re and 0.7124 cm for Ti.
The EGS4-calculated positron spectra from <strong>the</strong> electron beam hitting <strong>the</strong> W-Re and Ti target are
shown in Figure 3. The yield <strong>of</strong> high-energy positrons (de ned here as above 25 MeV) per incident
electron is 0.00048 for <strong>the</strong> W-Re target and 0.00035 for <strong>the</strong> Ti target. The corresponding longitudinal
2

polarization <strong>of</strong> positron as a function <strong>of</strong> positron energy (relative to beam energy), shown in Figure
4, indicated that <strong>the</strong> higher <strong>the</strong> positron energy, <strong>the</strong> higher <strong>the</strong> polarization. The mean polarization
for positrons above 25 MeV is 0.84 for W-Re and 0.86 for Ti targets.
For <strong>the</strong> same beam-target condition, Potylitsin[6] calculated analytically a high-energy positron
yield <strong>of</strong> 0.002, about 5 times higher than our EGS4 value. Potylitsin also estimated a mean polarization
<strong>of</strong> 0.6, which is 30% smaller than ours this could be due to Potylitsin's assumption <strong>of</strong> linear relationship
between photon polarization and photon energy in <strong>the</strong> bremsstrahlung process (see Figure 3 <strong>of</strong> [6]).
Table 3 summarizes <strong>the</strong> above comparison between our results and Potylitsin's.
The positron spectrum from a polarized 50-MeV photon beam hitting <strong>the</strong> W-Re target is shown
in Figure 5. The yield <strong>of</strong> positrons above 25 MeV per incident photon is 0.034, about 70 times higher
than that <strong>of</strong> <strong>the</strong> electron beam. A comparison <strong>of</strong> positron polarization from <strong>the</strong> W-Re target hit by
<strong>the</strong> electron and photon beams is shown in Figure 6. The mean polarization for positrons above 25
MeV is 0.88 for <strong>the</strong> photon beam, slightly higher than that <strong>of</strong> <strong>the</strong> electron beam. On <strong>the</strong> o<strong>the</strong>r hand,
for low-energy positrons, <strong>the</strong> mean polarization from <strong>the</strong> photon beam is lower than that from <strong>the</strong>
electron beam, although <strong>the</strong> yield is 10 time higher. The comparison between electron and photon
beamsisalsoshown in Table 3.
The 3-D energy-angle distribution <strong>of</strong> positrons from <strong>the</strong> 0.2-radiation-length W-Re target hit by
<strong>the</strong> 50-MeV electron beam, shown in Figure 7, indicates that high-energy positrons are more forward
peaked. Figure 8 shows that almost all positrons above 25 MeV are emitted within a small angle <strong>of</strong>
20 degrees. It was also found that <strong>the</strong> angular pro le <strong>of</strong> <strong>the</strong> emitted positrons is not a strong function
<strong>of</strong> beam type or target material.
4 Conclusion
High mean longitudinal polarization (>0.8) <strong>of</strong> positrons above 25 MeV was calculated using EGS4
for a W-Re or Ti target (0.2-radiation-length thick) struckby a electron or photon beam (longitudinally
polarized, 50 MeV). Most high-energy positrons were emitted within a forward angle <strong>of</strong> 20 degrees.
The yield <strong>of</strong> positrons above 25 MeV per incident photon is 0.034, 70 times higher than that <strong>of</strong> <strong>the</strong>
electron beam.
Acknowledgements
We appreciate K. Flottmann for giving us his polarization routines and assistance in its implemention
into our EGS4 user code.
3

References
[1] T. Ketseroglou et al., \Recent development in <strong>the</strong> design <strong>of</strong> <strong>the</strong> NLC positron source", 1999
Particle Accelerator Conference, New York, March 29;; April 2, 1999.
[2] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, \EGS4 Code System", SLAC, Stanford, CA
94309, SLAC Report 265, 1985.
[3] A. Fasso, A. Ferrari, J. Ranft, P. R. Sala, \FLUKA: present status and future developments",
Proc. IV Int. Conf. On Calorimetry in High Energy Physics, La Biodola, Italy, 21-26, Spetember
1993, Ed. A. Menzione and A. Scribano, World Scienti c, p.493.
[4] T. Omori, \A polarized positron beam for linear colliders", KEK preprint 98-237, March 1999.
[5] K. Flottmann, \Investigation toward <strong>the</strong> development <strong>of</strong> polarized and unpolarized high intensity
positron sources for linear colliders", Ph.D. <strong>the</strong>sis, DESY, Report DESY-93-161A, November
1993.
[6] A. P.Potylitsin, \Production <strong>of</strong> polarized positrons through interaction <strong>of</strong> longitudinally polarized
electrons with thin targets", NIM A398, p.395-398, 1997.
4

Table 1. Comparison <strong>of</strong> positron yields from W-Re targets hit by 30-MeV electron beam, calculated
between EGS4 and FLUKA99.
W-Re Target 0.1 MeV le E 30 MeV 20 MeV E 30 MeV
Thickness (mm) EGS4 FLUKA99 EGS4 FLUKA99
0.5 0.0035 0.0035 0.000056 (11%) 0.000088 (25%)
1.0 0.0099 0.010 0.00013 (7%) 0.00013 (17%)
2.0 0.023 0.024 0.00017 (6%) 0.00019 (3%)
5.0 0.026 0.029 0.00013 (7%) 0.00014 (3%)
Note: W-Re has 75% (by weight) tungsten and 25% rhenium and a density <strong>of</strong> 19.65 g cm ;3 .
Table 2. Comparison <strong>of</strong> positron yield and mean longitudinal polarization from calculations between
Omori and this work.
Positron Positron Yield Mean Polarization
Energy Omori This Work Omori This Work
E e + > 17 MeV 0.045 0.047 0.6 0.87
E e + > 27 MeV 0.022 0.024 0.8 0.93
Note: Positrons from backward-Compton scattered laser photons (maximum energy 60 MeV)
hitting a 1.5-mm-thick tungsten target.
Table 3. Comparison <strong>of</strong> positron yield and mean longitudinal polarization for positrons > 25 MeV
calculated between EGS4 and Potylitsin.
Beam Target Positron Yield Mean Polarization
EGS4 Potylitsin EGS4 Potylitsin
Electron W-Re 0.00048 0.002 0.84 0.6
Ti 0.00035 0.86
Photon W-Re 0.034 NA 0.88 NA
Note: 0.2-radiation-length target hit by monoenergetic 50-MeV, polarized beam.
5

Figure1.Comparison<strong>of</strong>energyspectra<strong>of</strong>positrons,calculatedbyEGS4andFLUKA99,emanating
from<strong>the</strong>downbeamside<strong>of</strong>W-Retargetshavingthicknesses<strong>of</strong>0.5,1,2and5mmforanincident
electronwith<strong>the</strong>kineticenergy<strong>of</strong>30MeV.
Figure2.EGS4-calculatedpositronyield(withinenergyrange<strong>of</strong>0.1–30MeV)asafunction<strong>of</strong>polar
angleemittedfrom<strong>the</strong>backplane<strong>of</strong>W-Retargetsatfourthicknesseshitby30-MeVelectronbeam.
6

Figure3.Energyspectra<strong>of</strong>positronsemanatingfromaW-ReorTitarget(0.2radiationlengththick)
struckbyalongitudinallypolarized,50MeVelectronbeam.Numbersinsideparen<strong>the</strong>sesare<strong>the</strong>yields
forpositronsabove25MeVperbeamparticle.
Figure4.Longitudinalpolarization<strong>of</strong>positronasafunction<strong>of</strong>positronenergy,relativetobeam
energy,from<strong>the</strong>W-ReandTitargetshitbyalongitudinallypolarizedelectronbeam.Numbers
insideparen<strong>the</strong>sesare<strong>the</strong>meanpolarizationforpositronsabove25MeV.
7

Figure5.Positronspectrumfrom<strong>the</strong>W-Retargethitbyalongitudinallypolarized,50-MeVphoton
beam.Numberis<strong>the</strong>yieldforpositronsabove25MeVperbeamparticle.
Figure6.Acomparison<strong>of</strong>longitudinalpolarization<strong>of</strong>positronsfrom<strong>the</strong>W-Retargethitbypolarized
electronandphotonbeams.Numbersinsideparen<strong>the</strong>sesare<strong>the</strong>meanpolarizationforpositronsabove
25MeV.
8

Figure7.Energy-angledistribution<strong>of</strong>positronsfrom<strong>the</strong>0.2-radiation-lengthW-Retargethitby<strong>the</strong>
50-MeVelectronbeam.
Figure8.Distribution<strong>of</strong>emissionangle<strong>of</strong>positronsfrom<strong>the</strong>W-Retargetstruckbyelectronand
photonbeams.
9

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.124-129
EGS4 Simulation <strong>of</strong> <strong>the</strong> Positron Converter
at <strong>the</strong> BEPC Linac-Based Slow Positron Beam
R. S. Yu, C. X. Ma, G. X. Pei, L. Wei, B. Y. Wang, and T. B. Chang
Institute <strong>of</strong> High Energy Physics, Academia Sinica
P.O. Box 918, Beijing, 100039, The Peoples Republic <strong>of</strong> China
Abstract
The Beijing Intense Slow Positron Beam is in <strong>the</strong> preparation stage <strong>of</strong> construction. This paper
describes <strong>the</strong> simulations by EGS4 code toward <strong>the</strong> positron converter and <strong>the</strong> radiation shield
problem. Results show that Beijing Electron-Positron Collider (BEPC) LINAC can produce slow
positrons in order <strong>of</strong> 10 6 ; 10 7 e + =s when running under parasitic mode and 10 8 ; 10 9 e + =s under
dedicated mode.
1 Introduction
In recent years, <strong>the</strong> interest in <strong>the</strong> use <strong>of</strong> slow positron beam as a probe for nuclear physics
and solid-state physics has greatly increased. Usually <strong>the</strong> slow positron beams are created by <strong>the</strong> reemission
<strong>of</strong> slow positrons from solid surfaces. Primary fast positrons are usually from a radioactive
source or from <strong>the</strong> target bombarded by a linear accelerator. The former type <strong>of</strong> facilities is <strong>of</strong>ten
used, but <strong>the</strong> slow positron intensity is restricted to 10 7 e + =s by <strong>the</strong> activity <strong>of</strong><strong>the</strong>available radioactive
source. The Linac-based positron source can enable an increase <strong>of</strong> <strong>the</strong> slow-positron intensity by more
than several orders <strong>of</strong> magnitude[1, 2, 3].
Utilizing <strong>the</strong> 1.55 GeV Linac <strong>of</strong> BEPC, we will start construction <strong>of</strong> an intense positron beam,
aiming to produce about 10 6 ;10 7 e + =s slow positrons when BEPC is running under conventional mode
(Mode I, 2.5 ns pulse width, 12.5 pulses/s repetition rate, 1000 mA peak current) and 10 8 ; 10 9 e + =s
slow positrons under dedicated operation mode (Mode II-in construction, 1.6 s pulse width, 50
pulses/s repetition rate, 50 mA peak current). As one <strong>of</strong> <strong>the</strong> most important parts to obtain <strong>the</strong>
slow positrons, <strong>the</strong> positron converter should be carefully designed[4, 5]. Since no simple relation
exists which correlates <strong>the</strong> converter thickness to <strong>the</strong> energy <strong>of</strong> <strong>the</strong> impinging electrons, we performed
Monte-Carlo simulations as a function <strong>of</strong> <strong>the</strong> electron energy and <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> converter to
obtain <strong>the</strong> optimum thickness <strong>of</strong> <strong>the</strong> converter. The angular spread and <strong>the</strong> energy distribution <strong>of</strong>
<strong>the</strong> outgoing positrons were studied. Detailed calculation about <strong>the</strong> <strong>the</strong>rmal power distribution as a
function <strong>of</strong> depth and radius <strong>of</strong> <strong>the</strong> converter was also performed. Some simulation results toward
radiation shield problem are also reviewed in this paper.
2 Simulation Results
The EGS4 code[6] was used on a Windows PC to perform <strong>the</strong> Monte-Carlo simulations. The
geometry <strong>of</strong> <strong>the</strong> converter and <strong>the</strong> radiation shield wall is presented in gure 1. We used tantalum
or tungsten as <strong>the</strong> converter material, which was considered being a cylindrical slab surrounded by
vacuum and bombarded by <strong>the</strong> electron with energy <strong>of</strong> 1.55 GeV. The electrons were considered at
normal incidence and a total <strong>of</strong> 10000 events were followed. The radiation shield wall is made up
<strong>of</strong> a 0.2 m thick square Fe plate and a 1.8 m thick square concrete wall, which isinstalled after <strong>the</strong>
1

target. The Monte-Carlo process was followed down to energy <strong>of</strong> 1.02 MeV for electrons, positrons
and photons, since <strong>the</strong>re will be no pair production occurring below this energy.
The thickness <strong>of</strong> <strong>the</strong> converter was varied between 10 mm and 35 mm for nding <strong>the</strong> optimal
thickness which representing <strong>the</strong> largest fast positron yield. The relationship between <strong>the</strong> fast positron
yield and <strong>the</strong> target thickness is shown in gure 2. This gure shows that <strong>the</strong> optimal thickness is equal
to 18 mm and <strong>the</strong> converting e ciency from <strong>the</strong> incident electrons to fast positrons equals to about
9.5% for both tantalum and tungsten materials. If <strong>the</strong> moderation e ciency <strong>of</strong> <strong>the</strong> positron moderator
located behind <strong>the</strong> converter equals to 10 ;4 ,<strong>the</strong>slow positron yield will equal to 10 6 ; 10 7 e + =s when
<strong>the</strong> BEPC LINAC is running under mode I and 10 8 ; 10 9 e + =s under mode II. Figure 3 gives <strong>the</strong>
angular dependence <strong>of</strong> <strong>the</strong> outgoing fast positrons. One can see that <strong>the</strong> fast positrons are peaked in
<strong>the</strong> forward direction. The number <strong>of</strong> fast positrons as function <strong>of</strong> <strong>the</strong> emitting angle decreases very
fast. This means that <strong>the</strong> positron moderator has to be placed as close as possible to <strong>the</strong> positron
converter in order to moderate as much as possible fast positrons.
Figure 4 shows <strong>the</strong> energy spectrum <strong>of</strong> <strong>the</strong> fast positrons out <strong>of</strong> <strong>the</strong> 18 mm thick tantalum converter,
it has a steep decrease towards lower energies and a long tail towards higher energies. The spectrum
is peaked below 10 MeV and <strong>the</strong>re is a small shift for <strong>the</strong> number <strong>of</strong> positrons between 5 MeV and 10
MeV.
The <strong>the</strong>rmal power distributions as a function <strong>of</strong> <strong>the</strong> injection depth and radius <strong>of</strong> <strong>the</strong> converter
are shown in gure 5 and gure 6, respectively. For <strong>the</strong> pencil beam <strong>of</strong> electrons, <strong>the</strong> e ective radius
near showrr maximun is about 0.5 mm. The temperature rises <strong>of</strong> tungsten target during <strong>the</strong> e ective
radius accompanying one beam pulse is approximately
T =
1
C P
a 2
dQ 1
dzdt v =290C Where
( )= <strong>the</strong> density (( =19:25g=cm 3 ) for tungsten)
(C P )=<strong>the</strong> speci c heat (0.138 J/g ( C) for tungsten)
a=<strong>the</strong> radius <strong>of</strong> energy deposition (0.5 mm)
dQ/(dzdt)=<strong>the</strong> rate <strong>of</strong> heat deposition
( ) =<strong>the</strong> accelerator repetition rate (12.5 pulses/sec)
So, a water-cooled converter, with a water ow <strong>of</strong> at least 4 (cm 3 =s), is crucially required for heat
transferring.
Since <strong>the</strong> electrons are accelerated to an extreme high energy by <strong>the</strong> LINAC, <strong>the</strong> radiation shield
around <strong>the</strong> target is ano<strong>the</strong>r critical technical problem. Simulation results by EGS4 showed that
when <strong>the</strong> length <strong>of</strong> <strong>the</strong> square side <strong>of</strong> <strong>the</strong> Fe plate and <strong>the</strong> concrete wall both equal to 1 m, <strong>the</strong>
energy deposited in <strong>the</strong> tantalum slab, Fe plate and <strong>the</strong> concrete wall shares 31.2%, 45.7% and 11.2%,
respectively. The energy deposited in <strong>the</strong> outer region (region 3 in g.1) between <strong>the</strong> target and <strong>the</strong>
shield wall shares about 11.9%. Total energy deposited outside <strong>of</strong> <strong>the</strong> concrete wall (region 6 in g.1)
equals to (1:067 10 ;7 ) kW when <strong>the</strong> LINAC is running under Mode I, which has been supplying a
safe operation environment.
3 Conclusion
Detailed simulations toward <strong>the</strong> converter on <strong>the</strong> Beijing intense slow positron beam were performed.
It has been shown that a realistic number <strong>of</strong> (10 6 ; 10 7 e + =s) slow positrons when BEPC
LINAC is running under parasitic mode and (10 8 ; 10 9 e + =s) slow positrons under dedicated mode
can be produced. Meanwhile, experiment using a real target to con rm <strong>the</strong> feasibility and test <strong>the</strong>
validity <strong>of</strong> <strong>the</strong> above simulations is <strong>the</strong> future work.
2

Acknowledgements
This work is supported by <strong>the</strong> National Natural Science Foundation <strong>of</strong> China under grant
No.19927001 and <strong>the</strong> Key-project <strong>of</strong> Chinese Academy <strong>of</strong> Sciences under grant No. KJ952-S1-416.
We arevery appreciated to Pr<strong>of</strong>. Hirayama for his kindly help about <strong>the</strong> EGS code, and o<strong>the</strong>r useful
information. R. S. Yu acknowledge KEK for nancial support. L.Wei would like tothank to Dr. T.
Kurihara for useful discussions.
References
[1] R. Ley, Materials Science Forum.105-110,1927-1930(1992).
[2] T. Akahae, T. Chiba, N. Shiotani et al., Appl.Phys. A 51(1990)146-150.
[3] T. Kurihara, A. Shirakawa, A. Enomoto, et al., Applied Surface Science 85(1994)178-181.
[4] S. Okada and H. Sunaga, Nucl. Instr. and Meth. B 56/57(1991)604-609.
[5] S. Okada and H. Kaneko, Proceeding <strong>of</strong> <strong>the</strong> First <strong>International</strong> <strong>Workshop</strong> on EGS4, KEK,
Tsukuba, Japan, 302-309(1997).
[6] W. R. Nelson, H. Hirayama and D. W. O. Roger, \The EG4 Code System", SLAC-265. Stanford
Linear Accelerator Center(1985).
3

1
Vacuum
Electron
Beam
2
Target
3
Vacuum
4
Feplate
5
concretewall
6
Vacuum
Figure 1: Simulation geometry <strong>of</strong> <strong>the</strong> converter and <strong>the</strong> radiation shield wall.
PositronYield(CPS)
210 10
1.810 10
1.610 10
1.410 10
1.210 10
110 10
810 9
610 9
TaConverter
Wconverter
10 15 20 25 30 35 40
Angular(degree)
Figure 2: Relationship between <strong>the</strong> fast positron yield and <strong>the</strong> target thickness.
4

Number<strong>of</strong>Positrons
200
180
160
140
120
100
80
60
40
20
0
0 20 40 60 80 100 120 140
Angular(degree)
Figure 3: Angular dependence <strong>of</strong> <strong>the</strong> outgoing fast positrons.
Number<strong>of</strong>Positrons
250
200
150
100
50
0
0 10 20 30 40 50 60 70 80
PositronEnergy(MeV)
Figure 4: Energy spectrum <strong>of</strong> <strong>the</strong> fast positrons out <strong>of</strong> <strong>the</strong> 18 mm thick converter.
5

EnergyDeposition(W)
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 0.5 1 1.5 2 2.5
BulkConverterLength(cm)
Figure 5: Thermal power distributions as a function <strong>of</strong> <strong>the</strong> injection depth.
EnergyDeposited(W)
16
14
12
10
8
6
4
2
0
0 1 2 3 4 5 6
RadialDistancefrom<strong>the</strong>center<strong>of</strong>tantalumtarget(mm)
Figure 6: Thermal power distributions as a function <strong>of</strong> <strong>the</strong> radial distance.
6

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.130-134
Measurements <strong>of</strong> Photoneutron Spectra
from Thick Pb Target Bombarded by 1.2 and 2.0 GeV Electrons
S. Ban, Y. Namito, H. Hirayama, N. Terunuma, J. Urakawa
T. Sato 1 , R. Yuasa 1 , K. Shin 1 , H. S. Lee 2 and J .S. Bak 2
High Energy Accelerator Research Organization (KEK),
Oho, Tsukuba, Ibaraki, 305-0801, Japan
1 Department <strong>of</strong> Nuclear Engineering, Kyoto University,
Yoshida, Sakyo-ku, Kyoto 606-8501, Japan
2 Pohang Accelerator Laboratory, POSTECH, Nam-gu, Pohang, 790-784, Korea
Abstract
Photoneutron spectra were measured using <strong>the</strong> TOF method when thick targets were bombarded
by high-energy electrons. At <strong>the</strong> ATF Linac in KEK, 1.2 GeV electrons bombarded a thick Pb
target. At <strong>the</strong> injection Linac <strong>of</strong> <strong>the</strong> Pohang Accelerator Laboratory, 2.04 GeV electrons were used.
The detector was 5.6 m distant from <strong>the</strong> target. Several detectors were tested. Neutrons toward
90 degrees from <strong>the</strong> target were measured up to 150 MeV at <strong>the</strong> ATF, and 200 MeV at PAL.
Calculations <strong>of</strong> neutron energy spectra were also done using PICA3 and EGS4.
1 Introduction
There are only a few measurements <strong>of</strong> photoneutron energy spectra from thick targets <strong>of</strong> highenergy
electrons. The highest energy <strong>of</strong> those experiments was 0.27 GeV [1], and <strong>the</strong> long ight
path, 25-m, was needed in <strong>the</strong> TOF measurements because <strong>of</strong> <strong>the</strong> strong background <strong>of</strong> electrons and
photons.
We started <strong>the</strong> measurements[2] in Jan. 1996 at <strong>the</strong> Accelerator Test Facility (ATF) in KEK.
The 1 GeV electrons hit 2cm-thick Pb targets. Several detectors were tested. The plastic scintillator
with Pb collimator was calibrated using quasi-monoenergetic neutron sources between 5 and 132 MeV.
Neutrons toward 90 degrees were measured by <strong>the</strong> TOF method at <strong>the</strong> ATF. Because <strong>the</strong> shielding
concrete around <strong>the</strong> target was not thick enough, <strong>the</strong> background was large in <strong>the</strong> measurements. At
<strong>the</strong> Linac <strong>of</strong> <strong>the</strong> Pohang Accelerator Laboratory (PAL) in POSTECH, 2.04 GeV electrons were used
and <strong>the</strong> target was placed in well shielded beam dump room. Neutron spectra up to 200 MeV were
measured at PAL[3,4].
2 Experiments using 1.2 GeV electrons at <strong>the</strong> ATF in KEK
At <strong>the</strong> Linac <strong>of</strong> <strong>the</strong> ATF in KEK, <strong>the</strong> 1-m-thick overhead concrete shields were drilled and a
16cm-diameter collimator was placed. The liquid scintillator, 5"Diam.x5" BC501A, was placed at
<strong>the</strong> exit <strong>of</strong> <strong>the</strong> collimator because <strong>the</strong> neutron detection e ciency <strong>of</strong> <strong>the</strong> BC501A detector was well
known. But <strong>the</strong> dead time <strong>of</strong> <strong>the</strong> detector was long after <strong>the</strong> strong pulsed X-rays. Next, 5"-diam.x1"
NE102A plastic scintillator was used to reduce <strong>the</strong> dead time. The situation became better. Because
<strong>the</strong> overhead concrete shield <strong>of</strong> <strong>the</strong> ATF is only 1-m thick, additional Pb collimator was needed
surrounding <strong>the</strong> detector, and its shape was not suitable to place in <strong>the</strong> collimator.
1

Finally 51mm-diam.x49mm-long PILOT-U (BC418) scintillator was used. It was surrounded by
<strong>the</strong> 40-cm long Pb collimator. The e ciency <strong>of</strong> <strong>the</strong> detector without <strong>the</strong> collimator was calculated by
SCINFUL and Cecil's code. The collimator a ected <strong>the</strong> neutron detection e ciency. It was calibrated
using quasi-monoenergetic neutron sources, 132, 86.5 and 66 MeV at RRC in RIKEN, 64.7MeV at
TIARA in JAERI, 33.0 MeV at CYRIC in Tohoku Univ., and 14.9 MeV at OKTAVIAN in Osaka
Univ., 5 MeV at <strong>the</strong> FNL in Tohoku Univ. It was found <strong>the</strong> e ciency was not a ected by <strong>the</strong> collimator
when <strong>the</strong> pulse height discrimination level <strong>of</strong> <strong>the</strong> detector was high. But <strong>the</strong> discrimination level was
low, 1.1 MeVee, at <strong>the</strong> ATF, and measured detection e ciency was used.
The experimental setup at <strong>the</strong> ATF is shown in Fig.1. The detector in Pb collimator was placed on
<strong>the</strong> top <strong>of</strong> <strong>the</strong> tower 2.5 m high. The detector was 5.6 m distant from <strong>the</strong> target. To suppress X-rays,
several thicknesses <strong>of</strong> Pb blocks were placed in <strong>the</strong> middle point <strong>of</strong> <strong>the</strong> ight path between <strong>the</strong> target
and detector. Some neutrons were scattered in <strong>the</strong>se Pb blocks, and <strong>the</strong>se e ects were evaluated using
LAHET 2.7[6]. The beam frequency was 6 Hz and <strong>the</strong> pulse width was 0.02 ns, and <strong>the</strong> rf timing
signal was used for <strong>the</strong> start signal. The TOF spectra were measured using 2 GHz multi-channel
scaler. Preliminary results are shown in Fig.2 when 1.2 GeV electrons hit 5x5cm-wide and 2cm-thick
Pb target placed in <strong>the</strong> vacuum chamber in <strong>the</strong> Linac tunnel. The 15-cm-thick Pb blocks were placed
on <strong>the</strong> ight path. The bar in Fig.2 shows only counting statistical errors. The beam intensity was
reduced to minimize <strong>the</strong> dead time and was approximately 50 pC/pulse. This was far from <strong>the</strong> normal
operation condition <strong>of</strong> <strong>the</strong> Linac, and <strong>the</strong> beam status was not accurately known. Background was
estimated from <strong>the</strong> measurements using 35-cm-thick Fe and 20-cm-thick Pb. Neutrons up to 150 MeV
were measured at <strong>the</strong> ATF.
Calculations <strong>of</strong> neutron energy spectra were also done. Photon track length in <strong>the</strong> target was
calculated using EGS4. Photo-nuclear cross sections were evaluated using PICA3 code[5]. Transport
<strong>of</strong> secondary neutron and pion etc. was calculated by LAHET 2.7[6]. The calculated results are shown
in Fig.2. Though <strong>the</strong> measured results were not accurate due to large background and uncertainty
<strong>of</strong> <strong>the</strong> detection e ciency and <strong>the</strong> beam condition <strong>of</strong> <strong>the</strong> Linac, calculated results were smaller than
measured ones.
3 Experiments using 2 GeV electrons at PAL
In 1998, <strong>the</strong> TOF beam line was newly constructed at PAL. The ight path length was <strong>the</strong> same
as that in <strong>the</strong> ATF, and was 5.6 m. But <strong>the</strong> overhead shielding concrete was 2.2m thick. So <strong>the</strong>
background was reduced. The experimental setup at PAL[3,4] is shown in Fig.3. The discrimination
level <strong>of</strong> <strong>the</strong> detector was 4.2 MeVee. The collimator did not a ect <strong>the</strong> detection e ciency and <strong>the</strong> dead
time <strong>of</strong> <strong>the</strong> counter after <strong>the</strong> pulsed X-rays became smaller. The results are shown in Fig.4 when 2.04
GeV electrons hit 5x5cm-wide and 5.5cm-thick (10-radiation-length) Pb targets. The beam frequency
was 10 Hz and <strong>the</strong> pulse width was about 1 ns. The start signal was given from a beam-current
monitor. The beam intensity <strong>of</strong> each pulse was about 500pC, and higher than that at <strong>the</strong> ATF. So
thicker Pb blocks, 15-30 cm, were placed in <strong>the</strong> middle <strong>of</strong> <strong>the</strong> ight path to suppress X-rays. These Pb
blocks also reduced neutrons toward <strong>the</strong> detector, and this e ect was evaluated using LAHET 2.7[6].
Even in such a case, <strong>the</strong> background neutrons and photons were small because <strong>the</strong> target was well
shielded except <strong>the</strong> ight path.
4 Summary
We started <strong>the</strong> measurements <strong>of</strong> photo-neutron spectra toward 90 degrees from thick targets <strong>of</strong>
1.2 and 2 GeV electrons. Neutrons between 10 and 200 MeV were measured. The experimental setup
was smaller compared to <strong>the</strong> previous one at 0.3 GeV[1].
The neutron spectra were calculated using EGS4/PICA3[5]/LAHET2.7[6]. Calculated ones tend
to underestimate <strong>the</strong> measured ones. More experimental data were needed for di erent angles and
energy range.
2

Acknowledgments
The authors wish to thank to <strong>the</strong> operating crews <strong>of</strong> <strong>the</strong> ATF in KEK. We are also thankful to <strong>the</strong>
stu <strong>of</strong> <strong>the</strong> Linac in PAL. We wish to thank S. Tanaka(JAERI), Y. Uwamino(RIKEN), T. Nakamura,
M. Baba(Tohoku Univ.), I. Murata(Osaka Univ.), H. Nakamura, N. Nakao, K. Omata(KEK) and
S. Rokni(SLAC).
References
[1] H. J. von Eyss, and G. Luhrs, Z. Phys. 262(1973)393.
[2] K. Shin, T. Sato, S. Ban, H. Nakamura, Y. Namito, H. Hirayama and S. Rokni, \Measurement
<strong>of</strong> photo-neutron yield from thick lead target bombarded by 1.2 GeV electrons", Proc. 7th EGS4
users meeting in Japan, KEK <strong>Proceedings</strong> 98-7 (1998).
[3] T. Sato, K. Shin, R. Yuasa, S. Ban, H. S. Lee, \Measurement <strong>of</strong> <strong>the</strong> Neutron Spectrum by <strong>the</strong>
Irradiation <strong>of</strong> a 2.04-GeV Electron Beam into Thick Targets", to be published to Nucl. Instrum.
Meth. A (KEK Preprint 2000-109).
[4] H. S. Lee, S. Ban, T. Sato, K. Shin, J. S. Bak, C. Chung, and H. D. Choi, \Photoneutron Spectra
from Thin Targets Bombarded with 2.0 GeV Electrons", J. Nucl. Sci. Tech., Suppl. 1(2000)207-
211.
[5] R. E. Prael and H. Lichtenstein, \User's Guide to LCS: The LAHET Code System", LA-UR-89-
3014 (1989).
[6] T. Sato, K. Shin, S. Ban, T. A. Gabriel, C. Y. Fu and H. S. Lee, \PICA3, An Updated code
<strong>of</strong> Photo-Nuclear Cascade Evaporation Code PICA95, and its Benchmark Experiments", Proc.
Int. Conf. on Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and
Applications (MC2000), 23-26 Oct. 2000, Lisbon, Portugal.
3

Figure 1: Experimental setup at <strong>the</strong> ATF when 1.2 GeV electrons irradiated 2-cm-thick Pb target.
Neutron/MeV/Sr/e
1.E-04
1.E-05
1.E-06
1.E-07
0 20 40 60 80 100 120 140 160 180 200
NeutronEnergy(MeV)
Figure 2: Preliminary results <strong>of</strong> neutron spectra toward 90 degrees from 2-cm-thick Pb target irradiated by 1.2
GeV electrons. Full circle: Measured at <strong>the</strong> ATF. Open circle : Calculated using EGS4/PICA3[5]/LAHET2.7[6].
4

PbCollimator
(10cmthickcylinder
on5cmthickbase)
Concrete
ShadowBar
PbAttenuator
Concrete
Collimator
(D=15.8cm)
PbCollimator
(30x30x10(T)cm)
e -
BeamPr<strong>of</strong>ile
Monitor
n
560cm
195cm
60cm
320cm
220cm
Figure 3: Experimental setup at PAL when 2.04 GeV electrons irradiated Pb targets[3,4].
Neutron/Sr/MeV/Electron
0.001
0.0001
10 -5
10 -6
10 -7
50cm
0 50 100 150 200
NeutronEnergy(MeV)
Figure 4: Measured neutron spectra toward 90 degrees from 5.5-cm-thick Pbtargets irradiated by 2.04 GeV
electrons.
5

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.135-143
Response Calculations <strong>of</strong> <strong>the</strong> CdZnTe Detector Using EGS4 1
J. C. Liu, W. R. Nelson and R. Seefred
Stanford Linear Accelerator Center,
MS 48, P. O. Box 4349, Stanford, CA 94309, USA
Abstract
The spectral response <strong>of</strong> a CdZnTe semiconductor detector has been calculated with <strong>the</strong> EGS4
Code System. The latest low-energy photon production and transport routines developed at KEK,
which consider <strong>the</strong> KandL shell uorescent photon production in compounds, bound Compton
scattering, Doppler broadening, etc., were included in <strong>the</strong> EGS4 code. The calculations <strong>of</strong> <strong>the</strong>
CdZnTe detector also took into account <strong>the</strong> collection e ciency <strong>of</strong> <strong>the</strong> produced electron-hole pairs
(described by Hecht equation) and <strong>the</strong> modi cation on spectral peaks due to both <strong>the</strong> Fano factor
and electronic-noise broadening. The calculated results are compared with measurements made
with encapsulated 241 Am and 137 Cs disk sources. It was found that, by trying various mobilitylifetime
values for holes, <strong>the</strong> calculated spectral response still did not have perfect agreement with
measurements.
1 Introduction
In a previous study[1], <strong>the</strong> EGS4 Code System[2] was used to calculate <strong>the</strong> spectral response
for a CdZnTe detector (called CZT hereafter) that was used to measure <strong>the</strong> synchrotron radiation
leakage spectra in a PEP-II accelerator radiation environment. In that paper, minor disagreements
were found when <strong>the</strong> EGS4-calculated photon spectra were compared with measurements made using
encapsulated 241 Am, 133 Ba and 109 Cd disk sources.
In <strong>the</strong> previous study, <strong>the</strong> following processes were standard with EGS4: photoelectric e ect
(with angular sampling from <strong>the</strong> Sauter formula), coherent (Rayleigh) and Compton scattering (unbound),
discrete Moller and Bhabha interactions, positron annihilation (in- ight and at-rest), continuous
energy loss, Moliere multiple scattering applied to charged-particle tracks, and pair production/bremsstrahlung
(with angular sampling). In addition to <strong>the</strong>se processes, <strong>the</strong> simulations also
speci cally took into account:
1. production <strong>of</strong> K-shell uorescence from a CZT mixture, using an improvement to a method
developed for EGS4 by Del Guerra et al[3],
2. collection <strong>of</strong> electron-hole pairs (<strong>the</strong> signal) using <strong>the</strong> Hecht equation[4],
3. narrowing <strong>of</strong> <strong>the</strong> signal by considering Fano factor and broadening <strong>of</strong> <strong>the</strong> signal due to electronicnoise.
Recently Hirayama and Namito at KEK have developed routines to treat low-energy photon production
and transport in materials[5, 6]. The routines mainly consider bound Compton scattering,
Doppler broadening, and <strong>the</strong> K and L shell uorescent photon production in elements, as well as in
compounds. Therefore, in this study we incorporated <strong>the</strong> KEK routines into <strong>the</strong> EGS4 Code System
in order to compare with <strong>the</strong> previous study. In addition, to fur<strong>the</strong>r resolve <strong>the</strong> above-mentioned
1 Work supported by <strong>the</strong> US Department <strong>of</strong> Energy under contract DE-AC-03-76SF00515
1

discrepancy between EGS4 calculations and measurements, this time we have studied in depth <strong>the</strong>
calculation algorithm <strong>of</strong> spectral response, particularly by using various mobility-lifetime values in <strong>the</strong>
Hecht equation. Additional photon spectra measurements using 241 Am and 137 Cs disk sources were
also made to compare with EGS4 calculations.
2 EGS4 Calculations
2.1 Detector Material and Energy Cuto s
The CZT detector was made by eV Products, Inc. (model eV-180-3-3-2-S 375 Saxon Blvd.,
Saxonburg, PA 16056, USA). The CZT material data was created with <strong>the</strong> MIXT option <strong>of</strong> PEGS4
using a density <strong>of</strong> 5.86 g/cm 3 and RHOZ values <strong>of</strong> 50.58, 3.27 and 63.80 for Cd, Zn and Te, respectively
(corresponding to atomic percentages <strong>of</strong> 45, 5 and 50%). The PEGS4 energy limits were chosen to be
(AP=0.001, UP=10.0) and (AE=0.521, UE=10.511) MeV for photons and electrons, respectively. In
addition to turning on <strong>the</strong> Rayleigh scattering option (IRAYL=1) and <strong>the</strong> option <strong>of</strong> radiative stopping
powers compliant with ICRU-37 (IAPRIM=1), all <strong>the</strong> KEK low-energy photon options (IXRAY=1,
IBOUND=1, INCOH=1, ICPROF=-3, IMPACT=1) were turned on.
The photon transport cuto PCUT was set at 0.001 MeV. The electron cuto energy ECUT
was set at 1.511 MeV, forcing <strong>the</strong> kinetic energy <strong>of</strong> <strong>the</strong> electrons to be deposited at <strong>the</strong>ir points <strong>of</strong>
creation, except for 137 Cs (ECUT was <strong>the</strong>n 0.561 MeV). The rationalization for doing this is based on
<strong>the</strong> fact that <strong>the</strong> ranges <strong>of</strong> secondary electrons from all radioisotopic source photons (except 137 Cs) in
CZT are much smaller than <strong>the</strong> dimensions <strong>of</strong> <strong>the</strong> CZT crystal. In any case, acheck was made with
ECUT=AE=0.521 MeV (i.e., 10 keV kinetic energy) and <strong>the</strong> results were essentially <strong>the</strong> same as with
higher ECUT values. It was also found that <strong>the</strong> use <strong>of</strong> PRESTA[7] did not change <strong>the</strong> results.
2.2 Measurements and EGS4 Geometry
The measurement and <strong>the</strong> corresponding EGS4 geometry in this study (see Figure 1) were similar
to that in <strong>the</strong> previous study. X-ray photographs showed that <strong>the</strong> CZT crystal (3x3 mm 2 and 2 mm
thick), mounted inside a BNC-type connector, is 0.575 cm from <strong>the</strong> 0.25-mm-thick beryllium window
<strong>of</strong> CZT detector. An aluminum cylinder <strong>of</strong> 0.45 cm inner radius and 0.1 cm thickness surrounds <strong>the</strong>
crystal. Our EGS4 user code utilized a generalized cylinder/azimuthal plane/slab geometry package
(ucRTZ.mortran and ucRTZ.data), with <strong>the</strong> cylindrical radius <strong>of</strong> <strong>the</strong> CZT crystal chosen to be 0.17 cm
to provide an equivalent cross-sectional area <strong>of</strong> 9 mm 2 . The 241 Am or 137 Cs disk source was positioned
at 10 cm away from <strong>the</strong> beryllium window. The radiation sources were sealed in plastic discs, 25 mm
in diameter and 5 mm thick (<strong>the</strong> source was actually about 1 mm deep).
The input gamma and X-ray energies, and <strong>the</strong>ir corresponding intensities, were taken from ICRP
Publication 38[8] for each <strong>of</strong> <strong>the</strong> three sources: 241 Am, 133 Ba and 109 Cd. A single energy <strong>of</strong> 662 keV
was used for 137 Cs source. Energy sampling was done by means <strong>of</strong> a simple cumulative distribution
table. Due to <strong>the</strong> large distance, a point source and a monodirectional photon beam toward <strong>the</strong> front
face <strong>of</strong> CZT detector were assumed in <strong>the</strong> calculations.
To reduce electronic noises, <strong>the</strong> BNC-CZT unit was attached directly to a matching connector
on an inverting low-noise, charge-sensitive preampli er (eV Products, model eV-550). A bias voltage
<strong>of</strong> +200 V (+400 V for 137 Cs) was supplied to <strong>the</strong> detector through <strong>the</strong> preampli er, with <strong>the</strong> front
surface <strong>of</strong> <strong>the</strong> crystal negatively biased in order to maximize <strong>the</strong> collection <strong>of</strong> holes. Output pulses
were processed with a pulse-shaping ampli er having a 0.5 sec shaping time and sent to a PC-based
multi-channel analyzer.
2.3 Scoring <strong>of</strong> Electron-Hole Pair Collection
Electron-hole pairs are created whenever energy is deposited in a semiconductor. The average
energy required to create an electron-hole pair is denoted as <strong>the</strong> W value (we used W = 4.6 eV for <strong>the</strong>
2

CdZnTe). The output pulse is proportional to <strong>the</strong> charge that is collected which, in turn, is controlled
primarily by <strong>the</strong> mobility-lifetime products, e e and h h (units: cm 2 /V), for electrons and holes,
respectively. The mobility <strong>of</strong>charge carriers in CdZnTe ismuch smaller than in Si and Ge detectors
and, thus, <strong>the</strong> charge carriers are easily trapped in <strong>the</strong> crystal while <strong>the</strong>y drift to <strong>the</strong> electrodes.
The charge-collection e ciency is de ned as <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> number <strong>of</strong> charge carriers collected
at <strong>the</strong> electrodes to <strong>the</strong> total number <strong>of</strong> carriers generated by <strong>the</strong> radiation energy deposition. If <strong>the</strong>
e ect <strong>of</strong> detrapping is neglected, <strong>the</strong> charge-collection e ciency (z) for charge carriers at depth z in
a semiconductor crystal <strong>of</strong> thickness d (cm) can be determined by means <strong>of</strong> <strong>the</strong> Hecht equation[4]:
(z) =( e=d)(1 ; e ;(d;z)= e) +( h=d)(1 ; e ;z= h ) (1)
where e = e eE and h = h hE are <strong>the</strong> mean free paths (units: cm) for electrons and holes,
respectively, z is <strong>the</strong> depth into <strong>the</strong> crystal from <strong>the</strong> negatively-biased (voltage V in volts) front
surface and E is <strong>the</strong> electric eld strength (E=V/d) in <strong>the</strong> detector.
Typical mobility-lifetime values we used in <strong>the</strong> Hecht equation were e e =7 10 ;3 cm 2 /V and
h h =5 10 ;5 cm 2 /V. With a high voltage <strong>of</strong> 200 V and a detector thickness <strong>of</strong> d = 0.2 cm, <strong>the</strong> e
is 7 cm and h is 0.05 cm. Therefore, it is clear that holes can be easily trapped particularly when
<strong>the</strong>y are produced at depths far away from <strong>the</strong> negatively-biased electrode.
Since <strong>the</strong> low-energy photons from 241 Am deposit energy primarily near <strong>the</strong> front face while <strong>the</strong>
662-keV photons <strong>of</strong> 137 Cs deposit energy uniformly along <strong>the</strong> depth, <strong>the</strong> charge collection e ect is
more pronounced for 137 Cs photons, which also makes it a better source to examine <strong>the</strong> e ect <strong>of</strong>
mobility-lifetime value.
2.4 Fano Factor and Electronic Noise Broadening
To compare <strong>the</strong> EGS4-calculated spectra with experimental results, <strong>the</strong> Fano factor and <strong>the</strong> peak
broadening due to electronic noise, etc. were also considered[9]. Namely, for each incident photon,
a running sum <strong>of</strong> <strong>the</strong> total number <strong>of</strong> electron-hole pairs that are created at <strong>the</strong> EDEP sites in <strong>the</strong>
detector is kept with each contribution multiplied by <strong>the</strong> corresponding charge-collection e ciency
determined by <strong>the</strong> Hecht equation. To be more speci c, we rst determine <strong>the</strong> charge collected
(unstraggled) per photon event N:
N = (z)E dep(z)=W (2)
where E dep(z) is <strong>the</strong> energy deposited at depth z from <strong>the</strong> front surface <strong>of</strong> <strong>the</strong> crystal. The total
standard deviation is <strong>the</strong>n determined from:
2 2 = fN + (3)
enc
where f is <strong>the</strong> Fano factor for CZT and enc is a standard deviation to account for <strong>the</strong> equivalent noise
charge <strong>of</strong> <strong>the</strong> electronics[9]. We used values for W, f and enc similar to those reported by Bencivelli
et al.[10] for Cd-Te f=0.14 and enc=150 e-h pairs.
Finally, <strong>the</strong> straggled (broadened) charge that is collected, N s, is statistically determined by sampling
from a Gaussian peak, centered about N with . The corresponding energy, Es=WN s, is <strong>the</strong>n
histogrammed for each incident photon event for comparison with experiment.
3 Results
Figure 2 shows that 241 Am spectra calculated using EGS4 with <strong>the</strong> latest KEK low-energy photon
production and transport routines and that with Nelson's approach for compounds (<strong>the</strong> previous study)
have perfect agreement for <strong>the</strong> major peaks above 10 keV. Similar comparisons for 133 Ba and 109 Cd
also gave good agreement. Hereafter throughout <strong>the</strong> paper <strong>the</strong> results will be those calculated using
<strong>the</strong> EGS4 with <strong>the</strong> KEK routines.
Figure 3 indicates that, as expected, <strong>the</strong> choice <strong>of</strong> di erent values for parameters W, Fano factor
f, and density <strong>of</strong> CdZnTe did not a ect <strong>the</strong> spectrum much.
3

The measured photon spectrum is shown in Figure 4 for 241 Am (+200 V and 0.5 s) and Figure
5for 137 Cs (+400 V and 0.5 s).
To illustrate our response calculation algorithm, Figure 6 shows <strong>the</strong> 241 Am photon spectrum at
di erent stages <strong>of</strong> CZT spectral response calculations. The top gure is <strong>the</strong> energy deposition spectrum,
<strong>the</strong> middle one is <strong>the</strong> spectrum taking into account <strong>the</strong>charge collection and peak modi cation
from Fano factor and electronic noise (but W value is not included yet), and <strong>the</strong> bottom one is <strong>the</strong>
nal photon spectrum with <strong>the</strong> W value included.
To examine <strong>the</strong> Hecht equation and its parameters, we rst studied <strong>the</strong> e ect <strong>of</strong> hole's mobilitylifetime
value. Figure 7 shows three 241 Am photon spectra calculated using three values <strong>of</strong> h h while
Figure 8 gives three corresponding 137 Cs photon spectra. After comparing <strong>the</strong>se calculated spectra
with <strong>the</strong> measurements in Figure 4 and 5, it is clear that a h h value <strong>of</strong> 5x10 ;5 cm 2 /V gave better
(not perfect yet) agreements for both cases <strong>of</strong> 241 Am and 137 Cs. The results using <strong>the</strong> o<strong>the</strong>r two
extreme values (3x10 ;4 and 7x10 ;6 ) are not correct. This seems to be consistent with <strong>the</strong> h h values
stated in [11,12].
Setting <strong>the</strong> h h value at 5x10 ;5 cm 2 /V, Figure 9 shows <strong>the</strong> 241 Am photon spectra calculated with
two di erent values <strong>of</strong> e e (1x10 ;3 and 7x10 ;3 cm 2 /V) and enc (150 and 200 e-h). A e e value <strong>of</strong>
7x10 ;3 seems to be correct and <strong>the</strong> value <strong>of</strong> 1x10 ;3 gave a wrong peak position result. The choice <strong>of</strong>
enc at 150 and 200 e-h does not a ect <strong>the</strong> results. Similar conclusions were obtained for <strong>the</strong> case <strong>of</strong>
137 Cs source.
4 Conclusions
In this study wehave used EGS4 to simulate <strong>the</strong> response <strong>of</strong> a CZT crystal, mounted within a BNC
connector, taking into account <strong>the</strong> incomplete collection <strong>of</strong> charge by means <strong>of</strong> <strong>the</strong> Hecht equation. We
have found perfect agreement for <strong>the</strong> calculated spectra between <strong>the</strong> EGS4 with <strong>the</strong> latest KEK lowenergy
photon routines and <strong>the</strong> standard EGS4 with Nelson's approach for compounds. This study has
also shown that all <strong>of</strong> <strong>the</strong> photo and escape peaks appear at <strong>the</strong> correct energies, but <strong>the</strong> peak widths
are not in perfect agreement with experiment. The most important parameter, mobility-lifetime for
hole h h, should be around 5x10 ;5 cm 2 /V, while <strong>the</strong> mobility-lifetime for electron e e, should be
about 7x10 ;3 cm 2 /V. The o<strong>the</strong>r parameters do not a ect <strong>the</strong> spectra as much as <strong>the</strong> mobility-lifetime
value. The remaining discrepancy may be due to that <strong>the</strong> Hecht model itself is too simple.
4

References
[1] W. R. Nelson, T. Borak, R. Malchow, W. Toki and J. Kadyk, \EGS4 calculations for a CdZnTe
detector to measure synchrotron radiation at PEP-II", <strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> First <strong>International</strong>
<strong>Workshop</strong> on EGS4, KEK, Tsukuba, Japan, August 26-29, 1997.
[2] W. R. Nelson, H. Hirayama and D. W. O. Rogers, \The EGS4 Code System", SLAC Report 265,
1985.
[3] A. Del Guerra, W. R. Nelson and P. Russo, \A simple method to introduce K-Edge sampling
for compounds in <strong>the</strong> code EGS4 for x-ray element analysis", Nucl. Instr. Meth. A306(1991)378,
[Erattum: Nucl. Instr. Meth. A359(1995)637].
[4] G. Baldazzi, D. Bollini, F. Casali, P. Chirco, A. Donati, W. Dusi, G. Landini, M. Rossi and
J. B. Stephen, \Timing response <strong>of</strong> CdTe detectors", Nucl. Instr. Meth. A326(1993)319.
[5] H. Hirayama and Y. Namito, \Implementation <strong>of</strong> a general treatment <strong>of</strong> photoelectric-related
phenomena for compounds or mixtures in EGS4", KEK Internal 2000-3, 2000.
[6] Y. Namito and H. Hirayama, \LSCAT: low-energy photon-scattering expansion for <strong>the</strong> EGS4
code (inclusion <strong>of</strong> electron impact ionization)", KEK Internal 2000-4, 2000.
[7] A. F. Bielajew and D. W. O. Rogers, \PRESTA: The Parameter Reduced Electron Step Transport
Algorithm for Electron Monte Carlo Transport", Nucl. Instr. Meth. B18(1987)165 also NRC-
PIRS-0042, 1986.
[8] Radioactive Transformations, Publication 38, <strong>International</strong> Commission <strong>of</strong> Radiological Protection,
Annals <strong>of</strong> <strong>the</strong> ICRP 11-13, 1983.
[9] W. R. Leo, Techniques for Nuclear and Particle Physics Experiments (Springer-Verlag, <strong>Second</strong>
Edition, 1994 see Chapter 10.
[10] W. Bencivelli, E. Bertolucci, U. Bottigli, A. Del Guerra, A. Messineo, W. R. Nelson, P. Randaccio,
V. Rosso, P. Russo and A. Stefanini, \Evaluation <strong>of</strong> elemental and compound semiconductors for
x-ray digital radiography", Nucl. Instr. Meth. A310(1991)210.
[11] H. Nishizawa, et al., \Calculation <strong>of</strong> CdTe semiconductor detector response", <strong>Proceedings</strong> <strong>of</strong> <strong>the</strong>
First <strong>International</strong> <strong>Workshop</strong> on EGS4, KEK, Tsukuba, Japan, August 26-29, 1997.
[12] G. A. Johansen and E. Abro, \A new CdZnTe detector system for low-energy gamma-ray measurement",
Sensors and Actuators A54(1996)493-498.
5

0.55
Imax = 3
0.45
2
I = 1
7-2000
8556A7
0.17
R
Plastic
0.1
Air
10.0
Be
Jmax = 1
0.025 0.2
Al
CZT
0.575 1.0
γ
0 0.1 10.0 10.025 10.6 10.8 11.8
K = 1 2 3 4 5 6
Kmax
Z
All Units in cm
241 137
Figure1.Irradiationgeometryfor<strong>the</strong>CdZnTedetectorusing Amand Csdisksources.
Events
10 7
10 6
10 5
10 4
10 3
10 2
7-2000
8556A1
KEK
Nelson
0 20
40
Energy (keV)
60 80
241
Figure 2. Comparison<strong>of</strong> Am spectra calculated withEGS4 using twodifferentschemes;<strong>the</strong>
latest KEK low-energy photon production and transport routines and Nelson’s approach for
compounds.
Events
120
7-2000
8556A4
80
40
0
Curve W(eV) Fano ρ(gm/cm 3 )
Dash 5.0 0.20 5.78
Solid 4.6 0.14 5.86
0 20 40
Energy (keV)
60
80
241
Figure3.Comparison<strong>of</strong> AmspectracalculatedwithEGS4(with<strong>the</strong>KEKlow-energyphoton
routines)usingdifferentvaluesforparameters<strong>of</strong>W,Fan<strong>of</strong>actorf,anddensityρ<strong>of</strong>CdZnTe.
6

Counts(Arb.)
241
Figure4. AmphotonspectrummeasuredusingCdZnTedetector(+200Vand0.5µs).
Fractional Counts
0.012
0.010
0.008
0.006
0.004
0.002
0.000
10 –1
10 –2
10 –3
10 –4
7-2000
8556A14
0 200 400
Photon Energy (keV)
137
Figure5. CsphotonspectrummeasuredusingCdZnTedetector(+400Vand0.5µs).
0 10 20 30 40 50 60 70
PhotonEnergy(keV)
7
600

Figure6.
Events
10 8
10 6
10 4
10 2
50M Cases
100 0 20 40 60 80
7-2000
8556A10
Energy (keV)
Events
10 7
10 6
10 5
10 4
10 3
102 0 2 4 6 8 10 12 14
Number <strong>of</strong> e–h Pairs (x103 7-2000
8556A9 )
Events
10 7
10 6
10 5
10 4
10 3
10 2
0 10 20 30 40 50 60 70 80
7-2000
8556A8 Energy (keV)
241 Amphotonspectrumatthreestages<strong>of</strong>CdZnTeresponsecalculation:energydepositionspectrum(top),
electron-holepairspectrum(middle),andphotonspectrum(bottom).
8

Events x 10 6
1.2
0.8
0.4
0
7-2000
8556A5
7 x 10 –6
5 x 10 –5
3 x 10 –4
0 20 40 60 80
Energy (keV)
241
Figure7. AmphotonspectrumcalculatedwithEGS4usingthreevalues<strong>of</strong>µhτh(unitsincm 2 /V).
Events
10 5
10 4
10 3
10 2
7-2000
8556A15
7x10 –6
5x10 –5
3x10 –4
0 200
400
Energy (keV)
600
137
Figure8. CsphotonspectrumcalculatedwithEGS4usingthreevalues<strong>of</strong>µhτh(unitsincm 2 /V).
Figure9.
Events (x10 4 )
120
80
40
7-2000
8556A16
µτe σenc
Curve (cm2 /V) (e–h)
Dash 1x10 –3
Solid 7x10
150
–3
200
0
0 20
40
Energy (keV)
60 80
241 AmphotonspectrumcalculatedwithEGS4usingdifferentvalues<strong>of</strong>µeτe andσenc.
9

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.144-151
Development <strong>of</strong> Gamma Ray Monitor
Using CdZnTe Semiconductor Detector
A. H. D. Rasolonjatovo, T. Shiomi, T. Nakamura, H. Nishizawa 1 ,
Y. Tsudaka 1 , H. Fujiwara 1 , H. Araki 1 , and K. Matsuo 1
Department <strong>of</strong> Quantum Science and Energy Engineering, Tohoku University
Aza-aoba, Amaraki, Aoba-ku, Sendai, Miyagi 980-8578, JAPAN
1 Mitsubishi Electric Corporation
8-1-1, Tsukaguchi-Honmachi, Amagasaki, Hyogo 661, JAPAN
Abstract
In this study, we aimed to develop a new X-ray and gamma ray monitor using <strong>the</strong> CdZnTe
semiconductor detector, whichhave high sensitivity at room temperature. The pulse height spectra
and <strong>the</strong> detection e ciencies <strong>of</strong> 10x10 mm 2 by 2 mm thick CdZnTe detector were measured in <strong>the</strong>
energy range <strong>of</strong> 10 keV to 1.8 MeV by using monoenergetic X-ray and gamma ray sources. The
measured results showed very good agreement with <strong>the</strong> results calculated using <strong>the</strong> EGS4 Monte
Carlo code taking into account <strong>the</strong> charge collection e ciency in <strong>the</strong> detector. By using two CZT
detectors <strong>of</strong> 10x10x2 mm 3 and 3x3x2 mm 3 coupled with a lter, <strong>the</strong> weighted sum <strong>of</strong> a few energy
channels with di erent cut-o energies was nally found out to realize a at energy response to
equivalent dose (counts per mSv) within 30% or 10% deviation.
1 Intoroduction
In recent years <strong>the</strong> CdZnTe (CZT) semiconductor detector is preferred for X-ray andlow energy
gamma ray detection in many situations, because <strong>of</strong> its high e ciency, low bias voltage, good energy
resolution and its capability <strong>of</strong> operation at room and higher temperatures[1, 2, 3]. The CZT detector
has a great advantage to have <strong>the</strong> high density ( =5:86 g cm ;3 ) and <strong>the</strong> high atomic number (Z=48
for Cd, 30 for Zn and 52 for Te) compared with Si ( =2.4 g cm ;3 , Z=14) and Ge ( =5.36 g cm ;3 ,
Z=32) semiconductor detectors. Nowadays a larger crystal size <strong>of</strong> CZT becomes available and <strong>the</strong> CZT
detector can be used for higher energy gamma ray detection. In this study, we aimed to develop a new
gamma ray monitor using a Cd0:5Zn0:5Te semiconductor detector. The present gamma ray monitor,
<strong>the</strong>refore, possesses higher sensitivity than <strong>the</strong> commercially available Si semiconductor gamma ray
monitor and at <strong>the</strong> same time has a at energy response to dose-equivalent in <strong>the</strong> wide photon energy
region from 10 keV to 7 MeV. This gamma ray monitor could be used to operate at higher temperature
such asin<strong>the</strong>power reactor core.
2 Materials and Methods
As a gamma ray sensor, a Cd0:5Zn0:5Te detector having 10 mm x 10 mm size by 2 mm thickness
(fabricated by eV Product, USA) was used. Table 1 shows <strong>the</strong> physical characteristics <strong>of</strong> <strong>the</strong> CZT
detector used in this study. The detector was directly coupled to <strong>the</strong> low noise preampli er (Model 850,
fabricated by Clear-Pulse Co. Ltd, Japan). The bias voltage <strong>of</strong> +24 V was supplied to <strong>the</strong> detector
from <strong>the</strong> regulated power supply (PR 36-1.2 A fabricated by Kenwood, Japan). The preampli er
was connected to a linear ampli er ORTEC 571 with a 2 s shaping time. The detector and <strong>the</strong>
preampli er were covered with an Al foil <strong>of</strong> 0.015 mm thickness to decrease <strong>the</strong> electromagnetic noise.
1

In order to get <strong>the</strong> energy response <strong>of</strong> <strong>the</strong> CZT detector, <strong>the</strong> measurements were done using <strong>the</strong>
mono-energetic X-ray beam sources from 10 to 40 keV and <strong>the</strong> radioactive photon sources <strong>of</strong> 241 Am,
57 Co, 137 Cs, 60 Co and 88 Yhaving photon energies <strong>of</strong> 59.54 keV to 1836 keV.
The experiments using X-ray beam sources were performed at a beam line <strong>of</strong> <strong>the</strong> Photon Factory
<strong>of</strong> High Energy Accelerator Research Organization (KEK), Tsukuba, Japan. Because a direct photon
beam intensity from <strong>the</strong> beam line <strong>of</strong> synchrotron radiation is too high, a beam scattered at 90 was
used. In order to investigate <strong>the</strong> variation <strong>of</strong> <strong>the</strong> energy response with <strong>the</strong> lters, we also measured
<strong>the</strong> pulse height distributions <strong>of</strong> <strong>the</strong> CZT detector covered with Al, Cu, Cd and Pb lters <strong>of</strong> various
thicknesses.
The measurements using point sources were carried out at <strong>the</strong> Hot Laboratory <strong>of</strong> <strong>the</strong> Cyclotron and
Radioisotope Center (CYRIC), Tohoku University, Japan. The point sources <strong>of</strong> about 2 mm diameter
are encapsulated within thin vinyl cover. The source was placed at 10 cm from <strong>the</strong> detector surface.
The fraction <strong>of</strong> backscattered photons was about 2%. In order to get <strong>the</strong> angular dependence <strong>of</strong> <strong>the</strong>
detection e ciency, <strong>the</strong> CZT detector was rotated to <strong>the</strong> source-to-detector axis in <strong>the</strong> directions <strong>of</strong> 0
to 90 . The 137 Cs source was covered with a 1.5 mm thick Al foil to absorb <strong>the</strong> 661.7 keV conversion
electrons from <strong>the</strong> electron capture reaction and <strong>the</strong> rays <strong>of</strong> 511 keV. The 60 Co was also covered
with a 1 mm thick Al foil to absorb <strong>the</strong> rays <strong>of</strong> 318 keV.
3 Calculations
The pulse height spectra <strong>of</strong> <strong>the</strong> detector were also calculated using <strong>the</strong> electron-photon cascade
Monte Carlo code EGS4[4] taking into account <strong>the</strong> carrier trapping e ect[5]. The charge collection
depends on <strong>the</strong> drift distance <strong>of</strong> <strong>the</strong> hole and <strong>the</strong> electron, which vary with <strong>the</strong> depth <strong>of</strong> interaction
in <strong>the</strong> detector.
For <strong>the</strong> CZT, <strong>the</strong> product <strong>of</strong> <strong>the</strong> mobility and lifetime , ( ), is very low, especially for holes
and <strong>the</strong>n most <strong>of</strong> <strong>the</strong> holes are trapped before reaching <strong>the</strong> cathode. The mean free path is given by
= F = V
where F is <strong>the</strong> electric eld, d is <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> detector and V is <strong>the</strong> applied voltage.
In <strong>the</strong> present case, we calculated <strong>the</strong> deposited energy E in <strong>the</strong> CZT detector for <strong>the</strong> geometry
that a plane parallel photon beam is incident normal to <strong>the</strong> detector surface using <strong>the</strong> EGS4-PRESTA
code[4], and taking into account <strong>the</strong> carrier trapping e ect. According to <strong>the</strong> work by Nishizawa et
al.[5], three cases were considered: energy absorption only, constant drifting distance <strong>of</strong> <strong>the</strong> carrier
and exponential distribution <strong>of</strong> <strong>the</strong> drifting distance <strong>of</strong> <strong>the</strong> carrier.
For <strong>the</strong> rst case where energy absorption only is considered, <strong>the</strong> induced charges are independent
to <strong>the</strong> interaction depth, <strong>the</strong>n
Q(x) =Q0 = E
d
(1)
" e (2)
" is <strong>the</strong> energy needed to create an electron-hole pair and is equal to 4.43 eV[6], E is <strong>the</strong> deposited
energy and e is <strong>the</strong> charge <strong>of</strong> <strong>the</strong> electron (e =1:6 10 ;19 C).
For <strong>the</strong> second case, <strong>the</strong> induced charges can be written as <strong>the</strong> rst-order approximation <strong>of</strong> <strong>the</strong>
Fetch's equation[7] as follows[5]
If e >d; x and h >x ;! Q(x) = E
" e
If e >d; x and h

If e x ;! Q(x) = E
" e
d
e
+ x
d
(3)
where x is <strong>the</strong> interaction depth, e, h are <strong>the</strong> mean free paths <strong>of</strong> <strong>the</strong> electron and hole, respectively.
Similarly for <strong>the</strong> third case, <strong>the</strong> equation <strong>of</strong> <strong>the</strong> induced charges is written as follows
is a random number between 0 and 1.
Q(x) =e
E "X
i=1
P e + P h
d
(4)
(5)
= (; ln ) (6)
If e >d; x and h >x ;! P e = d ; x P h = x
If e >d; x and h

oader than that <strong>of</strong> 14 keV. This is because <strong>the</strong> charge collection e ciency in <strong>the</strong> detector decreases
for low applied voltage <strong>of</strong> only +24V and also <strong>the</strong> energy loss through <strong>the</strong> Compton scattering increases
with increase <strong>of</strong> photon energy.
The energy responses <strong>of</strong> two photon energies <strong>of</strong> 1836 keV and 898 keV for 88 Y, were calculated
separately and added taking into account <strong>the</strong> branching ratio <strong>of</strong> each energy. For higher energy
photons from 137 Cs and 88 Y, <strong>the</strong> photopeak cannot clearly be seen because <strong>of</strong> energy loss dominated
by Compton scattering and a small fraction <strong>of</strong> energy deposition in 2 mm thick CZT detector. Then,
<strong>the</strong> measured spectra have monotonically decreasing shapes. The agreement between <strong>the</strong> measured
and calculated pulse height spectra for <strong>the</strong>se three photon sources is very good.
In this study, we used low biasvoltage <strong>of</strong> +24V sacri cing better energy resolution obtained with
higher bias voltage. Since our aim is to develop a gamma ray monitor <strong>of</strong> high sensitivity in this work,
<strong>the</strong> low bias voltage is preferred for reasons <strong>of</strong> portability. Generally speaking, <strong>the</strong> agreement between
<strong>the</strong> measured and <strong>the</strong> calculated pulse height spectra is good in absolute values over <strong>the</strong> wide energy
range <strong>of</strong> 10 keV (not shown here) up to 1836 keV.
4.2 Energy dependence <strong>of</strong> <strong>the</strong> detection e ciency
To get <strong>the</strong> detection e ciency, <strong>the</strong> measured and calculated pulse height spectra were rst summed
up above <strong>the</strong> cut-o energy xed at 6 keV. But for 241 Am <strong>the</strong> subsidiary peaks from K X-rays and <strong>the</strong>
26.4 keV gamma ray were not considered and <strong>the</strong> two peaks <strong>of</strong> 14 and 136 keV gamma rays <strong>of</strong> 57 Co
were also excluded from <strong>the</strong> measured results in <strong>the</strong> e ciency estimation. The counts thus-obtained
were normalized to unit photon uence incident on <strong>the</strong> detector to get counts per cm 2 . This value was
converted to countsperunitequivalent dose in mSv by using <strong>the</strong> uence-to-equivalent dose conversion
factor (mSv per cm ;2 ) for <strong>the</strong> A-P (anterior-posterior) geometry given by ICRP Publ.74[8]. We nally
obtained <strong>the</strong> detection e ciency in cps (count per second) per mSv/h from 10 keV to 1836 keV as
shown in Fig. 5.
For 60 Co gamma rays <strong>the</strong> measured result is 20% higher than <strong>the</strong> calculated result, while for
o<strong>the</strong>r photon energies <strong>the</strong> agreement between experiment and calculation is quite good within 3%.
The e ciency is high for 10 keV and ra<strong>the</strong>r at from 20 keV to 120 keV, and rapidly decreases with
energy. The high e ciency at 10 keV is due to <strong>the</strong> small value <strong>of</strong> <strong>the</strong> uence-to-equivalent dose
conversion factor.
4.3 Angular dependence <strong>of</strong> <strong>the</strong> detection e ciency
The angular dependence <strong>of</strong> <strong>the</strong> detection e ciency with 241 Am, 57 Co, 137 Cs, 60 Co and 88 Y photon
sources were also studied and we found a good agreement between experimental and calculated results
except for 60 Co with a standard deviation <strong>of</strong> about 20%. The angular dependence <strong>of</strong> <strong>the</strong> e ciency is
almost constant for 137 Cs, 60 Co and 88 Y in <strong>the</strong> directions <strong>of</strong> 0 to 90 , but for lower energy photons
<strong>of</strong> 241 Am and 57 Co, <strong>the</strong> e ciency decreases beyond 60 because <strong>of</strong> <strong>the</strong> self-absorption through <strong>the</strong>
thicker layer for slant incidence. These results revealed that this CZT detector has an almost isotropic
e ciency within 60 .
4.4 E ect <strong>of</strong> various lters
Figure 6 shows <strong>the</strong> variation <strong>of</strong> <strong>the</strong> e ciencies for 10, 20 and 40 keV X-rays with various thicknesses
(mm) <strong>of</strong> Al lter. Solid lines are <strong>the</strong> measured results and <strong>the</strong> dotted lines <strong>the</strong> calculated results. The
cut-o energy was also xed at 6 keV. The variation <strong>of</strong> <strong>the</strong> e ciency with Al lter thicknesses is
signi cant at10keV but is negligible at 40 keV. The agreement between measurement and calculation
is good.
4

5 Con guration <strong>of</strong> Flat Energy Response
By utilizing <strong>the</strong> results obtained, we tried to obtain at energy response to e ective dose <strong>of</strong>
<strong>the</strong> CZT semiconductor detector in <strong>the</strong> energy range <strong>of</strong> 10 keV to 7 MeV. This is an indispensable
characteristic for use as a gamma-ray monitor. As very good agreement between experiment and
calculation was obtained, we extend to obtain at energy response for higher energies up to 7 MeV by
calculation. Three parameters were considered for this realization:
size.
lters, cut-o energy and detector
The energy responses <strong>of</strong> <strong>the</strong> detector with di erent kinds <strong>of</strong> lter materials such as Al, Cu, Cd,
Fe and Pb with various thicknesses were calculated in <strong>the</strong> energy range from 10 keV to 7 MeV. Low
energy photons are very sensitive to lter material while high energy photons are almost insensitive
to any kind <strong>of</strong>
lters.
lters. We <strong>the</strong>refore found that it is ra<strong>the</strong>r di cult to get a at response only using
At <strong>the</strong> same time, we varied <strong>the</strong> cut-o energy <strong>of</strong> <strong>the</strong> pulse height spectra from 6 to 1500 keV.
For low energy below 100 keV, a at energy response <strong>of</strong> <strong>the</strong> detection e ciency can be obtained with
a cut-o energy around 6 keV but for higher energy, a cut-o energy higher than hundreds <strong>of</strong> keV is
necessary.
By combing <strong>the</strong>se above-mentioned results parametrically, we tried to get <strong>the</strong> at energy dependence
<strong>of</strong> <strong>the</strong> detection e ciency to equivalent dose in units <strong>of</strong> cps per mSv/h within 30% and 10%
di erences over a wide energy region <strong>of</strong> 10 keV to 7 MeV. After many parametric surveys on lters,
cut-o energies and detector sizes, we nally optimized to achieve <strong>the</strong> at detection e ciency to equivalent
dose, ", by using two sizes <strong>of</strong> <strong>the</strong> CZT detectors 3x3 mm2 by 2 mm thick CZT, and 10x10 mm2 by 2mm thick CZT as follows,
"(cps per Sv=h) = X
ai"1 + X
(9)
where "1 and "2 are <strong>the</strong> detection e ciencies <strong>of</strong> 3x3x2 mm 3 and 10x10x2 mm 3 CZT, respectively, and
a i and b i are multiplication factors. Fig. 7 and 8 show <strong>the</strong> results obtained by <strong>the</strong>above process using
Eq.(9).
6 Conclusion
In this study, <strong>the</strong> pulse height spectra and <strong>the</strong> detection e ciencies <strong>of</strong> <strong>the</strong> CZT detector <strong>of</strong> 10x10
mm 2 by 2 mm thickness are presented for 10 keV to 1.8 MeV photon energies from both experiment
and calculation using EGS4 code. The agreement between <strong>the</strong> experiment and <strong>the</strong> calculation is very
good in absolute values.
The variation <strong>of</strong> <strong>the</strong> detection e ciency with <strong>the</strong> cut-<strong>of</strong> energy and with various lters was also
obtained by calculation in <strong>the</strong> photon energy <strong>of</strong> 10 keV to 7 MeV. By using two CZT detectors, 10x10
mm 2 by 2 mm thick CZT with 1.2 mm Pb lter and 3x3 mm 2 by2mmthick CZT without lter, we
nally obtained <strong>the</strong> at energy response to e ective dose within 30% and 10% deviations in <strong>the</strong>
photon energy 15 keV to 7 MeV by taking <strong>the</strong> weighted sum <strong>of</strong> counts integrated above a few di erent
cut-o energies for <strong>the</strong> two CZT detectors. From <strong>the</strong>se results, it is evident that it is possible to
realize a gamma ray monitor <strong>of</strong> good quality having a at energy response to equivalent dose in a wide
photon energy range. Field measurements will be fur<strong>the</strong>r needed to compare with o<strong>the</strong>r commercially
available survey meters.
Acknowledgement
We are grateful to Pr<strong>of</strong>essors H. Hirayama and S. Ban, Drs. T. Kurosawa and Y. Namito for <strong>the</strong>ir
fruitful collaboration and advices during <strong>the</strong> calculation and experiment at KEK.
5
i
i
b i"2

References
[1] J. Franc, P. Haschl, E. Belas, R. Grill, P. Hledek, P. Moravec, J. Bok, \CdTe and CdZnTe crystals
for room temperature gamma-ray detectors", Nucl. Instrum. Methods A 434(1999)146-151.
[2] A. S. Zerrai, K. Cherkaoui, G. Marrakchi, G. Bremond, P. Fougeres, M. Hage-Ali, J. M. Koebel,
P. Si ert, \In uence <strong>of</strong> deep levels on CdZnTe nuclear detectors", Journal <strong>of</strong> Crystal Growth
197(1999)646-649.
[3] S. E. Pfantiel, K. J. H<strong>of</strong>stetter, T. A. DeVol, \Comparison <strong>of</strong> four types <strong>of</strong> gamma and X-ray
detectors for environmental applications in <strong>the</strong> 10-450 keV energy range", Journal <strong>of</strong> Radioanalytical
and Nuclear Chemistry 223 1-2(1997)89-98. for air, nitrogen at 30 keV", Appl. Radiat.
Isot. 44(1993)769-772.
[4] H. Hirayama, \Overview <strong>of</strong> <strong>the</strong> EGS4 Code System", KEK Internal 97-10, High Energy Accelerator
Research Organization, 1997, pp. 6-14.
[5] H. Nishizawa, K. Ikegami, K. Takashima, T. Usami, T. Hayakawa, T. Yamamoto, \Development
<strong>of</strong> Multi-layered CdTe Semiconductor Detectors", Ionizing Radiation Journal Vol.22,
No.3(1996)27-36.
[6] Y. X. Dardenne, T. F. Wang, A. D. Lavietes, G. J. Mauger, W. D. Ruhter, S. A. Kreek, \Cadmium
Zinc Telluride Spectral modeling", Nucl. Instrum. Methods A 422(1999)159-163.
[7] Y. Eisen, A. Shor, \CdTe and CdZnTe materials for room temperature X-ray and gamma ray
detectors", Journal <strong>of</strong> Crystal Growth 184/185(1998)1302-1312.
[8] <strong>International</strong> Commission on Radiological Protection, \ Conversion Coe cients for use in Radiological
Protection against External Radiation", ICRP Publication 74, Annals <strong>of</strong> <strong>the</strong> ICRP
Vol.26/3, 1995.
6

Table 1. Physical characteristics <strong>of</strong> <strong>the</strong> CZT detector
Size 10x10x2mm 3
Density 5.86 g cm ;3
Resistivity 3x10 10 cm
Band gap 1.56 eV
Mobility and lifetime product 3x10 ;3 cm 2 V ;1 for electron and 2x10 ;5 cm 2 V ;1 for hole
Depletion layer 2mm
Fig.1Comparison<strong>of</strong>measuredpulseheightspectrafor Fig.2Pulseheightspectra<strong>of</strong> 57 Cophotonsource
40keVX-rayswith<strong>the</strong>calculatedspectraforthreemodels
<strong>of</strong>chargecollection.Case1:Energyabsorptiononly;
case2:Constantdriftdistance<strong>of</strong>carriers;case3:The
driftdistance<strong>of</strong>carriershasanexponentialdistribution
Countsperunitincidentfluence
Countsperunitincidentfluence
0.016
0.012
0.008
0.004
1.E-03
1.E-04
1.E-05
0
0 200 400 600 800 1000 1200
Channel
Experiment
Case1
Case2
Case3
1.E-06
0 200 400 600 800 1000
Energy[keV]
Experiment
Calculation
1.E-05
0 50 100 150 200
Fig.3Pulseheightspectra<strong>of</strong> 137 Csphotonsource Fig.4Pulseheightspectra<strong>of</strong> 88 Yphotonsource
7
Countperunitincidentfluence
Countperunitincidentfluence
1.E-02
1.E-03
1.E-04
1.E-02
1.E-04
Energy[keV]
Experiment
Calculation
1.E-06
0 500 1000 1500 2000
Energy[keV]
Calculation
Experiment

Fig.5Measuredandcalculateddetectionefficiencies<strong>of</strong><strong>the</strong>
Fig.6Variation<strong>of</strong><strong>the</strong>detectionefficiencywith
CdZnTesemiconductordetectorasafunction<strong>of</strong>photonenergy aluminumfilterfor10to40keVphotons
Efficiency perequivalentdose
[cps/( Sv/h)]
10000
1000
100
10
1
1 10 100 1000 10000
µ
Energy [keV]
Experiment
Calculation
Efficiencyperequivalentdose
[cps/( Sv/h)]
10000
1000
100
0.1mm
0.2mm
0.5mm
No filter
10 0.8mm
Calculation
Experiment
1
1.0mm
0 5 10 15 20 25 30 35 40 45
Energy [keV]
µ
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.152-160
A Monte-Carlo Method
for Determining Absolute Scintillation-Photon Yields
and Energy Resolution <strong>of</strong> Scintillators for Gamma Rays
H. Tawara, S. Sasaki, K. Saito 1 , and E. Shibamura 2
High Energy Accelerator Research Organization
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
1 The Graduate University for Advanced Studies
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
2 College <strong>of</strong> Health Science, Saitama Prefectural University
820 Sannomiya, Koshigaya, Saitama 343-8250, Japan
Abstract
The gamma-ray spectra from NaI(Tl) scintillation detectors have been studied quantitatively
by a combination <strong>of</strong> experimental measurements and Monte-Carlo simulations. In this report,
we describe <strong>the</strong> full-energy peak for an isotropic point source <strong>of</strong> 662-keV gamma rays measured
with a NaI(Tl) crystal <strong>of</strong> 3-inch diameter by 3-inch long, as a typical case. We simulated three
di erent kinds <strong>of</strong> spectra generated as results from gamma-rayinteractions in NaI(Tl) and detection
processes <strong>of</strong> scintillation photons with a photocathode: (1) an energy-deposition spectrum, (2) a
scintillation-photon spectrum and (3) a photoelectron spectrum. The calculated photoelectron
spectra were compared with those from experiments. Using <strong>the</strong> present method, <strong>the</strong> W s value,
which is de ned as <strong>the</strong> mean energy required to produce one scintillation photon corresponding
to <strong>the</strong> full-energy deposition <strong>of</strong> <strong>the</strong> 662-keV gamma rays, was preliminary obtained to be 11.4 eV.
Under <strong>the</strong> present experimental condition, <strong>the</strong> total energy resolution <strong>of</strong> <strong>the</strong> full-energy peak can
be explained in terms <strong>of</strong> an intrinsic energy resolution caused by <strong>the</strong> non-linear energy response
<strong>of</strong> NaI(Tl) for electrons, <strong>the</strong> transfer variance <strong>of</strong> <strong>the</strong> scintillation-photon number in <strong>the</strong> detector
system, <strong>the</strong> photoelectron statistics and electric noise. These resolution losses were also estimated
quantitatively.
1 Introduction
Scintillation detectors are widely used for gamma-ray spectroscopy. However, <strong>the</strong> precise measurements
<strong>of</strong> absolute scintillation e ciency <strong>of</strong> various scintillators for gamma rays are di cult, because
<strong>the</strong> energy deposition due to gamma rays in <strong>the</strong> scintillators, and <strong>the</strong> transport and detection <strong>of</strong>
scintillation photons in a scintillation detector system are quite complicated processes to analyze
quantitatively.
Our study has two objectives: (1) to determine <strong>the</strong> mean energy required to produce one scintillation
photon (W s value) <strong>of</strong> various scintillators for radiation, and (2) a quantitative understanding <strong>of</strong>
<strong>the</strong> energy resolution <strong>of</strong> a scintillation detector system. In <strong>the</strong> present study, <strong>the</strong>W s value is de ned
for gamma-rays having monochromatic energy:
W s = T
N s
(eV) (1)
where T is <strong>the</strong> energy <strong>of</strong> incident gamma rays in eV and N s is <strong>the</strong> mean number <strong>of</strong> scintillation photons
produced in <strong>the</strong> scintillator by <strong>the</strong> full-energy deposition <strong>of</strong> <strong>the</strong> gamma rays. A detailed description
<strong>of</strong> <strong>the</strong> W s value for gamma rays is given elsewhere[1].
1

The method used in our study is a combination <strong>of</strong> experimental measurements and Monte-Carlo
simulations. Monte-Carlo simulations have been conducted with two computer codes, EGS4[2] and
SPC[1]. These codes have been improved continuously and now incorporate experimental and <strong>the</strong>oretical
data indispensable for analyzing <strong>of</strong> <strong>the</strong> gamma-ray spectrum measured by NaI(Tl) scintillation
detectors: generation <strong>of</strong> photoelectrons, characteristic X-rays and Auger electrons in K- and L-shell
photoelectric e ects <strong>of</strong> Na, I and Tl energy dependence <strong>of</strong> <strong>the</strong> scintillation response for electrons in an
energy region from 1 keV to 1 MeV <strong>the</strong> quantum e ciency <strong>of</strong> a photocathode, which is coupled with
<strong>the</strong> NaI(Tl) crystal, and its non-uniform distribution. These Monte-Carlo codes allow us to determine
<strong>the</strong> gross conversion e ciency <strong>of</strong> <strong>the</strong> NaI(Tl) scintillation detector system from scintillation photons
to photoelectrons. In addition, <strong>the</strong>y can be used to estimate <strong>the</strong> individual sources <strong>of</strong> <strong>the</strong> energy
resolution losses <strong>of</strong> <strong>the</strong> detector system.
In <strong>the</strong> following sections, we treat <strong>the</strong> gamma-ray spectrum, which is obtained by a NaI(Tl) crystal
(3 inch diameter 3 inch long) irradiated with an isotropic point gamma-ray source <strong>of</strong> 137 Cs. As a
preliminary result, we show <strong>the</strong> W s value corresponding to <strong>the</strong> 662-keV full-energy peak. In addition,
it is clari ed that <strong>the</strong> main sources <strong>of</strong> <strong>the</strong> energy resolution losses <strong>of</strong> <strong>the</strong> full-energy peak are <strong>the</strong>
intrinsic energy resolution, transfer variance, photoelectron statistics and electric noise, under <strong>the</strong>
present experimental conditions.
2 Method for analyzing <strong>the</strong> gamma-ray spectra
In <strong>the</strong> case <strong>of</strong> a scintillator exposed to gamma rays, <strong>the</strong> scintillation photons are generated
as a result from energy deposition due to secondary electrons, such as photoelectrons, Comptonrecoil
electrons and electron-positron pairs. When <strong>the</strong> scintillation response for electrons (electron response)
depends on electron energy, <strong>the</strong> gamma-ray spectrum expressed in scintillation-photon number
(scintillation-photon spectrum) becomes deformed from <strong>the</strong> original one, expressed in energy deposition
(energy-deposition spectrum). In general, this scintillation-photon spectrum cannot be observed
directly. When <strong>the</strong> scintillator is coupled with a photomultiplier (PMT), <strong>the</strong> scintillation photons are
converted into photoelectrons by <strong>the</strong> photocathode <strong>of</strong> <strong>the</strong> PMT. Therefore, <strong>the</strong> gamma-ray spectrum
can be observed as counts per unit photoelectron number (photoelectron spectrum).
The method for analyzing <strong>the</strong>se three kinds <strong>of</strong> gamma-ray spectra consists <strong>of</strong> three parts: (1)
Monte-Carlo simulations <strong>of</strong> gamma-ray interactions with scintillation materials and <strong>the</strong> generation <strong>of</strong>
scintillation photons, by <strong>the</strong> EGS4 code incorporating <strong>the</strong> electron response data <strong>of</strong> <strong>the</strong> scintillator
(2) Monte-Carlo simulations <strong>of</strong> Scintillation-Photon Transport (SPT) inside <strong>the</strong> scintillation detector
system and <strong>the</strong> generation <strong>of</strong> photoelectrons at <strong>the</strong> photocathode by <strong>the</strong> SPC code incorporating <strong>the</strong>
quantum-e ciency data <strong>of</strong> <strong>the</strong> photocathode and (3) experimental measurements <strong>of</strong> <strong>the</strong> absolute
number <strong>of</strong> photoelectrons emitted from <strong>the</strong> photocathode.
In <strong>the</strong> case <strong>of</strong> a scintillator coupled with a photomultiplier, <strong>the</strong> number <strong>of</strong> photoelectrons, N pe, is
described in terms <strong>of</strong> N s and four parameters,
N pe = N sF cQ eF sF g (2)
where F c is <strong>the</strong> collection e ciency <strong>of</strong> <strong>the</strong> detector system for scintillation photons to <strong>the</strong> photocathode,
Q e is <strong>the</strong> quantum e ciency <strong>of</strong> <strong>the</strong> photocathode, F s is <strong>the</strong> collection e ciency <strong>of</strong> a collection electrode
for <strong>the</strong> photoelectrons and F g is a total gain <strong>of</strong> a PMT. Thus, N s in eq.(1) can be estimated by
N s =
N pe
F cQ eF sF g
3 Experimental measurement <strong>of</strong> Npe
: (3)
Fig. 1 shows a schematic diagram <strong>of</strong> an experimental apparatus. The NaI(Tl) scintillator is
irradiated with an isotropic gamma-ray sources <strong>of</strong> 137 Cs. The scintillation photons are converted into
2

Figure 1: Apparatus for photoelectron measurements.
Figure 2: Saturation curve <strong>of</strong> <strong>the</strong> full-energy peak measured by <strong>the</strong> PMT in <strong>the</strong> PD-mode.
3

Figure 3: Electron-response data[12] <strong>of</strong> NaI(Tl) used for <strong>the</strong> present simulations.
photoelectrons with <strong>the</strong> photocathode (K). In order to measure <strong>the</strong> precise number <strong>of</strong> photoelectrons,
<strong>the</strong> PMT is operated in <strong>the</strong> Photo-Diode mode (PD mode). A grid (G), <strong>the</strong> rst dynode (D1) and <strong>the</strong>
second dynode (D2) are connected toge<strong>the</strong>r and act as a collector electrode for those photoelectrons
emitted from <strong>the</strong> photocathode. The photocathode, <strong>the</strong> o<strong>the</strong>r dynodes and an anode (A) are connected
toge<strong>the</strong>r and act as a negative-bias electrode. The charge signals from <strong>the</strong> collector electrode are fed
into a charge-sensitive preampli er. The electric circuit including <strong>the</strong> charge-sensitive preampli er
is calibrated with a high-precision pulser in order to obtain <strong>the</strong> absolute number <strong>of</strong> photoelectrons
collected by <strong>the</strong> collector electrode. The details <strong>of</strong> experiments have been described in <strong>the</strong> previous
publications[3, 4,5,6,7].
Figure 2 shows a saturation curve <strong>of</strong> N pe corresponding to <strong>the</strong> full-energy peak in <strong>the</strong> PD-mode.
This saturation curve indicates that <strong>the</strong> photoelectrons are fully collected with <strong>the</strong> collector electrode
around -100 V and multiplication <strong>of</strong> photoelectrons does not take place. Therefore, both F g and F s
are unity under <strong>the</strong> present experimental conditions.
4 Monte-Carlo simulations
TheEGS4codewas used to score <strong>the</strong> secondary electrons generated from gamma-ray interactions
in NaI(Tl), which are photoelectrons, Compton recoil electrons, electron-positron pairs and Auger electrons.
In order to treat low-energy photon transport precisely, <strong>the</strong> following items were incorporated
into <strong>the</strong> default EGS4 code[8, 9, 10, 11]: photoelectrons from <strong>the</strong> K-, L1-, L2- and L3-shell photoelectric
e ects, K- and L-X rays, energy deposition due to M- and higher-shell photoelectric e ects, K- and
L-Auger electrons, and Doppler broadening <strong>of</strong> Compton-scattered photons. The secondary-electron
transport was not simulated for reducing computation time. The energy <strong>of</strong> each secondary electron is
converted into scintillation photons using <strong>the</strong> relative electron-response in Fig. 3, which was measured
by Rooney et al.[12]. The electron response <strong>of</strong> NaI(Tl) is non-linear in an energy region less than 1
MeV, as shown in Figure 3.
Seven di erent processes relating to SPT are incorporated into <strong>the</strong> present SPC code, as shown
in Fig. 4. The SPC code was originally developed by our group and recently linked to an EGS4
usercode. The details <strong>of</strong> <strong>the</strong> Monte-Carlo simulations are described in a separate paper[1]. In <strong>the</strong>
present SPT simulations for NaI(Tl) detectors, we assumed following: <strong>the</strong> re ectivity <strong>of</strong> a re ector
for scintillation photons is 0.975 <strong>the</strong> re ection <strong>of</strong> scintillation photons on <strong>the</strong> re ector is di usive
(directions <strong>of</strong> scintillation photons after re ection is sampled randomly in <strong>the</strong> simulation) Snell's law
is valid at <strong>the</strong> interface between NaI(Tl) and a crystal window <strong>the</strong> refractive indices <strong>of</strong> NaI(Tl) and <strong>the</strong>
crystal windows <strong>of</strong> <strong>the</strong> scintillator and <strong>the</strong> PMT are 1.47 and 1.85, respectively and scintillation-light
4

γ
Figure 4: Processes treated in a scintillation photon transport (SPT) simulation.
Figure 5: Emission spectrum <strong>of</strong> NaI(Tl) and quantum e ciency (Q.E) <strong>of</strong> photocathode.
Figure 6: X, Y dependence <strong>of</strong> Q.E.
5

attenuation inside NaI(Tl) is negligible.
The photocathode conversion e ciency from photons to photoelectrons is generally called <strong>the</strong>
Quantum E ciency (Q e). The absolute value <strong>of</strong> Q e in a centralarea<strong>of</strong>4x4cm 2 <strong>of</strong> <strong>the</strong> photocathode
used was measured as a function <strong>of</strong> wavelength by <strong>the</strong> manufacturer <strong>of</strong> <strong>the</strong> PMT (Hamamatsu Photonics),
which isshown in Fig. 5, along with <strong>the</strong> emission spectrum <strong>of</strong> NaI(Tl). Figure 6 shows <strong>the</strong>
relative X- and Y-distribution <strong>of</strong> Q e, which was measured with a collimated light source. From <strong>the</strong>
data shown in Figs. 5 and 6, <strong>the</strong> averaged Q e <strong>of</strong> <strong>the</strong> photocathode was estimated to be 0.272. The
non-uniformity data <strong>of</strong> <strong>the</strong> photocathode was also incorporated into <strong>the</strong> SPT simulation.
5 Results and discussions
Figure 7 shows <strong>the</strong> results from Monte-Carlo simulations. The energy-deposition spectrum obtained
from <strong>the</strong> EGS4 simulation indicates a monochromatic full-energy peak at <strong>the</strong> right endpoint
<strong>of</strong> <strong>the</strong> spectrum, as shown in Fig. 7 (a). The non-linearity <strong>of</strong> <strong>the</strong> electron response broadens <strong>the</strong>
full-energy peak in <strong>the</strong> scintillation-photon spectrum, and causes ne structures on this peak[13], as
shown in Fig. 7 (b). The photoelectron spectrum obtained from an SPT simulation following <strong>the</strong>
EGS4 simulation is also shown in Fig. 7 (b). In measuring <strong>the</strong> photoelectron spectrum, <strong>the</strong> resolution
loss due to electric-noise ( noise) was 470 electrons (4.4%) in FWHM. In order to compare <strong>the</strong> simulated
spectrum with <strong>the</strong> measured one, <strong>the</strong> photoelectron spectrum in Fig. 7 (b) was obtained as a
convolution with Gaussian functions having a standard deviation <strong>of</strong> (470/2.35=) 200 electrons.
φ
φ
Figure 7: Monte-Carlo simulations. (a) The energy-deposition spectrum. (b) The scintillation-photon spectrum
(thin line) and <strong>the</strong> photoelectron spectrum (thick line).
Figure 8 is a comparison <strong>of</strong> <strong>the</strong> photoelectron spectra. This gure shows that <strong>the</strong> full-energy
6

peak from <strong>the</strong> simulation agrees very well with that from <strong>the</strong> measurement. Although <strong>the</strong>se spectra
are di erent around <strong>the</strong>ir back-scattered peaks, it can be explained from a lack <strong>of</strong> massive materials
surrounding NaI(Tl), such as <strong>the</strong> PMT etc., in <strong>the</strong> present geometry for <strong>the</strong> EGS4 simulation. The
total energy resolution in FWMM <strong>of</strong> <strong>the</strong> full-energy peak ( total) was 7.7% in <strong>the</strong> measurement and
7.6% in <strong>the</strong> simulation.
The gross conversion e ciency from scintillation photons to photoelectrons, which corresponds to
Fc photon spectrum and <strong>of</strong> <strong>the</strong> photoelectron spectrum, in Fig. 7(b). The measured full-energy peak in
Fig. (8) was estimated to be about 10600 electrons from tting with Gaussian functions. Therefore,
<strong>the</strong> mean number <strong>of</strong> scintillation photons produced by <strong>the</strong> full-energy deposition <strong>of</strong> 662-keV gamma
rays was calculated to be 58200 from eq.(3). We can thus obtain 11.4 eV as <strong>the</strong> preliminary value <strong>of</strong>
<strong>the</strong> Ws from eq.(1).
The energy resolution expected from photoelectron statistics ( pe )was calculated to be 2.3% from
10600 electrons. However, this value is too small to explain <strong>the</strong> measured total resolution <strong>of</strong> 7.7%,
even if <strong>the</strong> resolution loss due to electric noise <strong>of</strong> 4.4% is taken into account. The o<strong>the</strong>r main sources
<strong>of</strong> <strong>the</strong> resolution loss are an intrinsic resolution ( int) and a transfer variance ( trans). Figure 9 shows
a broadening <strong>of</strong> <strong>the</strong> full-energy peak (<strong>the</strong> intrinsic resolution) in <strong>the</strong> scintillation-photon spectrum
due to a di erence in <strong>the</strong> gamma-ray interaction and <strong>the</strong> non-linear electron response. From <strong>the</strong>
standard deviation <strong>of</strong> this distribution, <strong>the</strong> intrinsic resolution was calculated to be 3.5% in FWHM.
If <strong>the</strong> NaI(Tl) crystal has some defects, such as an inhomogeneity <strong>of</strong> Tl activators, <strong>the</strong>y would cause
additional resolution losses. However, such e ects on <strong>the</strong> energy resolution were not treated in <strong>the</strong>
present study. The transfer variance consists <strong>of</strong> <strong>the</strong> following sources: (1)scintillation-photon collection
loss <strong>of</strong> a scintillation detector system, (2) photoelectron conversion loss <strong>of</strong> <strong>the</strong> photocathode, (3) nonuniformity
<strong>of</strong> <strong>the</strong> quantum e ciency and (4) photoelectron collection loss. In <strong>the</strong> case <strong>of</strong> 662-keV
gamma-ray irradiation, <strong>the</strong> scintillation photons are generated almost uniformly over <strong>the</strong> entire volume
<strong>of</strong> <strong>the</strong> NaI(Tl) scintillator. In order to estimate <strong>the</strong> transfer variance, we simulated <strong>the</strong> distribution <strong>of</strong>
a collected number <strong>of</strong> scintillation photons under a condition similar to <strong>the</strong> present case. Namely, <strong>the</strong>
location <strong>of</strong> isotropic scintillation sources was randomly sampled inside a 3-inch-diameter, 3-inch-long
scintillation crystal each source generated 60000 scintillation photons. As a result <strong>of</strong> <strong>the</strong> simulation,
trans was estimated to be 4.6% in FWHM.
If <strong>the</strong>se sources <strong>of</strong> resolution loss are independent each o<strong>the</strong>r, we can calculate <strong>the</strong> total energy
resolution from <strong>the</strong> following relation:
q
2
2
total = + + int trans 2 + pe 2 : (4)
noise
Q e, was estimated to be 0.182 from a comparison <strong>of</strong> <strong>the</strong> full-energy peaks <strong>of</strong> <strong>the</strong> scintillation-
Using eq.(4) and values described above, <strong>the</strong> total resolution was calculated to be 7.6%, which agrees
well with <strong>the</strong> results <strong>of</strong> <strong>the</strong> measurement and <strong>the</strong> simulation.
6 Conclusions
The 662-keV gamma-ray spectra from NaI(Tl) scintillation detectors (crystal size, 3" 3") were
analyzed quantitatively by a combination <strong>of</strong> experimental measurements and Monte-Carlo simulations.
The W s value corresponding to <strong>the</strong> full-energy deposition <strong>of</strong> <strong>the</strong> 662-keV gamma rays was preliminary
determined to be 11.4 eV. The total energy resolution <strong>of</strong> <strong>the</strong> full energy peak in FWHM was obtained
to be 7.7% in <strong>the</strong> experiment and 7.6% in <strong>the</strong> simulations. This total resolution consists <strong>of</strong> <strong>the</strong> intrinsic
energy resolution (3.5%) caused by <strong>the</strong> non-linear energy response <strong>of</strong> NaI(Tl) for electrons, <strong>the</strong> transfer
variance (4.6%) <strong>of</strong> <strong>the</strong> scintillation-photon number in <strong>the</strong> detector system, <strong>the</strong> photoelectron statistics
(2.3%) and <strong>the</strong> electric noise (4.4%). It is considered that <strong>the</strong> present method will help to analyze
di erent types <strong>of</strong> scintillation detectors in <strong>the</strong> future.
7

φ
Figure 8: Comparison <strong>of</strong> <strong>the</strong> photoelectron spectra.
φ
γ
Figure 9: Intrinsic crystal resolution.
8

References
[1] H. Tawara, S. Sasaki, K. Saito, E. Shibamura and M. Miyajima, KEK <strong>Proceedings</strong> 99-15, 44
(1999).
[2] W. R. Nelson, H. Hirayama and D. W. O. Rogers, SLAC-265 (Stanford University, Stanford
1985).
[3] M. Miyajima, S. Sasaki and E. Shibamura, Nucl. Instrum. Meth. 224(1984)331.
[4] M. Miyajima, S. Sasaki, H. Tawara, and E. Shibamura, IEEE Trans. Nucl. Sci. 39, 536 (1992).
[5] M. Miyajima, S. Sasaki and H. Tawara, IEEE Trans. Nucl. Sci. 40(1993)417.
[6] S. Sasaki, H. Tawara, and M. Miyajima, KEK <strong>Proceedings</strong> 93-8, 20 (1993).
[7] E. Shibamura, S. Sasaki, H. Tawara and M. Miyajima, KEK <strong>Proceedings</strong> 99-8, 175 (1999).
[8] Y. Namito, S. Ban and H. Hirayama, Radiat. Phys. and Chem. 53(1998)283.
[9] H. Hirayama, Y. Namito and S. Ban, KEK Internal 96-10 (1996).
[10] Y. Namito, S. Ban and H. Hirayama, Nucl. Instrum. Meth. A349(1994)489.
[11] Y. Namito, S. Ban and H. Hirayama, Nucl. Instrum. Meth. A332(1993)277.
[12] B. D. Rooney and J. D. Valentine, IEEE Trans. Nucl. Sci. 44(1997)509.
[13] J. D. Valentine, B. D. Rooney and J. Li, IEEE Trans. Nucl. Sci. 45(1998)512.
9

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.161-167
Development <strong>of</strong> Gamma-Ray Direction Detector
Based on MSGC
T. Nagayoshi 1 , H. Kubo 1 , A. Ochi 1 , S. Koishi 1 ,
T. Tanimori 2 , and Y. Nishi 3
1 Tokyo Institute <strong>of</strong> Technology, Meguro, Tokyo, 152-8551, Japan
2 Kyoto University, Sakyo, Kyoto, 602-8502, Japan
3 The Institure <strong>of</strong> Physical and Chemical Research (RIKEN), Wako, Saitama, 351-0198, Japan
Abstract
The Micro-Strip Gas Chamber (MSGC) has been developed as a real-time X-ray imaging detector.
The MSGC with a long drift space has been operated well as a Time Projection Chamber
(TPC), and detected ne tracks <strong>of</strong> charged particles with even less than 1mm, which we call this
\Micro TPC". Here we consider <strong>the</strong> possibility <strong>of</strong> <strong>the</strong> imaging detector <strong>of</strong> MeV gamma-rays based
on <strong>the</strong> Micro TPC having a wide solid angle. The direction <strong>of</strong> MeV gamma-rays, which interacts
via Compton process with matter, can be obtained only by observation <strong>of</strong> both <strong>the</strong> recoiled
electron and scattered gamma-ray. Full reconstruction <strong>of</strong> MeV gamma-rays would be enabled by
<strong>the</strong> measurement <strong>of</strong> both recoiled electron tracks using <strong>the</strong> Micro TPC and scattered gamma-rays
using ano<strong>the</strong>r gamma-ray position detector such asascintillator Angular camera combined with
<strong>the</strong> Micro TPC.
Behaviors <strong>of</strong> electrons in <strong>the</strong> gas volume <strong>of</strong> <strong>the</strong> Micro TPC and scintillation photons in <strong>the</strong>
scintillator were calculated using EGS4. Expected performances <strong>of</strong> this new gamma-ray detector
were estimated.
1 Introduction
The Micro-Strip Gas Chamber (MSGC) was proposed by Oed in 1988 [1] as a new type <strong>of</strong> position
sensitive proportional gas detector. Fine position resolution <strong>of</strong> 100 m is attained for MSGC, since
electrode strips are printed on substrate at narrow intervals <strong>of</strong> 200 m. We have developed <strong>the</strong> large
area MSGC with <strong>the</strong> fast data acquisition system for a real-time X-ray imaging. The ne position
resolution <strong>of</strong> less than 100 m and excellent timing resolution <strong>of</strong> about 100nsec are attained for our
MSGC. The schematic structure is shown in Fig. 1. In addition to anode and cathode, backstrip
electrodes are printed orthogonally to anodes behind thin substrate. Signals from anode and backstrip
enable us to obtain two-dimensional image. Stable operation is possible by a capillary plate installed
in our MSGC as a intermediate gas multiplier [2].
Our MSGC has been used for a time-resolved X-ray imaging [3] and an X-ray polarization measurement
[4]. Recently we have succeeded to observe images <strong>of</strong> ne tracks <strong>of</strong> charged particles using
<strong>the</strong> MSGC X-ray imaging system like a cloud chamber. Using this feature observed in this system,
a track <strong>of</strong> <strong>the</strong> electron recoiled by Compton scattering will be measured. In addition, if a scattered
gamma-ray via Compton process is also detected by some detector behind <strong>the</strong> gas chamber, <strong>the</strong> incident
direction <strong>of</strong> a gamma-ray could be fully determined from both <strong>the</strong> momentum vectors <strong>of</strong> <strong>the</strong>
recoiled electron detected in MSGC and <strong>the</strong> detected scattered gamma-ray. This method needs no
collimators, and fur<strong>the</strong>rmore provide a wide eld <strong>of</strong> view ( str). This new detector would be very
useful for a lot <strong>of</strong> application, e.g. gamma-ray astrophysics, medical diagnoses, radiation control, and
so on.
Here we presents <strong>the</strong> simulated performances <strong>of</strong> this new gamma-ray detector using <strong>the</strong> Micro
TPC and <strong>the</strong> scintillator Angular Camera.
1

2 Detection Principle
2.1 The Micro TPC based on MSGC
For <strong>the</strong> purpose <strong>of</strong> tracking charged particles, <strong>the</strong> MSGC having a deep gas volume has been
developed, which works as a Time Projection Chamber (TPC). When a charged particle pass through
<strong>the</strong> gas chamber, an electron cloud is generated along <strong>the</strong> track by <strong>the</strong> ionization. This electron
cloud drifts toward electrodes <strong>of</strong> <strong>the</strong> MSGC along electric eld formed by <strong>the</strong> drift electrode. Then
a two-dimensional image <strong>of</strong> <strong>the</strong> track is projected as a sequence <strong>of</strong> hit points <strong>of</strong> electrodes on <strong>the</strong>
MSGC (see Fig. 2). Three-dimensional track image is reconstructed from position information and
time intervals <strong>of</strong> each hit point. Fig. 3 shows an example <strong>of</strong> three-dimensional track observed in <strong>the</strong>
Micro TPC consisting <strong>of</strong> <strong>the</strong> 10cm 10cm two-dimensional MSGC and <strong>the</strong> 8cm deep drift-gas volume.
This track is considered due to particles emitted from <strong>the</strong> radioactive isotope <strong>of</strong> lead contained in
a glass capillary plate, which is set on <strong>the</strong> MSGC and used as a auxiliary gas multiplier. Here ne
tracks <strong>of</strong> charged particles less than milli-meter were observed.
2.2 Determination <strong>of</strong> incident gamma-ray direction
When an incident MeV gamma-ray interact <strong>the</strong> gas in <strong>the</strong> drift volume, an electron is recoiled
mainly by Compton process as following formula:
cos =1+ m ec 2
E k + E 0
; mec 2
E 0
where m e is rest mass <strong>of</strong> an electron and c is light velocity, and also E k, E 0, and is kinetic energy
<strong>of</strong> recoiled electron, energy <strong>of</strong> scattered gamma-ray, and polar angle <strong>of</strong> scattering, respectively. In this
process, all <strong>the</strong> momenta <strong>of</strong> incident gamma-ray, scattered gamma-ray, and recoiled electron lie on <strong>the</strong>
same plane as shown in Fig. 4. If <strong>the</strong> azimuthal angle <strong>of</strong> <strong>the</strong> scattering plane, one <strong>of</strong> two polar angles
and both <strong>the</strong> energies <strong>of</strong> <strong>the</strong> scattered gamma-ray and a recoiled electron are measured, <strong>the</strong> direction
<strong>of</strong> <strong>the</strong> incident gamma-ray is fully determined from above equation. In addition, residual polar angle
provide <strong>the</strong> good redanancy for <strong>the</strong> reconstruction, which enable us <strong>the</strong> good rejection power for <strong>the</strong>
accidental background and <strong>the</strong> false reconstruction.
The schematic view <strong>of</strong> <strong>the</strong> Micro TPC gamma-ray detector based on this idea is drawn in Fig. 5.
Three-dimensional tracks <strong>of</strong> a recoiled electron is reconstructed by <strong>the</strong> MSGC on both sides <strong>of</strong> <strong>the</strong> gas
chamber. In order to suppress <strong>the</strong> di usion <strong>of</strong> <strong>the</strong> drifted electron in <strong>the</strong> gas volume, <strong>the</strong> drift volume
is divided into two MSGCs. Also <strong>the</strong> scintillator Angular Camera consisting <strong>of</strong> <strong>the</strong> scintillator and <strong>the</strong>
photomultiplier array covers <strong>the</strong> half <strong>of</strong> <strong>the</strong> gas volume in order to detect <strong>the</strong> recoiled gamma-rays. A
trigger is generated from <strong>the</strong> signal <strong>of</strong> <strong>the</strong> Angular Camera.
3 EGS4 Simulation
In order to optimize <strong>the</strong> parameters <strong>of</strong> <strong>the</strong> detector and to estimate <strong>the</strong> performance <strong>of</strong> <strong>the</strong>
Micro TPC gamma-ray detector, <strong>the</strong> very convenient program package EGS4 is used, which can
simulate both <strong>the</strong> behaviors <strong>of</strong> Compton scattered gamma-ray photons and recoiled electrons. The
EGS4 is a general purpose package for Monte Carlo simulation <strong>of</strong> high energy electrons and photons [5].
Here we consider <strong>the</strong> GSO as a scintillator <strong>of</strong> <strong>the</strong> Angular Camera, which has a better stopping power
for gamma-rays than ano<strong>the</strong>r scintillator. Properties <strong>of</strong> GSO scintillator can be also simulated using
EGS4. In this simulation, a subroutine for <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> behavior <strong>of</strong> scintillation photons is
included.
The geometry <strong>of</strong> <strong>the</strong> Micro TPC in <strong>the</strong> calculation is a cubic shape, <strong>of</strong> which inside pure xenon
is lled with an atmospheric pressure. Also 1 3 cm thick GSO crystal covers around <strong>the</strong> cube (see
Fig. 5). Incident gamma-rays are assumed to be perpendicular to <strong>the</strong> upper surface <strong>of</strong> <strong>the</strong> cube. There
are four types <strong>of</strong> event patterns in <strong>the</strong> detector: (A) no interaction in <strong>the</strong> gas volume, (B) photoelectric
2

e ect ( uorescent X-ray is <strong>of</strong>ten absorbed in gas), (C) Compton scattering observed in <strong>the</strong> gas volume
but scattered gamma-ray missing, (D) both scattered electron and gamma-ray observed in <strong>the</strong> gas
volume and in <strong>the</strong> scintillator respectively. The available event is <strong>the</strong> last type in <strong>the</strong> four types. The
detection e ciency satis ed with <strong>the</strong> requirement <strong>of</strong> (D) is shown in Fig. 6 as a function <strong>of</strong> <strong>the</strong> incident
gamma-ray energy.
While electrons passing through gas <strong>the</strong> volume, <strong>the</strong> tracks are quite bent bymultiple scattering.
Averaged de ection angle <strong>of</strong> electron tracks determines <strong>the</strong> accuracy <strong>of</strong> a reconstructed direction <strong>of</strong>
<strong>the</strong> gamma-ray. Here <strong>the</strong> de ection angle <strong>of</strong> <strong>the</strong> scattered electron is de ned as an angular deviation
from <strong>the</strong> initial direction <strong>of</strong> <strong>the</strong> scattered electron at <strong>the</strong> point on <strong>the</strong> track passing through <strong>the</strong> 3mm
distance. Fig. 7 shows <strong>the</strong> distribution <strong>of</strong> <strong>the</strong> de ection angles <strong>of</strong> <strong>the</strong> recoiled electron track. Here <strong>the</strong>
energy written in each gure is not electrons', but those <strong>of</strong> incident gamma-rays. The energy become
higher, <strong>the</strong> de ection angles become smaller drastically. For high energy incident gamma-rays, most
<strong>of</strong> recoiled electrons pass straight through <strong>the</strong> 3mm thick gas layer without multiple scattering. In
this case, <strong>the</strong> electron track is determined within <strong>the</strong> accuracy <strong>of</strong> 1 degree.
While a ionized electron in <strong>the</strong> track drifts toward MSGC electrode, it gradually di uses by <strong>the</strong>rmal
collision between electrons and gas molecules. In order to estimate <strong>the</strong> accuracy <strong>of</strong> direction <strong>of</strong> <strong>the</strong>
recoiled electron, it is necessary to consider <strong>the</strong> di usion <strong>of</strong> electron track as well as <strong>the</strong> de ection.
However, it is not so easy to estimate di usion properties, because it strongly depend on <strong>the</strong> electric
eld, gas pressure, and concentration <strong>of</strong> quencher gas [6]. Now we are developing <strong>the</strong> simulation by
including above e ects.
Scintillators are used for <strong>the</strong> detection <strong>of</strong> scattered gamma-rays. Dispersion <strong>of</strong> scintillation light is
estimated quickly using <strong>the</strong> simpli ed simulation. In this simulation, <strong>the</strong> attenuation <strong>of</strong> scintillation
light is ignored, and it is assumed that all photons, which reach surface <strong>of</strong> crystal, is absorbed. Soon
we will use <strong>the</strong> full simulation including such e ects. As a result, <strong>the</strong> dispersion <strong>of</strong> light is estimated
to be about 1cm for 1cm thick GSO, and about 2cm for 2cm thick one (see Fig. 8).
4 Summary and Future Plan
Our MSGC is applied to Micro TPC, and three-dimensional tracks <strong>of</strong> charged particles ( particles)
were observed. An imaging detector for <strong>the</strong> MeV gamma-ray based on <strong>the</strong> Micro TPC is proposed,
which is expected to have a wide eld <strong>of</strong> view and provide <strong>the</strong> full reconstruction <strong>of</strong> <strong>the</strong> direction <strong>of</strong> one
gamma-ray. Expected performance <strong>of</strong> this gamma-ray detector was simulated using EGS4. Obtained
detection e ciency is about 1%, and <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong> direction <strong>of</strong> <strong>the</strong> gamma-ray is less than 1
degree for 1MeV gamma-ray. As a preliminary result, <strong>the</strong> dispersion <strong>of</strong> light in GSO crystal is about
1to2cm.
In <strong>the</strong> next step, energy resolution <strong>of</strong> <strong>the</strong> Micro TPC will be taken into account. On <strong>the</strong> o<strong>the</strong>r
hand, <strong>the</strong> estimation <strong>of</strong> position resolution <strong>of</strong> <strong>the</strong> scintillation detector combined with pixel type PMTs
is now in progress.
References
[1] A. Oed, \Position-sensitive detector with microstrip anode for electron multiplication with gases",
Nucl. Instrum. Meth. A263 (1988)351-359.
[2] Y. Nishi, T. Tanimori, A. Ochi, Y. Nishi, and H. Toyokawa, \Development <strong>of</strong>hybrid MSGC with
a conductive capillary plate", <strong>Proceedings</strong> <strong>of</strong> SPIE 3774(1999)87-96.
[3] A. Ochi, T. Tanimori, Y. Nishi, T. Nagayoshi, Y. Nishi, Y. Ohashi, H. Uekusa, H. Toyokawa,
K. Inoue, and T. Fujisawa, \Novel X-ray analyzing methods using a MicroStrip Gas Chamber",
<strong>Proceedings</strong> <strong>of</strong> SPIE 3774 (1999)76-86.
3

[4] A. Ochi, S. Aoki, Y. Nishi, and T. Tanimori, \Development <strong>of</strong> imaging microstrip gas chambers
and measurement <strong>of</strong> <strong>the</strong> polarization <strong>of</strong> X-rays", Nucl. Instrum. Meth. A392(1997)124-126.
[5] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, \The EGS4 code system", SLAC-265 (1985).
[6] A. Peisert, and F Sauli, \Drift and di usion <strong>of</strong> electrons in gases: a compilation" CERN 84-08
(1984).
4

Anode strip
(10ÉIm width)
Figure 2: Two-dimensional track image projected
on 2cm 2cm area <strong>of</strong> MSGC. Each sequence <strong>of</strong>
dots represents a track image projected on electrode
plane.
Drift plane substrate
(20ÉIm
polyimide)
200ÉIm
Cathode strip
(100ÉIm width)
200ÉIm
Back strip
(180ÉIm width)
Base
(Ceramic)
Figure 1: Schematic structure <strong>of</strong> 2D MSGC.
5
Figure 3: A three-dimensional track image <strong>of</strong> an
particle. A track is reconstructed from position
and timing data <strong>of</strong> each dot.

γ
(azimuth)
ϕ
θ
α
e
γ '
Figure 4: Direction <strong>of</strong> scattered gamma-ray
and recoiled electron.
efficiency [%]
6
5
4
3
2
0.9
0.8
0.7
0.6
0.5
1
electron
MSGC
e -
~1MeV
~50cm
pixel type PMTs
gamma ray
drift plane
e + e -
scintillator
~10MeV
~50cm
Figure 5: Schematic illustration <strong>of</strong> <strong>the</strong> Micro TPC
gamma-ray detector. Recoiled electron tracks are detected
<strong>the</strong> Micro TPC based on MSGC, and scattered
gamma-rays are absorbed in scintillators behind <strong>the</strong> gas
chamber.
gas (all interaction)
gas and GSO
0.2 0.4 0.6 0.8 1 1.2
energy [MeV]
Figure 6: Detection e ciency <strong>of</strong> Micro TPC gamma-ray detector. Round markers mean e ciency <strong>of</strong> interaction
only in gas region. E ciency shown as square marker is due to <strong>the</strong> e ective events.
6

Y[cm]
160
140
120
100
80
60
40
20
0
0 5 10 15 20 25 30 35 40 45
deflection angle [deg]
0.40 MeV γ-ray
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
X[cm]
thickness=1.0cm
3000
2500
2000
1500
1000
500
Figure 7: Distribution <strong>of</strong> de ection angle.
Y[cm]
0
0 1 2 3 4 5 6 7 8 9 10
deflection angle [deg]
1.00 MeV γ-ray
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
X[cm]
thickness=2.0cm
Figure 8: Distribution <strong>of</strong> scintillation photons. Energy <strong>of</strong> incident gamma-ray is 700keV. Total event number
is 20.
7

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.168-175
Response Function <strong>of</strong> a NE213 Liquid Saintillation Detector
Simulated by EGS4/PRESTA Code
for a Collimated -Ray Beam
N. Takeda, K. Kudo, S. Koshikawa, H. Ohgaki, H. Toyokawa, and T. Sugita 1
Quantum Radiation Division, Electrotechnical Laboratory
1-1-4 Umezono, Tsukuba-shi, Ibaraki 305-8568, Japan
1 Science System Laboratory
1342-6 Sumiyoshi, Tomobe-cho, Ibaraki 309-1716, Japan
Abstract
For photon spectrometry in a mixed neutron-photon eld, a NE213 liquid scintillation detector
is one <strong>of</strong> <strong>the</strong> useful instruments which has an excellent neutron-photon discrimination capability.
The -ray response function for a NE213 detector is required for unfolding measured pulse height
spectra. The EGS4/PRESTA codewas used to simulate <strong>the</strong> -ray response function taking into
accounts <strong>the</strong> detail information on <strong>the</strong> detector assembly. Experimental data were taken in <strong>the</strong>
energy range below 1.8 MeV using a collimated -ray beam <strong>of</strong> radioisotope reference sources. For
<strong>the</strong> higher energies up to 10 MeV, a laser-Compton-scattered (LCS) photon source was used as
a collimated quasi-monoenergetic photon beam. The simulated response function showed a good
agreement with experimental data at di erent energies.
1 Introduction
It is <strong>of</strong>ten required in neutron calibration elds to determine <strong>the</strong> dose <strong>of</strong> -rays produced in a
neutron source and in <strong>the</strong> surroundings, because some types <strong>of</strong> neutron detector are sensitive both
to neutrons and -rays. In <strong>the</strong> measurement <strong>of</strong> -rays mixed in a neutron eld, conventional -ray
detectors such as GM counter, NaI scintillator and Ge detector are in uenced by neutron-induced
reactions in a detector assembly, which can not be separated easily from photon detecting reactions.
Bueermann and Novotny etal.developed photon spectrometry using NE213 scintillation detectors
in mixed neutron-photon elds, because <strong>of</strong> its excellentn- separation properties [1-3]. They calculated
<strong>the</strong> response function due to photons induced by fast neutrons in NE213 scintillators using a coupled
MCNP4A/EGS4 simulation, and nally obtained <strong>the</strong> photon energy distribution existing in some
neutron-photon eld.
In this paper as a rst step to determine <strong>the</strong> -ray energy distribution, <strong>the</strong> gamma-ray response
function <strong>of</strong> a NE213 scintillation detector will be calculated by EGS4/PRESTA code and folded properly
with a resolution function. The light output function and <strong>the</strong> energy resolution will be determined
by using reference -ray sources. The simulated results would be compared with experimental data
for collimated beams <strong>of</strong> radioisotope reference sources below 1.8 MeV and a laser-Compton-scattered
(LCS) photon source at higher energies up to 10 MeV.
2 Experimental Setup
In order to measure <strong>the</strong> response function <strong>of</strong> -rays, a NE213 scintillation counter was set as shown
in Fig. 1. The NE213 scintillation detector was encapsulated in a standard BA1 cylindrical cell (inner
1

size: 5.08 cm in diameter and 5.08 cm length) and designed to avoid any air bubble in <strong>the</strong> sensitive
region with <strong>the</strong> use <strong>of</strong> an expansion reservoir <strong>of</strong> polyethylene tube around <strong>the</strong> circumference. A
conventional measuring system <strong>of</strong> pulse shape discrimination and multi-parameter data acquisition was
used to process <strong>the</strong> signals from a photomultiplier tube (R329-02 manufactured by HAMAMATSU)
and to separate photon signals from neutron induced ones.
The -ray response function <strong>of</strong> <strong>the</strong> NE213 scintillation counter was measured using gamma-ray
reference sources <strong>of</strong> 88 Y, 60 Co, 22 Na, 54 Mn and 137 Cs provided by Amersham Buchler GmbH & Co
KG. In <strong>the</strong> calibration <strong>of</strong> NE213 scintillation counter, <strong>the</strong> source was located at <strong>the</strong> distance <strong>of</strong> 23cm
from <strong>the</strong> center <strong>of</strong> NE213 scintillator on <strong>the</strong> cylindrical axis. The gamma-rays from <strong>the</strong> sources were
collimated by a lead collimator (10 cm x 10 cm cross section and 20 cm long) to make a narrow beam
<strong>of</strong> 3.85 mm diameter. In order to measure <strong>the</strong> precise response function depending on <strong>the</strong> irradiation
position <strong>of</strong> gamma-ray beam, <strong>the</strong> collimated beam was irradiated to <strong>the</strong> detector in <strong>the</strong> direction <strong>of</strong>
parallel or vertical to its axis, and scanned to radius or height direction, respectively.
In <strong>the</strong> experiment above 1.8 MeV, <strong>the</strong> NE213 detector was calibrated by using <strong>the</strong> LCS photon
beam which is expected as a new source <strong>of</strong> quasimonoenergetic photons between 2 MeV and 22
MeV [4,5]. As shown in Fig.2, <strong>the</strong> second harmonic light emitted from a Q-switched Nd:YLF laser
(maximum output: 20 W, wavelength: 527 nm, minimum pulse width: 150 ns, and pulse reputation
rate: 2-50 kHz), was guided into <strong>the</strong> laser-electron interaction region through <strong>the</strong> laser polarizing
controller, re ection mirror, and focusing lens. High-energy photons back-scattered by relativistic
electrons (maximum energy: 800 MeV, maximum beam: 300 mA, and pulse reputation rate: 166
MHz) were collimated to a beam diameter <strong>of</strong> 2 mm using a lead block. The second lead collimator
and <strong>the</strong> shielding lead surrounding a NE213 scintillation detector reduce background bremsstrahlung
photons generated in <strong>the</strong> synchrotron storage ring.
3 Calculation <strong>of</strong> Response Function by EGS4/PRESTA Code
The -ray response function for <strong>the</strong> NE213 scintillation counter was calculated using EGS4 code
coupled with <strong>the</strong> parameter reduced electron-step transport algorithm (PRESTA) routine which was
developed to minimize <strong>the</strong> dependence <strong>of</strong> results on step size in electron transport simulation [6].
The calculation <strong>of</strong> response functions for reference gamma-ray sources was made under <strong>the</strong> following
conditions:
1. <strong>the</strong> reference gamma-ray source was assumed to be an isotropic point source.
2. <strong>the</strong> calculation model and <strong>the</strong> composition <strong>of</strong> NE213 detector assembly were chosen precisely as
shown in Fig. 1.
3. In <strong>the</strong> simulation <strong>of</strong> <strong>the</strong> LCS facility, <strong>the</strong> geometry routine was written by taking into account <strong>the</strong>
detailed system con guration, consisting <strong>of</strong> a volume source <strong>of</strong> photons produced in an electronlaser
collision region, a lead collimator, and <strong>the</strong> cylindrical NE213 detector with all physical
processes necessary for accurate calculations in <strong>the</strong> electron energy region from 300 MeV to
800 MeV. The 527 nm coherent light generated by <strong>the</strong> 20 W Nd-YLF laser was guided to <strong>the</strong>
vacuum chamber located at <strong>the</strong> straight portion between two bending magnets <strong>of</strong> <strong>the</strong> storage
ring TERAS [4] and collided head-on with high-energy electrons. Back-scattered photon energy
and <strong>the</strong> emission angle corresponding to <strong>the</strong> backward direction were randomly generated by
following a kinematic formula for Compton scattering, as input data for <strong>the</strong> EGS4/PRESTA
calculation. The electron beam divergence and energy spread were ignored in calculation. To
shorten computing time, <strong>the</strong> maximum solid angle cone to <strong>the</strong> backward emission was limited
to be slightly little larger than <strong>the</strong> rst collimator, positioned 503.6 cm away from <strong>the</strong> center <strong>of</strong>
<strong>the</strong> volume source.
4. The NE213 detector used in <strong>the</strong> EGS4 calculation was assumed to be composed <strong>of</strong> multilayer
cylinders according to factory information, as shown in Fig.3.
2

5. The energy intervals for <strong>the</strong> calculation <strong>of</strong> response function were chosen as:
(a) 100keV in <strong>the</strong> energy range up to 400 keV,
(b) 20 keV in <strong>the</strong> range from 400 keV to 1.9 MeV,
(c) 100 keV from 1.9 MeV to 5 MeV and
(d) 500 keV up to 10MeV.
The pulse height axiswas divided into 1000 channels corresponding to <strong>the</strong> energy bin width <strong>of</strong>
10 keV/channel.
4 Results and Discussion
The pulse height spectra measured for <strong>the</strong> reference -ray sources <strong>of</strong> 88 Y, 60 Co, 22 Na, 54 Mn and
137 Cs were compared to <strong>the</strong> response functions calculated by <strong>the</strong> EGS4/PRESTA code. The calculated
spectrum was folded with <strong>the</strong> pulse height dependent resolution assuming to be dL/L =B/L 1=2 , where
L and B are <strong>the</strong> light output and arbitrary parameter, including only <strong>the</strong> region <strong>of</strong> <strong>the</strong> Compton
edge and tted to <strong>the</strong> measured distribution [7]. By changing <strong>the</strong> parameter B properly, a besttted
distribution to <strong>the</strong> experimental spectrum was determined by a least square t and <strong>the</strong>n <strong>the</strong>
precise position <strong>of</strong> Compton-edge could be determined for <strong>the</strong> reference sources. As an example, <strong>the</strong>
comparison <strong>of</strong> simulated spectra with measured ones for <strong>the</strong> -ray beam from a 137 Cs source is shown
in Fig. 4bychanging <strong>the</strong> incident position <strong>of</strong> a -ray beam corresponding to <strong>the</strong> bold arrows (in <strong>the</strong> left
hand sketches) incident on <strong>the</strong> detector. The arrows (in <strong>the</strong> right hand gures) in <strong>the</strong> spectra indicated
<strong>the</strong> precise Compton edge at di erent incident points perpendicular to <strong>the</strong> cylindrical detector axis.
The light output function <strong>of</strong> <strong>the</strong> NE213 scintillator resulted in linear output relationship, expressed
as L=E e - 0.0065, between <strong>the</strong> measured pulse height L and <strong>the</strong> corresponding equivalent electron
energy E e in <strong>the</strong> energy range below 1.6 MeV. Toverify qualitative simulation by EGS4/PRESTA code,
<strong>the</strong> radioactivities <strong>of</strong> <strong>the</strong> reference sources were determined by tting simulated response functions to
experimental data. The derived radioactivities agreed well within <strong>the</strong> reference uncertainty <strong>of</strong> 5%
for <strong>the</strong> di erent -ray sources.
The parameters <strong>of</strong> A, B and C in <strong>the</strong> formula <strong>of</strong> pulse height resolution dL/L described by (A 2 +
B 2 /L + C 2 /L 2 ) 1=2 were determined as 0.032, 0.103 and 0.002, respectively.
In <strong>the</strong> higher energies above 1.8 MeV, <strong>the</strong> comparison <strong>of</strong> simulated spectra with experimental
results were shown in Fig. 5 at energies <strong>of</strong> 3.43, 4.311, 5.151 and 5.985 MeV and in Fig. 6 at 6.816,
7.787, 8.780 and 9.869 MeV, respectively. The simulated response function showed a relatively better
agreement with experimental data at di erent energies. The light output function <strong>of</strong> <strong>the</strong> NE213
scintillator resulted in non-linear output relation to <strong>the</strong> deposited energy as shown in Fig 7.
5 Conclusion
The EGS4/PRESTA codewas used to simulate <strong>the</strong> -ray response function taking into accounts
<strong>the</strong> detail information on <strong>the</strong> detector assembly. Experimental data were taken in <strong>the</strong> energy range
below 1.8 MeV using a collimated -ray beam <strong>of</strong> radioisotope reference sources. For <strong>the</strong> higher energies
up to 10 MeV, a LCS photon source was used as a collimated quasi-monoenergetic photon beam. The
simulated response function showed a good agreement with experimental data at di erent energies.
The response matrix calculated by <strong>the</strong> EGS4/PRESTA code coupled with <strong>the</strong> light output and <strong>the</strong>
resolution function would be applied for unfolding pulse height spectra measured for <strong>the</strong> reference
-ray sources by using unfolding codes <strong>of</strong> <strong>the</strong> GRAVEL and <strong>the</strong> MIEKE [8].
3

Figure 2: Experimental setup for a collimated beam <strong>of</strong> LCS photon source.
φ
φ
φ
φ
ρ
φ
φ
Figure 3: Calculation model <strong>of</strong> NE213 Scintillator.
5
φ

Figure 4: Position dependent pulse height spectra for a photon beam <strong>of</strong> 137 Cs source.
6

Fig.5PositiondependentpulseheightspectraforaLCSphotonbeamatenergies<strong>of</strong>3-6MeV
Countsperchannel
Countsperchannel
Countsperchannel
Countsperchannel
Countsperchannel
Countsperchannel
1500
1000
500
2000
1000
3000
2000
1000
0
100 200 300 400
Channelnumber
2000
1000
Exp.
Cal. Cal.
0
0 100 200 300 400
Channelnumber
Channelnumber
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
6.816MeV
7.787MeV
3.43MeV
4.331MeV
0
0 100 200 300 400
Channelnumber
Channelnumber
0
100 200 300 400
Channelnumber
0
100 200 300 400
Channelnumber
Fig.6PositiondependentpulseheightspectraforaLCSphotonbeamatenergies<strong>of</strong>7-10MeV
CountsperChannel
CountsperChannel
Countsperchannel
Countsperchannel
Countsperchannel
Countsperchannel
Countsperchannel
2000
1000
2000
1000
2000
1000
1500
1000
7
0
100 200
Channelnumber
300 400
500
0
0 100 200 300 400
Channelnumber
Channelnumber
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
Exp.
Cal.
9.869MeV
LCSphotons
LCSphotons
LCSphotons
5.152MeV
5.985MeV
0
0 100 200 300 400
Channelnumber
Channelnumber
Channelnumber
8.780MeV

Figure 7: Light output function for <strong>the</strong> NE213 scintillator (PM tube: R329-02)
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.176-181
The E ect <strong>of</strong> <strong>the</strong> Build-up Wall
at <strong>the</strong> TLD Calibration Using Co-60
N. Nariyama
Nuclear Technology Division, Ship Research Institute,
Mitaka, Tokyo 181-0004, Japan
Abstract
Absorbed dose in <strong>the</strong>rmoluminescent dosimeter (TLD) material at <strong>the</strong> calibration using Co-60
gamma rays depends on <strong>the</strong> TLD thickness and <strong>the</strong> wall material used for electric equilibrium condition.
The relation was examined for LiF, BeO and CaF2 TLDs sandwiched with PMMA, Te on
and Pyrex glass walls using a Monte Carlo transport code and compared with cavity ionization
<strong>the</strong>ory calculations. For <strong>the</strong> mismatched combination <strong>of</strong> LiF, BeO/Pyrex glass and CaF2/PMMA,
it was found that <strong>the</strong> energy deposition did not change monotonously with TLD thickness from
small cavity to large cavityvalue: a depression observed around 1-mm thickness for LiF/Pyrex glass
and a peak around 0.6-mm thickness for CaF2/PMMA. The phenomena were explained by using
di erent exponential attenuation coe cients and ' for <strong>the</strong> weighting functions <strong>of</strong> cavity <strong>the</strong>ory.
Moreover, use <strong>of</strong> large cavity values was found to lead possibly to 3-5% errors in <strong>the</strong> calibration <strong>of</strong>
thin TLDs.
1 Introduction
Recently, increase <strong>of</strong> synchrotron radiation and ion beam facilities make <strong>the</strong> LET e ect <strong>of</strong> radiation
dosimeters an interesting and important subject because <strong>the</strong> radiation considerably di ers from that
<strong>of</strong> nuclear industry facilities and ordinary medical machines in regard to energy, strength and beam
quality. For <strong>the</strong> LET e ect, <strong>the</strong>rmoluminescent dosimeters (TLDs) have been extensively examined
[1] because TLDs are used for personal dosimetry and many kinds <strong>of</strong> materials are available.
For <strong>the</strong> use, TLDs are calibrated using Co-60 or Cs-137 in general. In <strong>the</strong> calibration, dose in <strong>the</strong>
TL material does not have to be estimated: only <strong>the</strong> relation between TL signal and dose equivalent is
important. The LET e ect, however, is <strong>the</strong> phenomenon <strong>the</strong> TL material itself shows. To investigate
<strong>the</strong> e ect quantitatively, estimation <strong>of</strong> <strong>the</strong> absorbed dose in <strong>the</strong> TL material is indispensable.
At <strong>the</strong> calibration, TL material is sandwiched with wall materials such asTe on to attain electric
equilibrium condition. The absorbed dose in <strong>the</strong> TL material is obtained as follows[2]:
DTLD = f( en= ) wall=( en= )airDair
where f is <strong>the</strong> response, which is obtained based on Burlin's cavity ionization <strong>the</strong>ory [3], ( en/ ) wall
and ( en/ )air are <strong>the</strong> mass energy absorption coe cients <strong>of</strong> <strong>the</strong> wall material and air, and Dair is <strong>the</strong>
absorbed dose in <strong>the</strong> air. If <strong>the</strong> in uence <strong>of</strong> <strong>the</strong> wall is neglected, which is a simpler method for rough
approximation, <strong>the</strong> dose in <strong>the</strong> TL material is obtained only by multiplying <strong>the</strong> air absorbed dose by
<strong>the</strong> ratio <strong>of</strong> <strong>the</strong> mass energy absorption coe cients <strong>of</strong> <strong>the</strong> TLD material and air.
Cavity ionization <strong>the</strong>ory for TLDs has been extensively investigated using Monte Carlo transport
codes [4]-[6], in which energy deposition distribution in <strong>the</strong> TLDs and electron spectra were calculated.
Practically, <strong>the</strong> sandwich materials <strong>of</strong>ten used are tissue-equivalent materials suchasTe on or PMMA.
Moreover, Pyrex glass is employed as powder capsule because <strong>of</strong> <strong>the</strong> good heat resistance. It is
important toestimate <strong>the</strong> di erence <strong>of</strong> f values for <strong>the</strong> materials as a function <strong>of</strong> TLD thickness.
1
(1)

In this study, to estimate <strong>the</strong> di erence <strong>of</strong> <strong>the</strong> wall material e ect at <strong>the</strong> calibration, energy deposition
in LiF, BeO and CaF2 TLDs sandwiched with Te on, PMMA and Pyrex glass were calculated
for Co-60 gamma rays as a function <strong>of</strong> TLD thickness with a Monte Carlo transport code. The result
was compared with that <strong>of</strong> cavity ionization <strong>the</strong>ory.
2 Monte Carlo Calculation
A Monte Carlo transport code used was TIGER <strong>of</strong> ITS package [7]. The geometry available is
one-dimensional slab. Cut-o energy used was 1keV for photons and electrons. The TLD thickness
was varied from 0.1 mm to 10 mm. The thickness <strong>of</strong> <strong>the</strong> wall was determined so as to establish electric
equilibrium condition, that is, 3 to 4 mm. The statistical errors were all below 1%.
3 Results and Discussion
Figure 1 shows <strong>the</strong> energy deposition <strong>of</strong> LiF between Te on walls as a function <strong>of</strong> TLD thickness.
The values change smoothly from small cavity to large cavity value. On <strong>the</strong> o<strong>the</strong>r hand, Fig. 2
represents <strong>the</strong> result <strong>of</strong> Pyrex glass. The value decreases from small cavity value and increase at 1-mm
thickness. When using large cavity value for 0.1-mm thickness, 3% error will appear.
The reason <strong>of</strong> <strong>the</strong> depression observed at 1-mm thickness was attributable to <strong>the</strong> di erent rates
<strong>of</strong> electron attenuation from <strong>the</strong> wall and electron buildup in <strong>the</strong> TLD. Cavity <strong>the</strong>ory calculation was
<strong>the</strong>n made using larger value than ' value in <strong>the</strong> weighting functions d and d' as suggested by
Attix[8]:
and
in <strong>the</strong> equation
d 0 =
d =
R g
0 e; x dx
R g
0 dx
R g
0 (1 ; e; 0 x )dx
R g
0 dx
f = dfs + d 0 f l
where fs and f l are small and large cavity values, respectively, and g is a mean chord <strong>of</strong> length in <strong>the</strong>
cavity. The result is shown in Fig. 3, in which <strong>the</strong> similar shape having a depression to that in Fig.
2was obtained. The depression was also found in <strong>the</strong> experimental deta <strong>of</strong> LiF/aluminum[9].
The result <strong>of</strong> BeO between PMMA is indicated in Fig. 4. Monotonous change was observed. On
<strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> result <strong>of</strong> Pyrex glass is shown in Fig. 5, in which a depression larger than that in
Fig. 2was seen because <strong>the</strong> e ective atomic number <strong>of</strong> BeO is smaller than that <strong>of</strong> LiF.
Figure 6 shows <strong>the</strong> energy deposition <strong>of</strong> CaF2 between PMMA walls. Contrary to Fig. 2, a peak
was observed: <strong>the</strong> values rise until 1-mm thickness and decrease. This time by using smaller value
than ' value, cavity <strong>the</strong>ory calculation was made. Figure 7 shows <strong>the</strong> result. The similar shape
including a peak was observed in Fig. 6. If <strong>the</strong> large cavity value is used for <strong>the</strong> 0.4-mm thickness,
5% error will be introduced.
4 Conclusion
The calculation <strong>of</strong> energy deposition in LiF, BeO and CaF2 as a function <strong>of</strong> TLD thickness showed
a depression and a peak for LiF, BeO/Pyrex glass and CaF2/PMMA, respectively. The behavior was
reproduced by cavity <strong>the</strong>ory calculation. Practically, if <strong>the</strong> large cavity value is used, 3-5% errors will
appear for <strong>the</strong> mismatched combination. The errors are in uential when a high accuracy is required.
2
(2)
(3)
(4)

References
[1] Y. S. Horowitz, Thermoluminescence and <strong>the</strong>rmoluminescent dosimetry, Vol. 2, CRC Press, Inc.
Florida (1984)
[2] N. Nariyama and S. Tanaka, J. Nucl. Sci. Tech., 34(1997)137-147.
[3] T. E. Burlin, Br. J. Radiol., 39(1966)727-734.
[4] K. O'Brien, Phys. Med. Biol., 22(1977)836-851.
[5] A. F. Bielajew and D.W.O Rogers, AAPM Meeting, Lexington, USA (1986).
[6] Y. S. Horowitz, M. Moscovitch, J. M. Mack, H. Hsu and E. Kearsley, Nucl. Sci. Eng., 94(1986)233-
240.
[7] J. A. Halbleib, et al., SAND91-1634, (1992).
[8] F. H. Attix, Introduction to radiological physics and radiation dosimetry, John Wiley & Sons, Inc.
New York (1986)
[9] O. T. Ogunleye, F. H. Attix and B. R. Paliwal, Phys. Med. Biol., 25(1980)203-213.
Energy deposition (MeV cm2/g)
0.032
0.031
10 –1
10 0
LiF/Teflon
TLD thickness (mm)
Figure 1: Energy deposition <strong>of</strong> LiF between Te on walls as a function <strong>of</strong> TLD thickness
3
10 1

Energy deposition (MeV cm2/g)
0.032
0.031
10 –1
10 0
LiF/Pyrex glass
TLD thickness (mm)
Figure 2: Energy deposition <strong>of</strong> LiF between pyrex glass walls as a function <strong>of</strong> TLD thickness
f
0.95
0.94
0.93
0.92
10 –1
10 0
f=df s +d'f l
TLD thickness (mm)
Figure 3: fvalue calculation <strong>of</strong> LiF with cavity ionization <strong>the</strong>ory as a function <strong>of</strong> TLD thickness
4
10 1
10 1

Energy deposition (MeV cm2/g)
0.033
0.032
10 –1
10 0
BeO/PMMA
TLD thickness (mm)
Figure 4: Energy deposition <strong>of</strong> BeO between PMMA walls as a function <strong>of</strong> TLD thickness
Energy deposition (MeV cm2/g)
0.033
0.032
10 –1
10 0
BeO/Pyrex glass
TLD thickness (mm)
Figure 5: Energy deposition <strong>of</strong> BeO between Pyrex glass walls as a function <strong>of</strong> TLD thickness
5
10 1
10 1

Energy deposition (MeV cm2/g)
0.034
0.033
10 –1
10 0
CaF 2/PMMA
TLD thickness (mm)
Figure 6: Energy deposition <strong>of</strong> CaF2 between PMMA walls as a function <strong>of</strong> TLD thickness
f
1
0.95
0.9
10 –1
10 0
TLD thickness (mm)
f=df s+d'f l
Figure 7: fvalue calculation <strong>of</strong> CaF2 with cavity ionization <strong>the</strong>ory as a function <strong>of</strong> TLD thickness
6
10 1
10 1

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.182-192
A Convolution Method for Determining Temperature Rise
in Targets Struck by Beams <strong>of</strong> Various Size 1
W. R. Nelson, S. Ecklund and S. Rokni
Stanford Linear Accelerator Center,
P.O. Box 4349, Stanford, CA 94309, USA
Abstract
The temperature rise in targets struckby high-energy electrons can be calculated using <strong>the</strong> EGS4
code[1] simply by scoring <strong>the</strong> energy-deposition density in small cylindrical volumes centered upon,
and divided along, <strong>the</strong> direction <strong>of</strong> <strong>the</strong> beam. The temperature rise per pulse, Tp ( C/pulse), is
<strong>the</strong>n obtained for each volume using <strong>the</strong> speci c heat <strong>of</strong> <strong>the</strong> material, and <strong>the</strong> time dependence
<strong>of</strong> <strong>the</strong> heat ow can be calculated using conventional heat-transfer principles. Most typically <strong>the</strong>
beam size is accounted for in a straight-forward way by sampling <strong>the</strong> incident coordinates, but this
involves yet ano<strong>the</strong>r statistical process that can result in a signi cant increase in computation time
in order to reduce <strong>the</strong> variance, particularly for thick targets at very high energies. In this paper an
o -line convolution method is presented in which <strong>the</strong> symmetry <strong>of</strong> <strong>the</strong> geometry and <strong>the</strong> Gaussian
shape <strong>of</strong> <strong>the</strong> beam is used, along with a set <strong>of</strong> EGS4 runs made with a -function (i.e., pencil)
beam, to quickly obtain <strong>the</strong> temperature rise on <strong>the</strong> pulse for beams <strong>of</strong> any size. Examples are
given for studies that have recently been performed at SLAC in <strong>the</strong> design <strong>of</strong> <strong>the</strong> Next Linear
Collider.
1 Introduction
There are three important quantities which must be determined when designing targets capable
<strong>of</strong> handling large temperature-rise excursions. Namely, <strong>the</strong> temperature rise on <strong>the</strong> pulse, <strong>the</strong>
maximum stress at <strong>the</strong> central core and <strong>the</strong> steady-state temperature. The latter two, however, are
derivable from <strong>the</strong> temperature rise per pulse, T p ( C/pulse), and this, in turn, is obtained from <strong>the</strong>
energy-deposition density (i.e., fractional energy-loss per unit volume), dE=E 0dV , as follows[2] [3] [4]
:
where
T p = C NE 0
C p
1
E 0
dE
dV
= material density (g=cm 3 )
C p = heat capacity
N = electrons=pulse
6:0
A
(1)
(cal=g C)
E 0 = incident beam energy (MeV)
A = atomic weight (g=mole)
C = 1:6 10 ;13 =4:184 (cal=MeV): :
1 Work supported in part by <strong>the</strong> Department <strong>of</strong> Energy contract DE-AC03-76SF00515.
1

The maximum radial stress (r=0) in a pulse, r (psi), is <strong>the</strong>n obtained with
where
r = Ey Tp (2)
2(1 ; p)
p = Poisson ratio (0:25 to 0:30)
= coe cient <strong>of</strong><strong>the</strong>rmal expansion ( C ;1 )
E y = Young 0 s modulus (psi) :
The steady state temperature pro le, T (r), is given by equating <strong>the</strong> heat input, _ Q, inside a cylinder
<strong>of</strong> radius r to <strong>the</strong> heat conduction through <strong>the</strong> surface <strong>of</strong> <strong>the</strong> cylinder.
where
_Q = NE 0C
Z r
0
1
E 0
= pulse repetition rate (sec ;1 )
dE
dV 2 r dr = kT 2 r dT
(3)
dr
k T = <strong>the</strong>rmal conductivity coe cient (calsec ;1 cm ;1 C ;1 ) :
Therefore, one only needs to determine dE=E 0dV using <strong>the</strong> EGS4 code.
2 Accounting for <strong>the</strong> Radial Extent <strong>of</strong> <strong>the</strong> Beam
The straight-forward method <strong>of</strong> accounting for <strong>the</strong> beam size with EGS4 is to sample <strong>the</strong> incident
coordinates (X IY I) over an appropriate distribution, such as a Gaussian, just prior to each call to
SUBROUTINE SHOWER. However, several problems arise from this direct method. First <strong>of</strong> all, at high
energies (multi-GeV) and for thick targets (many radiation lengths), a large amount <strong>of</strong> computer time
is spent just tracking <strong>the</strong> particles in <strong>the</strong> shower to <strong>the</strong> very low energies required in determining <strong>the</strong>
energy-deposition density itself. A limit must <strong>the</strong>n be imposed on <strong>the</strong> number <strong>of</strong> incident particles
that can be sampled, for any given beam size, and <strong>the</strong> end result is that <strong>the</strong> radial distribution for <strong>the</strong>
temperature rise contains large uctuations.
<strong>Second</strong>ly, <strong>the</strong> calculation has to be run over and over again for each <strong>of</strong> <strong>the</strong> beam-spot sizes <strong>of</strong>
interest. Clearly, <strong>the</strong> time is better spent performing EGS4 calculations with good statistics, using a
(X I) (Y I) (i.e., pencil beam) input, and subsequently performing convolution-type integrations for
each <strong>of</strong> <strong>the</strong> beam sizes <strong>of</strong> interest.
The convolution method that we have developed applies to round Gaussian beams|i.e.,
x = y = . It was developed by Ecklund and Nelson in 1981 [5] and subsequently used in <strong>the</strong>
<strong>the</strong>sis by Donahue [6] .
3 Gaussian Convolution <strong>of</strong> Pencil Beams
The general form <strong>of</strong> a one-dimensional Gaussian distribution is
f(x) = 1
p 2
Z 1
;1
(x;x)
;
e 2 2 dx: (4)
If we assume that <strong>the</strong> energy-deposition density <strong>of</strong> <strong>the</strong> pencil beam is given by
W 0(r)
1
E 0
2
dE
dV
(5)

<strong>the</strong>n <strong>the</strong> convoluted energy-deposition density is
Z
W (r) =f W0 = f(x)W0(x) dx : (6)
For a two-dimensional Gaussian distribution in radial coordinates (x = r cos , y = r sin ),
W (r) =
=
1
Z 1
2 2
0
Z 1
1
2 2
0
dr
Z 2
d re ;( r2 +r 2 ;2rr cos( ; ))
2 2 W 0(r)
0
rdre ;(r;r)2
2 2 Z 2
W0(r) where we have taken = 0 without loss <strong>of</strong> generality.
0
d e
rr ; (1;cos )
Since <strong>the</strong> EGS4 output is in <strong>the</strong> form <strong>of</strong> a histogram averaged over radial bins, we have
W (i)
Z ri+1
r i
2
(7)
W (r) rdr : (8)
The convoluted distribution with <strong>the</strong> same binning is <strong>the</strong>n
W (i) = X
MijW (j) (9)
where
M ij =
1
2 2 (ri+1 ; r2
i )
Z Z ri+1 rj+1
r i
r j
j
rdr rdre ;(r;r)2
2 2
Z 2
0
rr ; 2 e (1;cos ) d : (10)
The integral over can be reduced to a modi ed Bessel function, I 0. The double integration is done
numerically, taking special care (along i = j) to provide <strong>the</strong> quadrature routine with an integrand that
is not ill-behaved over <strong>the</strong> bin in question. The above equation assumes that <strong>the</strong> energy-deposition
density does not vary signi cantly over <strong>the</strong> width <strong>of</strong> each bin.
4 Computer Codes for O ine Convolution
The following computer codes have been written in order to demonstrate <strong>the</strong> convolution technique
presented in this paper.
EGS4 User Code to create energy-deposition density data for small radial bins at various depths
into <strong>the</strong> target. The code can be run with a pencil beam input, =0:0. in order to generate <strong>the</strong>
W (j) required by <strong>the</strong> o -line convolution scheme. It can also be run with a Gaussian incident
beam, e.g., =10or = 100 microns.
A program that creates <strong>the</strong> Gaussian convolution matrix elements, M ij, foragiven set <strong>of</strong> beam
, and a second program to check <strong>the</strong> P j M ij =1:0 for any i-bin.
A program to convolute W (j) and M ij and produce a new output le for plotting <strong>the</strong> new
dE=E 0dV (left ordinate) and <strong>the</strong> corresponding temperature rise, T p ( C/pulse) (right ordinate).
A common element with all <strong>of</strong> <strong>the</strong>se codes is that <strong>the</strong>y must have <strong>the</strong> same radial binning structure.
In our example case (see Appendix 1), <strong>the</strong> target consists <strong>of</strong> 17 cylinders with radii <strong>of</strong> 1, 3, 5, 7, 10,
30, . . . , 3000, 5000, 7000 10000 microns.
These codes are <strong>of</strong> a general enough nature to be <strong>of</strong> use in a variety <strong>of</strong> temperature-rise (and o<strong>the</strong>r)
problems and can be downloaded from SLAC 2 .
2 The les are kept in /afs/slac.stanford.edu/public/groups/egs4/Convolution and can be obtained using anonymous
ftp|i.e., ftp ftp.slac.stanford.edu followed by cd groups/egs4/Convolutions).
3

4.1 EGS4 User Code to determine energy-deposition density, W (j)
A general-purpose EGS4 User Code, called ucRTZ temp.mortran, has recently been written at
SLAC foracylinder-slab geometry, with input read in from a .data le. This code is similar to <strong>the</strong>
DOSRZ code by <strong>the</strong> National Research Council <strong>of</strong> Canada, which comes with <strong>the</strong> standard distribution
<strong>of</strong> EGS4, but it is tailored for more general use o<strong>the</strong>r than dosimetry. For <strong>the</strong> problem <strong>of</strong>
interest in this paper, ano<strong>the</strong>r User Code was cloned from ucRTZ temp.mortran and given <strong>the</strong> name
ucRTZ temp spot.mortran, <strong>the</strong> only real di erence being <strong>the</strong> addition <strong>of</strong> <strong>the</strong> capability <strong>of</strong> sampling
<strong>the</strong> incident beam-spot size from a Gaussian distribution. Associated with this code is <strong>the</strong> input le
ucRTZ temp spot.data, an example <strong>of</strong> which is provided in Appendix 1.
In <strong>the</strong> section below entitled Veri cation <strong>of</strong> Convolution Method we will use ucRTZ temp to generate
10 computer runs, each with 1000 incident electrons, using two modes:
Pencil-beam mode: With =0:0 to create an output histogram, from <strong>the</strong> concatenation <strong>of</strong> ten
runs, to be used as input for <strong>the</strong> convolution code.
Direct-sampling mode: With set to ei<strong>the</strong>r 10 or 100 microns to create an output histogram,
again a concatenation <strong>of</strong> ten runs, that can be compared with <strong>the</strong> results <strong>of</strong> <strong>the</strong> convolution (at
10 and 100 microns).
4.2 Programs to create (and check) matrix elements, M ij
After getting <strong>the</strong> basic set <strong>of</strong> histogram data|i.e., ten separate runs <strong>of</strong> <strong>the</strong> User Code with
di erent random number seeds|<strong>the</strong> next step is to create a set <strong>of</strong> matrices for each <strong>of</strong> <strong>the</strong> values
<strong>of</strong> required in <strong>the</strong> problem. To facilitate this a program called RTZ mat.mortran was created,
documentation for which is contained within <strong>the</strong> code itself. Ano<strong>the</strong>r code, RTZ matck.mortran, has
also been created to check that <strong>the</strong> P j M ij =1:0 for any i-bin.
4.3 Program to convolute W (j) and M ij
The program that performs <strong>the</strong> actual convolution is called RTZ temp spot.mortran. As described
above, it requires <strong>the</strong> following two input les:
RTZ temp spot.data
RTZ mat.data
The rst le is a concatenation <strong>of</strong> EGS4 runs, ten in our example case, each created with <strong>the</strong> code
ucRTZ temp spot.mortran and its input data le ucRTZ temp spot.data. The second le is a concatenation
<strong>of</strong> <strong>the</strong> matrix output from one or more runs <strong>of</strong> RTZ mat.mortran for each <strong>of</strong> interest. In
our case, = 3.16, 10, 20, 30, 50, 100, 500, 1000, 2000 and 3000 microns. Note, however, that we will
only make use<strong>of</strong> = 10 and 100 microns in our veri cation <strong>of</strong> <strong>the</strong> method, which is presented next.
5 Veri cation <strong>of</strong> Convolution Method
If a beam-spot size is directly sampled prior to each SHOWER call in EGS4 a lot <strong>of</strong> computer time
is required in order to get adequate statistics, especially at high-energies, low cut-o s, and for thick
materials. Hence, <strong>the</strong> reason for developing <strong>the</strong> convolution method in <strong>the</strong> rst place. Never<strong>the</strong>less,
<strong>the</strong> direct-sampling method itself provides us with a way to verify that <strong>the</strong> convolution technique
works, provided that we limit <strong>the</strong> check to reasonably low-energy incident beams (note: a 1-GeV
shower takes 100 times less time than does a 100-GeV shower).
Using <strong>the</strong> ucRTZ temp spot User Code, we have done this veri cation for an 8-r.l. thick copper
target (1-cm radius) struck by 1-GeV electron beams. The target is broken up along Z into eight
cylindrical slabs, each cylinder composed <strong>of</strong> 17 subcylinders, as indicated earlier (see Appendix 1).
4

Accordingly, this same radial structure was also employed with <strong>the</strong> RTZ temp spot.mortran and and
RTZ mat.mortran codes.
The results are shown in Figures 1 and 2 for beam sizes <strong>of</strong> 10 and 100 microns, respectively. The
convoluted results (solid curves) are seen to be in excellant agreement with <strong>the</strong> directly-sampled results
(histograms), at both <strong>the</strong> front (0-1 r.l.) and back (7-8 r.l.) <strong>of</strong> <strong>the</strong> target, <strong>the</strong>reby demonstrating that
<strong>the</strong> convolution method works.
Figure 1: Comparision <strong>of</strong> direct-sampling (histogram) and convolution (solid curve) methods for a 1-GeV beam
striking an 8-radiation length Cu cylinder: x = y = 10 microns.
6 Temperature-Rise Examples from <strong>the</strong> NLC
The beam parameters for <strong>the</strong> Next Linear Collider (NLC)[7] create a very serious problem with
respect to <strong>the</strong> pulse temperature-rise in objects that <strong>the</strong> beam may inadvertantly strike. To illustrate
this problem using <strong>the</strong> codes described in this paper, we considered a pencil-beam energy <strong>of</strong> 500 GeV
impinging upon a 10-r.l. long Cu cylinder having a radius <strong>of</strong> 1 cm. The energy-deposition density and
<strong>the</strong> corresponding pulse temperature rise are shown as a function <strong>of</strong> radius in Figures 3 through 5, for
<strong>the</strong> beginning, middle and end <strong>of</strong> <strong>the</strong> target, respectively.
A full beam <strong>of</strong> 10 12 electrons/pulse was used in <strong>the</strong>se calculations and one sees that even in <strong>the</strong>
rst layer <strong>of</strong> <strong>the</strong> target (Figure 3), where <strong>the</strong> shower has yet to develop fully, <strong>the</strong> temperature rise on
<strong>the</strong> pulse exceeds 20-million C/p for <strong>the</strong> case <strong>of</strong> <strong>the</strong> pencil beam (histogram). In order to get <strong>the</strong>
temperature down to something more reasonable, say 100 C/p, <strong>the</strong> convolution curves tell us that
<strong>the</strong> beam would have to be larger than 500 microns.
As <strong>the</strong> shower develops in <strong>the</strong> target, multiple scattering also leads to a lateral spread <strong>of</strong> <strong>the</strong>
energy-deposition density. In Figures 4 and 5 we see that, indeed, <strong>the</strong> multiple scattering has some
e ect on reducing <strong>the</strong> temperature rise for incident beams with small emittance, but <strong>the</strong> shower
multiplication is just too strong for large beams (e.g., 500 microns), resulting in temperatures several
orders <strong>of</strong> magnitude higher deep in <strong>the</strong> shower, relative to what <strong>the</strong>y were near <strong>the</strong> surface.
5

Figure 2: Comparision <strong>of</strong> direct-sampling (histogram) and convolution (solid curve) methods for a 1-GeV beam
striking an 8-radiation length Cu cylinder: x = y = 100 microns.
Figure 3: Energy-deposition density and temperature rise as a function <strong>of</strong> radius at <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> target
( z = 0-1 r.l.)
6

Figure 4: Energy-deposition density andtemperature rise as a function <strong>of</strong> radius in <strong>the</strong> middle <strong>of</strong> <strong>the</strong> target
( z = 4-5 r.l.)
Figure 5: Energy-deposition density and temperature rise as a function <strong>of</strong> radius at <strong>the</strong> end <strong>of</strong> <strong>the</strong> target ( z =
9-10 r.l.)
7

To show <strong>the</strong> dramatic e ect <strong>of</strong> shower multiplicity onbeams <strong>of</strong> all sizes, we plot in Figure 6 <strong>the</strong>
maximum temperature rise as a function <strong>of</strong> depth, for <strong>the</strong> pencil beam and for <strong>the</strong> convolution curves
<strong>of</strong> each <strong>of</strong> <strong>the</strong> ten incident beams considered. Also shown is <strong>the</strong> melting temperature <strong>of</strong> Cu (dashed
line) and its stress limit (dotted line)[7].
Figure 6: Pulse temperature rise vs. target depth for a 500 GeV beam in Cu
From this gure it becomes clear that even beams as large as 3000 microns could damage <strong>the</strong>
copper target in a single pulse. The question <strong>the</strong>n becomes: \Is <strong>the</strong>re a material that is more suitable
for full beams <strong>of</strong> <strong>the</strong> order <strong>of</strong> 10 12 electrons/pulse?"
To answer this question we performed a similar analysis for Al and Be, with <strong>the</strong> results shown
in Figures 7 and 8, respectively. The results show that aluminum and beryllium might be able to
withstand a single pulse <strong>of</strong> <strong>the</strong> order <strong>of</strong> 1000 and 500 microns, respectively.
8

Figure 7: Pulse temperature rise vs. target depth for a 500 GeV beam in Al
Figure 8: Pulse temperature rise vs. target depth for a 500 GeV beam in Be
9

7 Conclusion
Running thick-target EGS4 calculations at high energies can be costly in computer time. That is,
<strong>the</strong> higher <strong>the</strong> energy <strong>the</strong> larger <strong>the</strong> shower multiplicity, implying that more particles must be followed
until <strong>the</strong>y reach <strong>the</strong>ir energy cuto s. This, in turn, makes it di cult and time-consuming to study
<strong>the</strong> temperature-rise in targets, where <strong>the</strong> size <strong>of</strong> <strong>the</strong> beam must also be incorporated into <strong>the</strong> Monte
Carlo calculation in order to study real beams. Direct sampling over <strong>the</strong> beam size simply introduces
yet ano<strong>the</strong>r statistical variance into <strong>the</strong> results, requiring longer and longer jobs to be run.
In <strong>the</strong> study presented in this paper, we have created a convolution technique in which a reasonable
set <strong>of</strong> computer runs, using a -function incident beam, can be used toge<strong>the</strong>r with a predetermined
set <strong>of</strong> beam matrices to obtain <strong>the</strong> temperature rise for a large number <strong>of</strong> beam sizes. We have
demonstrated, at 1 GeV, that <strong>the</strong> results are consistent with <strong>the</strong> more laborious \direct sampling"
approach, but <strong>the</strong> technique should be viable at any energy.
Also presented in this paper are some examples <strong>of</strong> <strong>the</strong> use <strong>of</strong> <strong>the</strong> convolution technique for
temperature-rise studies for <strong>the</strong> Next Linear Collider, where <strong>the</strong> basic problem <strong>of</strong> very-small emittance
beams <strong>of</strong> high-intensity and high-energy is shown to be formidable.
References
[1] W. R. Nelson, H. Hirayama and D. W. O. Rogers, \The EGS4 Code System", SLAC Report
265 (1985).
[2] H. DeStaebler, \Temperature Calculations for <strong>the</strong> Positron Target", SLAC Internal Report CN-
21 (1980).
[3] H. DeStaebler, \Calculations for Positron Target Test in ESA" SLAC Internal Report CN-23
(1980).
[4] H. DeStaebler, \More Calculations for Positron Target Test in ESA" SLAC Internal Report
CN-24 (1980).
[5] S. Ecklund and W. R. Nelson, \Energy Deposition and Thermal Heating in Materials Due to
Low Emittance Electron Beams", SLAC Internal Report CN-135 (1981).
[6] R. J. Donahue and W. R. Nelson, \Alternative Positron-Target Design for Electron-Positron
Colliders", LBL Internal Report LBL-30724 (1991) [and SLAC-PUB-5702 (1991)].
[7] \Zeroth-Order Design Report for <strong>the</strong> Next Linear Collider", SLAC Report 474 (May 1996).
10

ucRTZ_temp_spot.data
Appendix 1
Representative example <strong>of</strong> <strong>the</strong> data-input le: ucRTZ temp spot.data
1 NMED (I10)
CU MEDIA(J,1) (24A1)
0.0 0.0 ECUTin,PCUTin (Kinetic) (MeV) (2F10.0)
17 1 8 Imax,Jmax,Kmax (3I10)
0.0001 I=1 CYRAD (cm) (F10.0)
0.0003 =2
0.0005 =3
0.0007 =4
0.0010 =5
0.0030 =6
0.0050 =7
0.0070 =8
0.0100 =9
0.0300 =10
0.0500 =11
0.0700 =12
0.1000 =13
0.3000 =14
0.5000 =15
0.7000 =16
1.0000 =17=Imax
0.0 J=1=Jmax THEPL (degrees) (F10.0) (no azimuthal)
0.0 K=1 ZPL (r.l. here, hard coded to cm in program)
1.0 =2
2.0 =3
3.0 =4
4.0 =5
5.0 =6
6.0 =7
7.0 =8=Kmax
8.0 =9=Kmax+1
1 17 1 1 1 8 1 0.0 CU
0.0 0.0 0.0 Xin,Yin,Zin (3F10.0)
1 1 1 Iin,Jin,Kin (3I10)
0.0 0.0 1.0 Uin,Vin,Win (3F10.0)
1 1 IXX,JXX (2I10)
blank card (required EOF)
1000 0.0100 Ncases,Sigma (I10,F10.0) (Sigma=0.0 implies pencil beam)
1000.0 -1 0 EKEin(MeV),IQin,Isamp (F10.0,2I10)
1 2 0 0 IBRDST,IPRDST,IBRSPL,NBRSPL (4I5)
0 0 0 0 0.0 IPLC,IBCA,ILCA,IOLDTM,BLCMIN (4I5,F10.0)
11

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.193-198
Application <strong>of</strong> EGS4 for Evaluation <strong>of</strong> Material Damage
due to Gamma-ray Irradiation
O. Sato, T. Tobita 1 and M. Suzuki 1
Mitsubishi Research Institute, Inc.
2-3-6 Ohtemachi, Chiyoda-ku, Tokyo, 100-8141, Japan
1 Japan Atomic Energy Research Institute
Tokai-mura, Ibaraki-ken, Japan, 319-1195
Abstract
An EGS4 user code named UCDPA was developed for <strong>the</strong> simulation <strong>of</strong> material damages by
<strong>the</strong> electrons and photons considering electromagnetic cascade. The calculated depth distributions
<strong>of</strong> dpa in iron slab were compared to <strong>the</strong> measurements <strong>of</strong> material hardening due to 2 and 2.5MeV
electron beam irradiations. The calculated dpa distributions and <strong>the</strong> measured hardening distributions
were in a similar shape which have a peak at about 0.2mm from irradiated surface. The
depth distributions <strong>of</strong> dpa were also calculated for photons from 0.7 to 10 MeV.
1 Introduction
The unexpected acceleration <strong>of</strong> radiation-induced embrittlementwas discovered in <strong>the</strong> surveillance
materials <strong>of</strong> High Flux Isotope Reactor (HFIR) in 1986[1]. A lot <strong>of</strong> studies have been made to explain
this phenomena, and <strong>the</strong> gamma-ray induced reactions were supposed to be <strong>the</strong> dominant process[2],[3].
Because <strong>the</strong> energy required to displace atoms from metallic lattice (Lindhard cuto energy Ed) is
few ten eV, <strong>the</strong> electrons produced from gamma-ray can knock-on <strong>the</strong> atoms when <strong>the</strong> electron energy
is above several hundred keV. In preceding studies, <strong>the</strong> material damages due to gamma rays have
been evaluated with <strong>the</strong> primary knock-on atom (PKA) or displacement per atom (dpa) cross sections
for photons and photon ux in materials. These damage cross sections have been calculated assuming
<strong>the</strong> secondary electron spectrum in in nite media <strong>of</strong> metals, <strong>the</strong>refore <strong>the</strong> damage distributions in
depth <strong>of</strong> materials were not considered. These studies also have not been considered <strong>the</strong> contribution
<strong>of</strong> electrons produced at deep position by bremsstrahlang photons.
We developed an user code for EGS4[4] named UCDPA for <strong>the</strong> simulation <strong>of</strong> material damages
by <strong>the</strong> electrons and photons considering electromagnetic cascade. The user code calculates <strong>the</strong> PKA
and dpa cross sections <strong>of</strong> electrons with <strong>the</strong> kinetics <strong>of</strong> electron-atom collisions, and calculates damage
distributions in a semi-in nite slab geometry. We calculated <strong>the</strong> dpa depth distributions in iron slab
irradiated by 2 or 2.5MeV electrons and up to 10MeV photons with <strong>the</strong> user code.
2 Displacement Cross Sections
The mechanism <strong>of</strong> gamma-ray damage to metals is schematically shown in Fig.1. When <strong>the</strong> metal
irradiated by gamma-rays above several hundreds keV, <strong>the</strong> atoms <strong>of</strong> metal su er <strong>the</strong> collision with
energitic electrons produced by compton scatterings or pair creations. Because <strong>the</strong> binding energy <strong>of</strong>
atoms in metal lattice (displacement energy) is from 20eV to 40eV, and mass ratios <strong>of</strong> electron and
metal atoms are about 10 5 , <strong>the</strong> electrons above 400keV can remove an atom from <strong>the</strong> lattice. The
removed atom is so called "Primary Knock-on Atom (PKA)". The PKA cross section, <strong>the</strong> number <strong>of</strong>
1

PKA's per unit uence <strong>of</strong> electron, are calculated with following formula derived from Mott scattering
cross section,
where,
P = 4
1
4 2
Za0ER
"
mc 2
Tm
Ed
Z :atomic number <strong>of</strong> target atom,
2
; 1
a0 :Bohr radius (= 0:529 10 ;10 m),
ER :Rydberg energy : e 2 =2a0 =13:6eV,
=Z/137,
2 ln Tm
:ratio <strong>of</strong> electron velocity to light velocity,
Ed
+
(
2
s
Tm
Tm =2 m M E
mc 2 (E +2mc 2 )(maximum kinetic energy <strong>of</strong> recoil atom),
M :mass <strong>of</strong> target atom,
m :mass <strong>of</strong> electron,
E :electron kinetic energy,
Ed :displacement energy.
Ed
; 1
!
; ln Tm
Ed
If <strong>the</strong> recoil atom has <strong>the</strong> kinetic energy above <strong>the</strong> displacement energy, secondary atoms can be
knocked-on by PKA and removed from <strong>the</strong> lattice. The number <strong>of</strong> secondary displaced atoms per
PKA <strong>of</strong> kinetic energy T is approximately calculated as follows,
8
><
(T )=
>:
0 T

4 Electron Irradiation Experiment and Analysis
The UCDPA was applied to calculate <strong>the</strong> dpa distribution in a specimen <strong>of</strong> Fe-0.6wt%Cu alloy
used for <strong>the</strong> experiment performed by JAERI[5] using 3MV single-ended electron accelerator <strong>of</strong> TIARA
(JAERI-Takasaki). In this experiment, 5 10mm specimen was irradiated by 2MeV-10mA broad
parallel beam <strong>of</strong> electrons. The specimen was heated to 250 C, and placed in vacuum. The di erence
<strong>of</strong> hardenings between irradiated (5-15 hours) and un-irradiated specimen ( v) were measured.
The dpa and PKA distribution along <strong>the</strong> beam axis was calculated using UCDPA to compare <strong>the</strong>
measured distribution <strong>of</strong> hardening. Fig.3 shows <strong>the</strong> calculated dpa and PKA distribution in an iron
slab for electron energy <strong>of</strong> 2, 2.5 and 10MeV assuming that its displacement energy is 40eV. The dpa
and PKA was same for <strong>the</strong> electron energy <strong>of</strong> 2MeV and 2.5MeV, because <strong>the</strong> kinetic energy <strong>of</strong> PKA
was lower than displacement energy. The peak <strong>of</strong> dpa was observed at <strong>the</strong> depth <strong>of</strong> about 0.2mm from
irradiated surface where <strong>the</strong> total number <strong>of</strong> primary and secondary electrons was maximum. The
measured peak <strong>of</strong> hardening was also observed at <strong>the</strong> depth <strong>of</strong> few-hundred mm.
5 DPA Distribution From High Energy Photons
Depth distributions <strong>of</strong> dpa in an iron slab caused by photon irradiation were calculated for <strong>the</strong>
photon energy from 700keV to 10MeV. In Fig.4 and Fig.5 are shown <strong>the</strong> calculated dpa distributions
at depth from 0 to 10cm and <strong>the</strong> peak values <strong>of</strong> dpa at each photon energy, respectively. The peak
<strong>of</strong> dpa appeared at more deep position and <strong>the</strong> width <strong>of</strong> peak became broader at <strong>the</strong> higher photon
energy. The dpa decreases in exponential with depth at any photon energies. The peak value <strong>of</strong> dpa
increases linearly with photon energy above 2MeV, and it increases in exponential below 2MeV.
6 Conclusion
UCDPA is a tool to evaluate <strong>the</strong> depth distribution <strong>of</strong> <strong>the</strong> material damage caused by gamma-ray
or electron irradiation. The calculated dpa distributions showed that <strong>the</strong> peak <strong>of</strong> dpa is at <strong>the</strong> inside
<strong>of</strong> materials. The detailed estimation <strong>of</strong> material damage in nuclear reactors, such asreactorvessels,
shrouds, or o<strong>the</strong>r structures, can be performed by <strong>the</strong> combination <strong>of</strong> <strong>the</strong> neutron-gamma coupled
shielding calculations and gamma-ray damage calculations with UCDPA.
References
[1] R. D. Cheverton, J. G. Merkle and R. K. Nanstad, eds., \Evaluation <strong>of</strong> HFIR Pressure-Vessel
Integrity Considering Radiation Embrittlement", ORNL/TM-10444, 1988.
[2] K. Farrell, S. T. Mahmod, R. E. Stoller and L. K. Mansur, \An evaluation <strong>of</strong> low temperature
radiation embrittlement mechanism in ferritic alloys," J. Nucl. Mater. 210(1994)261-281.
[3] I. Remec, J. A. Wang, F. B. K. Kam and K. Farrell, \E ects <strong>of</strong> gamma-induced displacements
on HFIR pressure vessel materials," J. Nucl. Mater. 217(1994)258-268.
[4] W. R. Nelson, H. Hirayama, D. W. O. Rogers, \The EGS4 Code System", SLAC{65, Stanford
Linear Accelerator Center,1985.
[5] T. Tobita, M. Suzuki, Y. Idei, A. Iwase and K. Aizawa, \Study on -ray Induced Embrittlement
<strong>of</strong> Light Water Reactor Pressure Vessel steel," Trans. Int. Conf. Struct. Mech. React. Technol.
15(10)(1999)X.205-X.212.
3

Figure 2: Calculated PKA and dpa cross sections <strong>of</strong> iron for electrons. Displacement energy (Ed) is assumed
to be 40eV.
dpaorPKA[10 -24 /Incidentphoton]
10 2
10 0
10 -2
10 -4
10 -6
E=10MeV(dpa)
E=10MeV(PKA)
E=2.5MeV(dpa=PKA)
E=2.0MeV(dpa=PKA)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Depth(cm)
Figure 3: Calculated depth distribution <strong>of</strong> dpa in iron slab irradiated by 2.0, 2.5 and 10MeV broad parallel
electron beam. The uctuations at deep position are due to statistical errors <strong>of</strong> Monte Carlo calculations.
5

dpa[10 -24 /Incidentphoton]
10 1
10 0
10 -1
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Depth(cm)
Eγ=10MeV
Eγ=5MeV
Eγ=2MeV
Eγ=1MeV
Eγ=700keV
Figure 4: Calculated depth distribution <strong>of</strong> dpa in iron slab irradiated by 700keV - 10MeV broad parallel photon
beam. The uctuations for lower photon energies are due to statistical errors <strong>of</strong> Monte Carlo calculations.
maximumdpainiron[10 -24 /Incidentphoton]
10 1
10 0
10 -1
10 -2
10 -3
10 -4
10 -5
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Photonenergy(MeV)
Figure 5: Maximum dpa in iron slab irradiated by 700keV - 10MeV photons.
6

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.199-208
Examination <strong>of</strong> <strong>the</strong> X-Ray Piping Diagnostic System
using EGS4 (Examination <strong>of</strong> <strong>the</strong> Film and Iron Rust)
G. Kajiwara
Shimizu Corporation, Institute <strong>of</strong> Technology
3-4-17, Etchujima, Koto-ku, Tokyo, 135-8530 JAPAN
Abstract
In <strong>the</strong> X-ray piping diagnosis system, <strong>the</strong> old pipe is taken X-ray photograph, and from <strong>the</strong>
density <strong>of</strong> <strong>the</strong> image <strong>of</strong> <strong>the</strong> pipe in <strong>the</strong> lm, <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> pipe is measured using <strong>the</strong>
relationship between <strong>the</strong> density and <strong>the</strong> thickness.
First, as for <strong>the</strong> relationship between <strong>the</strong> density and <strong>the</strong> absorbed energy in <strong>the</strong> lm, though
good agreement was obtained last year, it is improved more by making energy bin smaller in <strong>the</strong>
calculation <strong>of</strong> EGS4. The reason <strong>of</strong> <strong>the</strong> agreement was researched and understood.
Next, using EGS4, <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> steel was carried out which iscovered
with <strong>the</strong> rust, using <strong>the</strong> element analysis result <strong>of</strong> <strong>the</strong> rust sample that was collected in <strong>the</strong> old
pipe.
When <strong>the</strong> thickness changes, <strong>the</strong> rate for <strong>the</strong> energy absorption <strong>of</strong> <strong>the</strong> steel and <strong>the</strong> rust layer
changes. This relationship between <strong>the</strong> energy absorption and <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> layers is expressed
approximately in <strong>the</strong> formula. It will be re ected on <strong>the</strong> diagnosis <strong>of</strong> <strong>the</strong> pipe.
1 Introduction
Since its development about ten years ago, <strong>the</strong> X-ray piping diagnostic system used for renewal
construction or planning has been an e ective and practical system for determining <strong>the</strong> number <strong>of</strong>
residual years <strong>of</strong> old piping, more than 500 actual results. The thickness <strong>of</strong> <strong>the</strong> wall in an old pipe is
estimated using <strong>the</strong> relationship between steel thickness and lm density. However, <strong>the</strong> system does
not work when <strong>the</strong> density <strong>of</strong> <strong>the</strong> steel changes due to <strong>the</strong> accumulation <strong>of</strong> rust. Electron Gamma
Shower 4 (EGS4) was used to overcome this problem.
2 X-ray Piping Diagnostic System
2.1 System outline
Fig.1 shows <strong>the</strong> X-ray piping diagnostic system [1]. Old pipe settled in a building is taken X-ray
photograph and <strong>the</strong> lm is observed and evaluated whe<strong>the</strong>r it is necessary to be analyzed fur<strong>the</strong>r or
not. When it is judged it is no use to analyze because <strong>the</strong>re is no corrosion or so, <strong>the</strong>n <strong>the</strong> report will
be made. When <strong>the</strong> analysis is necessary because damage seems to be proceeding, lms are put in <strong>the</strong>
analysis device and <strong>the</strong> residual year is computed through <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> pipe.
2.2 Main logic
Main logic <strong>of</strong> <strong>the</strong> analytical part is shown in Fig.2. Standard pipe that has four-step thickness is
set parallel to <strong>the</strong> pipe that is inspected. On <strong>the</strong> developed lm four points are selected and <strong>the</strong> curve
which is based on <strong>the</strong> four points is drawn on <strong>the</strong> thickness and density plane. Most damaged point is
1

selected and <strong>the</strong> density is measured, <strong>the</strong> point <strong>of</strong> density reaches <strong>the</strong> point <strong>of</strong>thickness through <strong>the</strong>
density-thickness curve.
There is a weak point in this system because <strong>the</strong> in uence <strong>of</strong> <strong>the</strong> rust appeared on <strong>the</strong> inner surface
<strong>of</strong> <strong>the</strong> pipe was neglected, because <strong>the</strong>re was no way to get <strong>the</strong>n. And when I knew <strong>the</strong> existence <strong>of</strong>
EGS4 three years ago, <strong>the</strong> trial was started.
3 The Improvement <strong>of</strong> <strong>the</strong> Spectrum
3.1 Improvement <strong>of</strong> <strong>the</strong> spectrum
Fig.3 shows <strong>the</strong> new X-ray spectrum and <strong>the</strong> old spectrum obtained last year, which showed good
agreement <strong>of</strong> <strong>the</strong> energy absorption and <strong>the</strong> density <strong>of</strong><strong>the</strong> lm.The new one is smooth in its shape,
and it is adopted in simulation in this paper.
3.2 The agreement <strong>of</strong> <strong>the</strong> density <strong>of</strong> <strong>the</strong> lm and <strong>the</strong> energy absorption
As for <strong>the</strong> agreement <strong>of</strong> <strong>the</strong> density <strong>of</strong> <strong>the</strong> lm and <strong>the</strong> energy absorption <strong>of</strong> <strong>the</strong> lm, <strong>the</strong>oretical
veri cation is delayed. An investigation result is described here to make <strong>the</strong> reason clear [2].
D is expressed approximately as following under conditions stated underneath.
D = log 10(I0=I) =kaN[1 ; exp(;aF )] (1)
N: Number <strong>of</strong> crystallized particles per unit area <strong>of</strong> <strong>the</strong> emulsion
a: average projection area <strong>of</strong> <strong>the</strong> crystallized particle
k: coe cient =log10e
F: particle uence
Conditions
1. The incidence angle <strong>of</strong> charged particles into <strong>the</strong> lm is perpendicular and <strong>the</strong> scattering and
<strong>the</strong> absorption in <strong>the</strong> emulsion is neglected.
2. Average area <strong>of</strong> a crystallized particle is a.
3. The collision between incident particle and crystallized particle surely yields <strong>the</strong> latent image.
In case F is small, <strong>the</strong> right side <strong>of</strong> <strong>the</strong> equation (1) becomes
Therefore D becomes
4 Simulation <strong>of</strong> <strong>the</strong> Steel with <strong>the</strong> Rust
4.1 Analysis <strong>of</strong> <strong>the</strong> rust
1 ; exp(;aF ) ! aF: (2)
D = ka 2 NF / F / Absorbed energy (3)
Table.1 shows <strong>the</strong> result <strong>of</strong> analysis <strong>of</strong> rust in <strong>the</strong> pipe. The rust was collected from <strong>the</strong> old pipe
removed for renewal in <strong>the</strong> building. Two kinds <strong>of</strong> pipe were selected, <strong>the</strong> pipe for <strong>the</strong> cooling water <strong>of</strong>
air-conditioning and <strong>the</strong> pipe for supplying water. The supplying water pipe was preferred. Whe<strong>the</strong>r
it is <strong>the</strong> representative <strong>of</strong> all <strong>the</strong> supplying water pipe, no one knows, and it isn't a problem here.
4.2 The analysis <strong>of</strong> <strong>the</strong> X-ray photograph <strong>of</strong> <strong>the</strong> steel with rust
The rust was taken X-ray photograph. Fig.4 shows <strong>the</strong> arrangement <strong>of</strong> <strong>the</strong> materials in taking
X-ray photograph, X-ray apparatus was moved every time X-ray photograph was taken to set <strong>the</strong>
incidence angle into <strong>the</strong> lm perpendicular. The rust was ga<strong>the</strong>red on <strong>the</strong> steel block and was enclosed
with <strong>the</strong> plastic plate.
2

4.3 The simulation <strong>of</strong> <strong>the</strong> steel with rust
Fig.5 shows <strong>the</strong> thickness vs. density <strong>of</strong> <strong>the</strong> rust on <strong>the</strong> X-ray photograph. Two lines are drawn
straight, and it seems 3 mm <strong>of</strong> <strong>the</strong> rust on <strong>the</strong> steel <strong>of</strong> 15 mm can be discriminated clearly, probably
1 mm can be discriminated.
Fig.6 shows <strong>the</strong> simulation result <strong>of</strong> <strong>the</strong> same model that was taken X-ray photograph, but <strong>the</strong>
thickness <strong>of</strong> <strong>the</strong> rust changes. It seems every line clearly separated though very long time it took. It
shows, by simulation, <strong>the</strong> di erence <strong>of</strong> rust thickness in 3 mm can be discriminated.
Fig.7 shows <strong>the</strong> model set up for <strong>the</strong> next simulation, upper part means X-ray apparatus surrounding
<strong>the</strong> bulb, and <strong>the</strong> bottom means <strong>the</strong> lm. In <strong>the</strong> midst steel plate and rust were set.
Fig.8 shows <strong>the</strong> energy absorption <strong>of</strong> <strong>the</strong> lm according to <strong>the</strong> rust thickness change set on <strong>the</strong>
steel plate.
Fig.9 shows <strong>the</strong> energy absorption, upper part is for rust and lower part is for steel, <strong>the</strong> top <strong>of</strong>
each bar is shown at, but in detail it makes curb as shown in Fig.10. But <strong>the</strong> di erence is so small
in comparison with <strong>the</strong> whole.
4.4 The application <strong>of</strong> <strong>the</strong> result <strong>of</strong> <strong>the</strong> simulation
The simulation result was obtained in <strong>the</strong> form <strong>of</strong> energy absorption in <strong>the</strong> lm that occurs in
accordance with <strong>the</strong> thickness change <strong>of</strong> <strong>the</strong> combination <strong>of</strong> steel and rust. It shows, because energy
absorption is proportional to <strong>the</strong> density <strong>of</strong> <strong>the</strong> lm, that <strong>the</strong> relationship between thickness <strong>of</strong> <strong>the</strong>
steel and <strong>the</strong> rust has been obtained concerning <strong>the</strong> density <strong>of</strong> <strong>the</strong> lm. In case when <strong>the</strong> thickness <strong>of</strong>
<strong>the</strong> mixture <strong>of</strong> <strong>the</strong> steel and <strong>the</strong> rust is got, which is expressed equivalently in steel with using <strong>the</strong> main
logic, <strong>the</strong> thickness is divided into two parts, <strong>the</strong> steel and <strong>the</strong> rust, using <strong>the</strong> relationship between
<strong>the</strong>m in Fig.6. This is <strong>the</strong> subject to make practically in <strong>the</strong> future system making. When ano<strong>the</strong>r
equation is got concerning <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> rust and <strong>the</strong> steel, <strong>the</strong>n by solving two equations, <strong>the</strong>
thickness <strong>of</strong> <strong>the</strong> steel and <strong>the</strong> rust can be measured.
5 Summary
Followings are got this time.
A smoo<strong>the</strong>r spectrum curve <strong>of</strong> <strong>the</strong> X-ray bulb can be got.
Therust<strong>of</strong>pipewas acquired and <strong>the</strong> element was analyzed.
The rust was placed on <strong>the</strong> steel plate and <strong>the</strong> simulation <strong>of</strong> <strong>the</strong>m was done. Satisfactory
resolution could be got.
The relationship between <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> mixture <strong>of</strong> rust and steel was obtained using <strong>the</strong>
energy absorption in <strong>the</strong> lm. It shows <strong>the</strong> possibility <strong>of</strong>measuring two material layers when
ano<strong>the</strong>r equation <strong>of</strong> thickness can be got.
Acknowledgement
The author is very grateful to Pr<strong>of</strong>. Hirayama <strong>of</strong> KEK (High Energy Research Organization) who
assisted me in using EGS4.
3

References
[1] G. Kajiwara, \X-ray piping diagnostic system", Journal <strong>of</strong> Testing and Evaluation Vol.
26(1998)346-351.
[2] G. Kajiwara, \EXAMINATION OF THE X-RAY PIPING DIAGNOSTIC SYSTEM USING
EGS4 (IN CASE CONSIDERING SPECTRUM OF X-RAY)", <strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> 8th Egs Users'
Meeting in Japan, p71.
[3] A. Sekiguchi, \An introduction to Measuring radiation", Tokyo University Press.
Tanble. 1(1) Speci c garavity <strong>of</strong> rust sample.
Usage <strong>of</strong> pipe Speci c gravity Bulk speci c gravity
Cooling water 4.08 0.66
Water supply 2.03 0.97
Table 1(2) Result <strong>of</strong> analysis <strong>of</strong> rust sample (%).
Usage <strong>of</strong> pipe O Fe Si Na C S Zn
Cooling water 33.00 56.50 0.03

6

20
Position<strong>of</strong>X-rayapparatus
Stepblock
60
Filmcassette
FFD=600
Rust
Fig.4Arrangement<strong>of</strong>devicesintakingX-rayphotograph
<strong>of</strong>rustandsteel
unit:mm
7

8

9

10

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.209-215
E ective Bending Point to Reduce Dose-Equivalent
<strong>of</strong> a Bending Duct Streaming System
K. Ueki
Nuclear Technology Division, Ship Research Institute
6-38-1 Shinkawa, Mitaka, Tokyo 181-0004, Japan
Abstract
In this study, <strong>the</strong> Monte Carlo analysis is carried out to nd out an e ective bending point
to reduce <strong>the</strong> neutron streaming on <strong>the</strong> outer surface <strong>of</strong> <strong>the</strong> two-bent rectangular duct streaming
system. As a function <strong>of</strong> <strong>the</strong> bending point <strong>of</strong> <strong>the</strong> rst leg, neutron dose-equivalent rate distributions
are calculated not only along <strong>the</strong> centerline in <strong>the</strong> bending duct but also on <strong>the</strong> extension line <strong>of</strong>
<strong>the</strong> rst leg. On <strong>the</strong> outer surface on <strong>the</strong> extension line <strong>of</strong> <strong>the</strong> rst leg, <strong>the</strong> neutron dose-equivalent
rates are increase exponentially as <strong>the</strong> bending point comes up to <strong>the</strong> surface. On <strong>the</strong> o<strong>the</strong>r hand,
those distributions along <strong>the</strong> centerline in <strong>the</strong> duct have a minimum point on <strong>the</strong> bending point <strong>of</strong>
it. Finding <strong>the</strong> e ective bending point is one <strong>of</strong> <strong>the</strong> most positive applications <strong>of</strong> <strong>the</strong> Monte Carlo
method to a shielding design.
1 Introduction
In this study, <strong>the</strong> following two-bend (three-legged) rectangular duct neutron streaming system is
prepared, and <strong>the</strong> neutron streaming <strong>the</strong> shielding system is analyzed by <strong>the</strong> continuous energy Monte
Carlo code MCNP 4B[1]. Concept <strong>of</strong> <strong>the</strong> duct neutron streaming system is shown in Fig. 1.
1. Dimensions <strong>of</strong> <strong>the</strong> duct streaming system are 150x150 2 x200 cm.
2. The shield around <strong>the</strong> duct is a homogenized material <strong>of</strong> 80 volume percents <strong>of</strong> stainless steel
and 20 volume percents <strong>of</strong> water. The homogenized shield is expected to have superior shielding
ability not only for fast neutrons but also for secondary gamma rays produced by H (n, ) reaction
<strong>of</strong> <strong>the</strong>rmal neutrons in water.
3. Diameter <strong>of</strong> <strong>the</strong> duct is xed on 15.0 cm and <strong>the</strong> bending angle between <strong>the</strong> rst duct and <strong>the</strong>
second one, and also <strong>the</strong> second duct and <strong>the</strong> third one is a right angle, respectively. The distance
between <strong>the</strong> inlet and <strong>the</strong> outlet <strong>of</strong> <strong>the</strong> second leg is xed on 50 cm, so that <strong>the</strong> dose-equivalent
rates are calculated as a function <strong>of</strong> <strong>the</strong> bending point <strong>of</strong> <strong>the</strong> rst leg, unirarerally.
4. Point isotropic neutron source <strong>of</strong> 14 MeV is located at 50 cm-distance from <strong>the</strong> inlet <strong>of</strong> <strong>the</strong>
rst-leg.
2 Simulation <strong>of</strong> E ective Bending Point
1. The point detector estimators are set along <strong>the</strong> center line <strong>of</strong> <strong>the</strong> duct and <strong>the</strong> NESXE's (Next
Event Surface Crossing Estimator)[2] are set along <strong>the</strong> extension line <strong>of</strong> <strong>the</strong> rst leg. The
NESXE estimator is not provided in <strong>the</strong> MCNP 4B code. Therefore, instead <strong>of</strong> <strong>the</strong> point
detector estimator, <strong>the</strong> NESXE estimator was newly built into <strong>the</strong> subroutine TALLYD <strong>of</strong> <strong>the</strong>
MCNP 4B code.
1

2. The weight window importance is assigned in every 5-cm-thik cell to get enough collisions in <strong>the</strong>
cells. As <strong>the</strong> results, <strong>the</strong> fsd's (fractional standard deviation) <strong>of</strong> <strong>the</strong> calculated dose-equivalent
rates are less than 0.075 (7.5 %).
The cells, 1 45, for weight window importance, detector locations <strong>of</strong> <strong>the</strong> point detectors and <strong>the</strong>
NESXE's are indicated in Fig. 2.
3 Results and Discussions
The neutron dose-equivalent rate distributions at Pout-1 and at Pout-2 in Fig.1 are shown in
Fig.3. As shown in Fig. 3, <strong>the</strong> pro le <strong>of</strong> <strong>the</strong> dose-equivalent rates at Point 2 that is <strong>the</strong> crossing
point on <strong>the</strong> extended line <strong>of</strong> <strong>the</strong> rst leg and <strong>the</strong> outer surface <strong>of</strong> <strong>the</strong> shielding system, increases
exponentially. On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> pro le <strong>of</strong> it at Point 1that is <strong>the</strong> outlet <strong>of</strong> <strong>the</strong> third leg has <strong>the</strong>
minimum point at <strong>the</strong> bending point <strong>of</strong> 100 cm. As <strong>the</strong> bending points coming up to <strong>the</strong> outer surface,
<strong>the</strong> more source neutrons coming up <strong>the</strong> Pout 1. Then <strong>the</strong> dose-equivalent rate at Pout-1 increases
exponentially as <strong>the</strong> function <strong>of</strong> <strong>the</strong> rst leg bending point. The dose-equivalent rate distributions
along <strong>the</strong> centerline <strong>of</strong> each duct are shown in Fig. 4 and <strong>the</strong> following attenuation factors (Fa) <strong>of</strong> <strong>the</strong>
dose-equivalent rates are obtained from Fig. 4 for each leg.
1. Bending point <strong>of</strong> <strong>the</strong> rst leg is at 50 cm.
Fa <strong>of</strong> <strong>the</strong> rst leg: 1/3
Fa <strong>of</strong> <strong>the</strong> second: 1/50
Fa <strong>of</strong> <strong>the</strong> third leg: 1/500
2. Bending point <strong>of</strong> <strong>the</strong> rst leg is at 100 cm.
Fa <strong>of</strong> <strong>the</strong> rst leg: 1/10
Fa <strong>of</strong> <strong>the</strong> second: 1/200
Fa <strong>of</strong> <strong>the</strong> third leg: 1/500
3. Bending point <strong>of</strong> <strong>the</strong> rst leg is at 150 cm.
Fa <strong>of</strong> <strong>the</strong> rst leg: 1/15
Fa <strong>of</strong> <strong>the</strong> second: 1/250
Fa <strong>of</strong> <strong>the</strong> third leg: 1/50
In <strong>the</strong> case <strong>of</strong> (1), Fa <strong>of</strong> <strong>the</strong> third leg, 1/500 is <strong>the</strong> maximum in <strong>the</strong> three, but Fa's <strong>of</strong> <strong>the</strong> rst
and <strong>the</strong> second leg is <strong>the</strong> minimum in <strong>the</strong> three. Because <strong>the</strong> length <strong>of</strong> <strong>the</strong> rst leg is only 50 cm and
<strong>the</strong> distance from <strong>the</strong> source point to <strong>the</strong> second leg is near than that <strong>of</strong> <strong>the</strong> o<strong>the</strong>r cases, <strong>the</strong> more
source neutrons enter <strong>the</strong> second leg directory. In <strong>the</strong> case <strong>of</strong> (2), Fa <strong>of</strong> <strong>the</strong> second leg, 1/250 is <strong>the</strong>
maximum in <strong>the</strong> three, but Fa <strong>of</strong> <strong>the</strong> third leg is <strong>the</strong> 1/10 <strong>of</strong> <strong>the</strong> (1) and (2). Because <strong>the</strong> length <strong>of</strong>
<strong>the</strong> third leg is only 50 cm, so <strong>the</strong> large attenuation factor is not expected for it. In <strong>the</strong> case <strong>of</strong> (2),
Fa <strong>of</strong> <strong>the</strong> second leg is a little bit small than that <strong>of</strong> <strong>the</strong> (3), but Fa <strong>of</strong> <strong>the</strong> third is <strong>the</strong> maximum in
<strong>the</strong> three. Accordingly, <strong>the</strong> minimum dose-equivalent rate at <strong>the</strong> outlet <strong>of</strong> <strong>the</strong> third leg is made up in
<strong>the</strong> case <strong>of</strong> (2).
4 Concluding Remarks
On <strong>the</strong> outer surface on <strong>the</strong> extension line <strong>of</strong> <strong>the</strong> rst leg, <strong>the</strong> neutron dose-equivalent rates
are increase exponentially as <strong>the</strong> bending point comes up to <strong>the</strong> surface. On <strong>the</strong> o<strong>the</strong>r hand, those
distributions along <strong>the</strong> centerline in <strong>the</strong> duct have a minimum point on <strong>the</strong> bending point <strong>of</strong> it.
2

In this study, Monte Carlo method is useful to nd out an e ective bending point <strong>of</strong> a duct
streaming system, and it is one <strong>of</strong> <strong>the</strong> most positive applications <strong>of</strong> <strong>the</strong> Monte Carlo method to a
shielding design.
References
[1] \MCNP TM - A General Monte Carlo N-Particle Transport Code Version 4B," J. F. Briesmeister,
Ed., LA-12625-M, Los Alamos National Laboratory (1997).
[2] K. Ueki, A. Ohashi and M. Kawai, \Continuous Energy Monte Carlo Analysis <strong>of</strong> Neutron Shielding
Benchmark Experiments with Cross Section JENDL-3," J. Nucl. Sci. Technol. 30(1993)4.
3

4
φ

5
φ

Dose-EquivalentRate(µSv -1 /SourceNeutron)
10 -9
10 -11
10 -13
10 -15
10 -17
10 -19
Distribution<strong>of</strong>NeutronDose-EquivalentRates
asaFunction<strong>of</strong><strong>the</strong>BendingPoint
AtPoint-1inFig.1
AtPoint-2inFig.1
0 50 100 150 200
BendingPointin<strong>the</strong>FirstLeg(cm)
Fig.3NCNP4Bcalculatedneutrondose-equivalentrate
distributionatPoint-1andPoint-2inFig.1,asa
function<strong>of</strong><strong>the</strong>BendingPoint.
6

7

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.216-223
EGS4 Simulation <strong>of</strong> Compton Scattering
for Nondestructive Testing
N. Shengli, Z. Jun, and H. Liuxing
Northwest Institute <strong>of</strong> Nuclear Technology,
P. O. Box 69, No.15, Xi'an, 710024,CHINA
Abstract
This paper presents <strong>the</strong> principle <strong>of</strong> nondestructive testing based on <strong>the</strong> measurement <strong>of</strong>
Compton-scattered photons. When a well-collimated beam <strong>of</strong> 0.662MeV gamma rays from Cs-
137 isotope source is radiated vertically into a concrete wall, scattered photons can be detected at
<strong>the</strong> same side <strong>of</strong> <strong>the</strong> wall by a NaI detector. The intensity <strong>of</strong>single Compton scattered photons
is proportional to <strong>the</strong> electron density at <strong>the</strong> point where <strong>the</strong> scattering occurs. However, most
<strong>of</strong> <strong>the</strong> incident photons are scattered more than one time. The single and multiple scattering are
studied by Monte Carlo program package EGS4. This paper presents <strong>the</strong> ow <strong>of</strong> single and multiple
scattered photons before reaching <strong>the</strong> NaI detector when a iron block isburiedin<strong>the</strong>wall or
not. Based on <strong>the</strong> results, it can be concluded that this system can detect <strong>the</strong> iron block buried
in <strong>the</strong> concrete wall. In this process, <strong>the</strong> di erence between ion and no ion for <strong>the</strong> single scattered
photons is more obvious than that for <strong>the</strong> multiple scattered photons. The system can also be used
to detect any non-iron object in o<strong>the</strong>r material with di erent electron densities.
1 Introduction
The CSI technique is based on <strong>the</strong> measurement <strong>of</strong> Compton scattered photons. In contrast to <strong>the</strong>
conventional transmission tomography, this process relies on measuring <strong>of</strong> <strong>the</strong> back-scattered radiation
from <strong>the</strong> interior <strong>of</strong> an object surface to achieve a three-dimensional image <strong>of</strong> <strong>the</strong> object interior. So
CSI is useful in imaging on extended industrial objects or in cases where access to two opposite sides
<strong>of</strong> <strong>the</strong> object is not possible[1, 2,3,4].
The objection <strong>of</strong> this paper is to <strong>the</strong>oretically analyze <strong>the</strong> feasibility <strong>of</strong> NDT technique to massive
extended structure. The emphasis <strong>of</strong> <strong>the</strong> study was to investigate <strong>the</strong> feasibility <strong>of</strong>detecting defects
or foreign object in concrete structures. The Compton scattering process is simulated using Monte
Carlo program package EGS4. Owing to EGS4's open-architecture, <strong>the</strong> intensity and energy spectrum
<strong>of</strong> <strong>the</strong> single and multiple scattering photons can be given separately. Meanwhile, program MCNP
is used to simulate <strong>the</strong> total scattered photons. The two results agreed very well. So <strong>the</strong> simulation
method is valid and <strong>the</strong> results are believable.
The paper is organized as follows. In section 2, a brief discussion <strong>of</strong> <strong>the</strong> CSI <strong>the</strong>oretical model is
presented. A description <strong>of</strong> <strong>the</strong> Monte Carlo simulation is contained in section 3. Section 4 summarizes
and concludes this paper.
2 Theoretical Model
An isotope source Cs-137 is assumed to be placed beside a concrete wall. Around <strong>the</strong> source, <strong>the</strong>re
is an annular NaI detector with its axis vertical to <strong>the</strong> wall. The well-collimated gamma ray from <strong>the</strong>
source is radiated vertically into <strong>the</strong> wall, and <strong>the</strong>n <strong>the</strong> detector will detect <strong>the</strong> scattered photons.
Before entering <strong>the</strong> NaI, photons will pass through a narrow collimator, which is used to determine
1

<strong>the</strong> particular point to focus at. The geometry sectional drawing <strong>of</strong> <strong>the</strong> structure is given in Figure 1.
Assume <strong>the</strong>re is a foreign object buried 60mm below <strong>the</strong> surface <strong>of</strong> <strong>the</strong> wall. It is a cylindrical block
<strong>of</strong> iron, 5mm in height, and 5mm in diameter. Out <strong>of</strong> <strong>the</strong> concrete wall 40mm in distance <strong>the</strong>re is
an iron double-frustum-<strong>of</strong>-cone-shape collimator. The conical angle is 120 , and <strong>the</strong> vertical height <strong>of</strong>
collimator is 100mm.
The energy <strong>of</strong> isotope Cs-137's gamma ray is 0.662 MeV. When it emits into <strong>the</strong> concrete, <strong>the</strong>
main interactions are photoelectric e ect and Compton scattering. The energy <strong>of</strong> electrons ejected
in <strong>the</strong> two interactions is too low to create new photons. So all <strong>of</strong> <strong>the</strong> photons detected by NaI are
Compton scattered photons.
The Compton scattering process is strictly an interaction between a photon and an individual
electron. In <strong>the</strong> interaction, <strong>the</strong> photon does not disappear (Figure 2). In stead, it is de ected
through a scattering angle and part <strong>of</strong> its energy is transferred to <strong>the</strong> recoil electron. The energy loss
in <strong>the</strong> process depends on <strong>the</strong> initial photon energy as well as on <strong>the</strong> scattering angle. Under <strong>the</strong>
assumption that <strong>the</strong> electron is free and stationary before collision, <strong>the</strong> energy change <strong>of</strong> <strong>the</strong> incident
photon and <strong>the</strong> scattering angle is related to each o<strong>the</strong>r by
E 0 =
E
1+ E
m0c 2 (1 ; cos )
where E 0 is <strong>the</strong> energy <strong>of</strong> scattered photon, E is <strong>the</strong> energy <strong>of</strong> incident photon, m0c 2 is <strong>the</strong> rest mass
energy <strong>of</strong> electron, and is <strong>the</strong> scattering angle.
The Compton photons is not isotropically scattered. The di erential total Compton scattering
cross sections are given by <strong>the</strong> formula[5]
d c
(E )=
d
"
2
0
2
E 0
E
# 2 "
E 0
E
+ E
E 0
; sin 2
where d c=d is <strong>the</strong> di erential scattering cross section, and r0 is <strong>the</strong> classical electron radius (cm).
The intensity <strong>of</strong> <strong>the</strong> single scattered photons can be written as
Z
d c
Nd = N0 4 n4Zexp ;
d
l1
dl exp ; Z
l2
#
(1)
(2)
0 dl 0 (3)
where, N0 is <strong>the</strong> number <strong>of</strong> photons in <strong>the</strong> source collimator, d c=d is <strong>the</strong> di erential Compton
scattering cross section, 4 and4Z are solid angle and depth focused by collimator <strong>of</strong> NaI, n is <strong>the</strong>
electron density at <strong>the</strong> focus point, exp(; R
R
0 0
1 dl) and exp(; 2 dl ) are respectively <strong>the</strong> attenuation
rate <strong>of</strong> incident photons and scattered photons. It can be concluded that Nd is proportional to <strong>the</strong>
electron density at <strong>the</strong> focus point if <strong>the</strong> geometry and source are given.
However, in <strong>the</strong> equation 3, we havejust talked about <strong>the</strong> single scattered photons. There will be
more photons scattered more than one time before reaching <strong>the</strong> NaI detector. Only <strong>the</strong> intensity <strong>of</strong>
single scattered photons entering detector is <strong>the</strong> designed signal. The intensity <strong>of</strong>multiple scattered
photons is <strong>the</strong> background. The aim <strong>of</strong> our study is to restrain <strong>the</strong> multiple scattering background.
And <strong>the</strong>n increase <strong>the</strong> signal-to-noise ratio. By adopting narrow collimator, <strong>the</strong> high signal-to-noise
ratio can be achieved.
3 Monte Carlo Simulation
The single and multiple scatterings are studied by Monte Carlo radiation transport simulation. In
order to distinguish <strong>the</strong> single and multiple scattered photons, <strong>the</strong> Monte Carlo program package EGS4
is adopted. The physical mechanism in <strong>the</strong> problem is only concerned with <strong>the</strong> shower <strong>of</strong> electron and
gamma ray, so <strong>the</strong> package EGS4 is feasible. Because <strong>the</strong> whole con guration, geometry condition,
information needed and <strong>the</strong> structure <strong>of</strong> source have not been determined, <strong>the</strong> open-architecture EGS4
2

is preferred[6]. The most important, <strong>the</strong> EGS4 can easily tell <strong>the</strong> information <strong>of</strong> particles' interactions,
so we can distinguish <strong>the</strong> multiple and single scattered photons.
The main program is edited by user in EGS4, thus <strong>the</strong> simulation process can be controlled well.
To distinguish <strong>the</strong> single and multiple scattering, we didn't choose <strong>the</strong> auxiliary subprogram already
in EGS4, like WATCH. By setting <strong>the</strong> appropriate ag IAUSFL (19) from 0 to 1 in <strong>the</strong> main program,
call AUSGAB with IARG=18 if a Compton interaction has occurred. An arithmometer is used to
record <strong>the</strong> number <strong>of</strong> Compton scattering. The arithmometer adds 1 if a Compton scattering occurs
except in <strong>the</strong> NaI detector. When this photon is terminated, <strong>the</strong> arithmometer can show how many
times <strong>of</strong> Compton-scattering have occurred.
In order to verify <strong>the</strong> simulation <strong>of</strong> EGS4, <strong>the</strong> Monte Carlo program MCNP [7] is also used to
calculate <strong>the</strong> total scattered photons.
4 Results and Conclusions
First, three cases are simulated, namely, no block, aimed (source rays emitted along <strong>the</strong> axe <strong>of</strong>
block cylinder), and deviated. Table 1 gives <strong>the</strong> intensities and energy deposited in NaI.
Table 1: Intensity and Energy Deposited
Intensity Energy Deposited(10 ;6 Mev/photon) Relative Error <strong>of</strong>
Single Total Single Total MCNP Total EGS & MCNP
Scattered Scattered
No Block 136 2455 0.2544 3.338 3.347 0.3%
Deviated 126 2459 0.2362 3.342 3.427 2.5%
Aimed 294 2887 0.5806 4.083 3.983 2.5%
It can be seen from <strong>the</strong> table that <strong>the</strong> intensity <strong>of</strong> total photons obtained by EGS4 is close to
that <strong>of</strong> MCNP. So <strong>the</strong> results <strong>of</strong> <strong>the</strong> simulation are believable. The single scattered photons are only
<strong>the</strong> small fraction <strong>of</strong> <strong>the</strong> total photons. But <strong>the</strong>y can distinctly tell if <strong>the</strong>re is a change <strong>of</strong> electron
density at<strong>the</strong> focus point. Because <strong>the</strong> scattered photons are attenuated by <strong>the</strong> deviated iron block,
<strong>the</strong> intensity <strong>of</strong> photons in deviated case is lower than that <strong>of</strong> no iron block.
Then, we change <strong>the</strong> width <strong>of</strong> <strong>the</strong> collimator at <strong>the</strong> front <strong>of</strong> NaI. We choose <strong>the</strong> width as 0.2cm,
0.6cm, or 2.0cm. The counts <strong>of</strong> single and multiple scattered photons detected by NaI are listed in
table 2. The pulse-height distribution <strong>of</strong> <strong>the</strong> three cases can be seen respectively in Figures 4, 5, and
6.
Table 2: Counts at di erent Collimator Width
Width (cm) Single multiple Single/multiple
0.2 283 2491 0.114
0.6 1929 23497 0.082
2.0 21079 263032 0.080
When <strong>the</strong> width is 0.2cm, <strong>the</strong> counts <strong>of</strong> detected photons are very low. But <strong>the</strong> signal-to-noise
ratio is high. It takes a long time to get enough counts. As shown in gure 4, <strong>the</strong>re is a peak at
0.225MeV. It just equal to <strong>the</strong> energy <strong>of</strong> scattered photon when scatter angle is 120 and incident
photon energy is 0.662MeV in Eq.1.
When <strong>the</strong> width is 0.6cm or 2.0cm, <strong>the</strong> counts <strong>of</strong> detected photons are high, but <strong>the</strong> signal-to-noise
ratio is low. Because <strong>the</strong> background is high, <strong>the</strong> counts <strong>of</strong> detected photons cannot tell <strong>the</strong> change <strong>of</strong>
electron density exactly. The broader collimator makes <strong>the</strong> larger <strong>of</strong> scattering angle, thus <strong>the</strong> energy
range increase. It is shown in Figure 6, energy peak is wider than that in Figure 4.
According to all <strong>of</strong> above analysis, one should prefer narrow collimator as possible, especially in
detecting small foreign body. We suppose <strong>the</strong> collimator width should be 0.2cm. The results and
analysis can be used as reference on this kind <strong>of</strong> experiment and apparatus.
3

In summary, this kind <strong>of</strong> complete process is easy to be simulated using EGS4.The results obtained
by MCNP shows that <strong>the</strong> EGS4 simulation is believable.
References
[1] J. Wehlburg, S. Keshavmurthy, Y. Watanabe, E. Dugan, and A. Jacobs, \Image restoration
technique using Compton backscatter imaging for <strong>the</strong> detection <strong>of</strong> buried landmines ", SPIE
<strong>Proceedings</strong>, 1995, Vol.2496:336-347.
[2] S. J. Norton, \Compton scattering tomography", J. Appl. Phys. 76(4)(1994)2007-2015.
[3] G. Harding, and J. Kosanetzky, \Scattered x-ray beam nondestructive testing", Nucl. Insru.
Meth. A280(1989)517-528.
[4] S. Anghaie, L. L. Humphries, and N. J. Diaz, \Material characterization and aw detection,
sizing, and gamma scattering spectroscopy technique", Nucl. Tech. 91(1990)361-387.
[5] R. L. Morin, Monte Carlo Simulation in <strong>the</strong> Radiological Science, CRC Inc., 1988.
[6] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, \The EGS4 Code System". SLAC-265 (1985).
[7] J. F. Briesmeister, \MCNP{A General Monte Carlo N-Particle Transport Code", America La-
12625-M.
4

Figure 1: Geometry sectional drawing
θ
Figure 2: Compton scattering.
5

ComScat?
Ncom=?
APhoton
Ncom=0
RecordIt
EndThisPhoton
SubAusgab
Ncom=ncom+1
RecordItasSingle
Figure 3: Block Diagram used to Distinguish Single and Multiple Scattering.
6

Figure 4: Pulse-height Distribution <strong>of</strong> <strong>the</strong> Detected Photons (Width=0.2cm).
Figure 5: Pulse-height Distribution <strong>of</strong> <strong>the</strong> Detected Photons (Width=0.6cm).
7

Counts
6000
5000
4000
3000
2000
1000
Total(NoIron)
Single(NoIron)
Double(NoIron)
Total(IronBlock)
Single(IronBlock)
Double(IronBlock)
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Energy(MeV)
Figure 6: Pulse-height Distribution <strong>of</strong> <strong>the</strong> Detected Photons (Width=2.0cm).
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.224-234
Implementation and Performance Evaluation <strong>of</strong>
Iterative Reconstruction Algorithms in SPECT:
A Simulation Study Using EGS4
T. Yokoi 1 , H. Shinohara 2 , T. Hashimoto 3 , T. Yamamoto 4 , and Y. Niio 4
1
Department <strong>of</strong> Research and Development for Nuclear Medicine,
Shimadzu Corporation, Kyoto, Japan
2
Department <strong>of</strong> Radiological Sciences,
Tokyo Metropolitan University <strong>of</strong> Health Sciences, Tokyo, Japan
3
Department <strong>of</strong> Information Processing, Yokohama Soei College, Yokohama, Japan
4Department <strong>of</strong> Radiology, Showa University Fujigaoka Hospital, Yokohama, Japan
Abstract
We implemented three iterative reconstruction algorithms (maximum likelihood-expectation
maximization (MLEM) algorithm, multiplicative simultaneous iterative reconstruction technique
(MSIRT) and additive simultaneous iterative reconstruction technique (ASIRT)) incorporating attenuation
correction (AC) and scatter correction (SC) for single photon emission computed tomography
(SPECT). The purpose <strong>of</strong> this study is to investigate <strong>the</strong> convergence properties <strong>of</strong> <strong>the</strong> three
iterative methods by computer simulation using EGS4. Digital brain and cyrindrical phantoms
were designed for activity distribution and linear attenuation coe cient maps. In this study, <strong>the</strong>
simulated radioisotope was Tc-99m (photon energy = 140keV). The photon attenuation and scatter
and <strong>the</strong> distance-dependent blurring due to <strong>the</strong> collimator were involved in <strong>the</strong> simulated SPECT
system. In <strong>the</strong> implemented reconstruction algorithms, modeling <strong>of</strong> <strong>the</strong> e ect <strong>of</strong> attenuation and
scattering were involved but <strong>the</strong> distance-depend blurring was not included. The progress <strong>of</strong> <strong>the</strong>
reconstruction was monitored by observing <strong>the</strong> residual squares error ( 2 )between <strong>the</strong> calculated
projections and measurement dataateach iteration.
The number <strong>of</strong> iterations needed to reach a constant 2 value were di erent for each algorithm.
ASIRT needed <strong>the</strong> largest number, MLEM <strong>the</strong> lowest number <strong>of</strong> iteration. The ASIRT required
more than 100 iteration to produce a comparable result <strong>of</strong> MLEM and MSIRT. We observed almost
equivalent performance between MLEM and MSIRT. All iterative reconstruction algorithms were
e ective in compensating for non-uniform attenuation distribution. There are potential in <strong>the</strong>
iterative reconstruction algorithms for improvement <strong>of</strong>quantitative SPECT capability. EGS4 is
powerful tool for investigating <strong>the</strong> properties <strong>of</strong> reconstruction algorithms without actual phantom
experiments using <strong>the</strong> radioactive isotopes.
1 Introduction
Many iterative reconstruction algorithms for single photon emission computed tomography
(SPECT) have been proposed[1-4]. One <strong>of</strong> <strong>the</strong> most important issues in SPECT is quantitative
accuracy <strong>of</strong> radionuclide distributions and concentrations. The concentration <strong>of</strong> <strong>the</strong> tracer gives physiological
information about <strong>the</strong> metabolism <strong>of</strong> a living tissue. The advantage <strong>of</strong> <strong>the</strong> iterative reconstruction
algorithms is that <strong>the</strong>y can easily incorporate a model <strong>of</strong> <strong>the</strong> physical processes in uencing
<strong>the</strong> absolute quantitation, such as photon attenuation and scatter in organ [5]. In SPECT, <strong>the</strong> spatial
resolution depends on <strong>the</strong> distance from <strong>the</strong> detector due to <strong>the</strong> nite hole-diameter <strong>of</strong> <strong>the</strong> collimator.
The compensation <strong>of</strong> <strong>the</strong> distance-dependent blurring can be also included into <strong>the</strong> algorithm [4].
Therefore <strong>the</strong> iterative reconstruction algorithms are expected to improve <strong>the</strong> quantitative capability
1

<strong>of</strong> SPECT. These methods have long been considered not to be suitable in clinical routine studies due
to <strong>the</strong> excessive computational requirement <strong>of</strong> each iteration step and slow convergence. Because <strong>of</strong>
increases in computer power, <strong>the</strong> iterative reconstruction for SPECT has recently become clinically
available as an alternative to conventional ltered backprojection algorithm.
We implemented three iterative reconstruction algorithms, maximum likelihood-expectation maximization
(MLEM) algorithm [1,2], multiplicative simultaneous iterative reconstruction technique
(MSIRT)[3,6] and additive simultaneous iterative reconstruction technique (ASIRT)[3], incorporating
<strong>the</strong> attenuation and scatter compensation for SPECT. The choice <strong>of</strong> <strong>the</strong> algorithm and selecting
<strong>of</strong> a stopping iteration number depend on <strong>the</strong> conditions in a given clinical environment. The object
<strong>of</strong> this study is to investigate <strong>the</strong> convergence properties <strong>of</strong> <strong>the</strong> iterative reconstruction algorithms
using EGS4 [7].
2 Theory <strong>of</strong> Iterative Reconstruction Algorithms
2.1 De nition <strong>of</strong> notation
Figure 1 shows <strong>the</strong> notation and coordination system for <strong>the</strong> reconstruction. k j is <strong>the</strong> value <strong>of</strong>
reconstructed image at <strong>the</strong> pixel j for <strong>the</strong> k-th iteration, yi is <strong>the</strong> measured projection data at i-th
bin, and Cij is <strong>the</strong> detection probability that give <strong>the</strong> fraction <strong>of</strong> photons from pixel j to projection
bin i. The value <strong>of</strong> Cij represents as <strong>the</strong> overlapped area between i-th ray tube and pixel j.
2.2 Iterative reconstruction algorithms
Maximum likelihood-expectation maximization (MLEM) algorithm is described as follows:
k+1
j
=
k
j Pmi Cij
mX i
Cij Pmj Cij k j
where k is <strong>the</strong> iteration number. This algorithm converges to <strong>the</strong> maximum likelihood estimate <strong>of</strong> a
probability distribution function from <strong>the</strong> observed data [8]. In this algorithm, <strong>the</strong> measured emission
data is assumed a spatially dependent Poisson model.
Additivesimultaneous iterative reconstruction technique (ASIRT) and multiplicative simultaneous
iterative reconstruction technique (MSIRT) are described as follows, respectively:
k+1
j = k j +
k+1
j = k j
1 Pmi Cij
mX i
(yi ; Pm j Cij k j )Cij Pmj Cij
P ni (Cijyi= P m j Cij)
P ni ( P m j Cij k j =P m j Cij)
In ASIRT and MSIRT methods, <strong>the</strong> measured emission data is assumed a Gauss distribution.
Figure 2 show <strong>the</strong> owcharts <strong>of</strong> each algorithm. The reconstruction images are iteratively upgraded
by <strong>the</strong> di erent manners. All algorithms must be started from positive initial estimates <strong>of</strong> 0 , and <strong>the</strong>
Cij is calculated at once before <strong>the</strong> iteration cycle. There is no ma<strong>the</strong>matical rule for stopping <strong>of</strong> <strong>the</strong>
iteration, so it must be found empirically.
2.3 Incorporation <strong>of</strong> attenuation and scatter correction into <strong>the</strong> algorithms
The e ect <strong>of</strong> photon attenuation can be easily incorporated into <strong>the</strong> probability Cij. The number
<strong>of</strong> photons are exponentially decreased passing through a pixel j. The attenuation factor is given
by exp(; P j2J i jlij), where j is <strong>the</strong> linear attenuation coe cient [cm ;1 ] at <strong>the</strong> pixel j, Ji is <strong>the</strong>
subset <strong>of</strong> pixels passing through <strong>the</strong> i-th ray and lij is <strong>the</strong> intersection length [cm]. The j map is
supplied as a prior information measured by <strong>the</strong> external radioisotope source or X-ray CT scanner. The
2
(1)
(2)
(3)

probability incorporating <strong>the</strong> attenuation consists in calculating Cij exp(; P j2J jlij). In practical
i
implementation, <strong>the</strong> value <strong>of</strong> was approximated by Cij x [pixel size].
The scatter component contaminated in <strong>the</strong> main window was approximated by <strong>the</strong> method <strong>of</strong>
Ogawa et al [9,10]. This method was assumed that <strong>the</strong> scatter component could be calculated by
linear interpolation using <strong>the</strong> images <strong>of</strong> sub-window as follows:
Si =0:5 CS i
Wm
Ws
where CS i is <strong>the</strong> measured counts in <strong>the</strong> sub-windowati-th bin, Ws and Wm are <strong>the</strong> width <strong>of</strong> sub- and
main- window [keV], respectively. In order to incorporate <strong>the</strong> scatter correction, <strong>the</strong> estimated scatter
component Si was subtracted from <strong>the</strong> measured projection data yi in each algorithm. Including
<strong>the</strong> above-mentioned procedures, <strong>the</strong> attenuation correction (AC) and scatter correction (SC) can be
accomplished. Although <strong>the</strong> blurring due to <strong>the</strong> solid angle <strong>of</strong> <strong>the</strong> collimator hole was included in <strong>the</strong>
simulation data, it was not included in <strong>the</strong> reconstruction algorithms.
3 Simulation
3.1 Digital phantoms and material data
To evaluate <strong>the</strong> properties <strong>of</strong> <strong>the</strong> implemented iterative reconstruction algorithms, we performed
<strong>the</strong> simulation study using <strong>the</strong> digital brain and cylindrical phantoms as shown in Fig.3. In <strong>the</strong>
brain phantom, <strong>the</strong> activity distribution map was modeled as <strong>the</strong> gray and white matter structures
segmented from autopsy brain phantom [11]. The activity ratio <strong>of</strong> gray/white matter was assumed to
4:1. The linear attenuation coe cient map consisted <strong>of</strong> brain tissue and skull regions. The component
<strong>of</strong> <strong>the</strong> brain tissue was assumed to equivalent <strong>of</strong><strong>the</strong>water (H 2O). On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> skull region
that has no activity consisted <strong>of</strong> six elements from H, C, N, O, P, and Ca. These data were supplied
into <strong>the</strong> PEGS program to produce <strong>the</strong> material le that contained <strong>the</strong> cross section <strong>of</strong> interaction. In
this study, <strong>the</strong> simulated radioisotope was Tc-99m (photon energy = 141keV). The linear attenuation
coe cients for <strong>the</strong> narrow beam <strong>of</strong> 141 keV were estimated about 0.15 and 0.26 cm ;1 for tissue and
skull, respectively. The cylindrical phantom was de ned as <strong>the</strong> same fashion but a uniform activity
distribution was assumed. The phantoms werea128x 128 matrix with a pixel size <strong>of</strong> 3.125 mm.
3.2 Generation <strong>of</strong> projection data using EGS4
The photons were generated using EGS4 [7] and user extended program for a SPECT system coded
by Narita et al. [12,13]. The codes were implemented into <strong>the</strong> Windows based computer (Pentium-
III, 600MHz, 128MB ) by Visual Fortran Ver 6.1(Compaq Corp.). The digital phantoms and <strong>the</strong>
pre-calculated material le by PEGS were supplied into <strong>the</strong> EGS4 program. The physical processes
<strong>of</strong> attenuation, scatter and <strong>the</strong> blurring due to <strong>the</strong> detector response were involved in <strong>the</strong> simulated
SPECT system. Two kinds <strong>of</strong> collimator (ultra high-resolution type (UHR) and high-sensitive type
(HS)) were examined. The parameters used in <strong>the</strong> simulation were summarized in Table 1.
3.3 Convergence criteria
To investigate <strong>the</strong> convergence properties <strong>of</strong> <strong>the</strong> implemented iterative algorithms, two criteria
have been examined. First <strong>the</strong> progress <strong>of</strong> <strong>the</strong> reconstruction was monitored by observing <strong>the</strong> residual
squares error ( 2 ) at each iteration. 2 is de ned as follows:
2 =
mX i
(4)
(p ;yi) (5)
2 is interpreted that how well <strong>the</strong> forward projection <strong>of</strong> <strong>the</strong> image matches with <strong>the</strong> measured data.
Therefore it will be expected to decrease with increasing <strong>the</strong> iteration number, and approach to <strong>the</strong>
3

plateau. <strong>Second</strong>ly,evaluating <strong>of</strong> gray/white count ratio also monitored <strong>the</strong> image contrast. The regions
<strong>of</strong> interest (ROI) were de ned on <strong>the</strong> deep gray matter and white matter by 3 x 3 square pixels. The
gray/white ratio will be approach to <strong>the</strong> assumed value <strong>of</strong> 4.0 if <strong>the</strong> AC, SC and compensation <strong>of</strong>
blurring by collimator are perfect.
4 Results and Discussion
The simulated energy spectra <strong>of</strong> Tc-99m using <strong>the</strong> UHR collimator and <strong>the</strong> brain phantom are
shown in Fig.4. The de ned energy windows are also indicated on <strong>the</strong> same gure. The primary
spectrum, which cannot be measured in actual experiment, represents that photon experience no
interaction passing through <strong>the</strong> organ. The total spectrum is summation <strong>of</strong> <strong>the</strong> primary and scatter.
The estimated energy spectra were similar with <strong>the</strong> results <strong>of</strong> previous report <strong>of</strong> simulation study [14].
Fig.5 shows <strong>the</strong> progress <strong>of</strong> reconstructed images <strong>of</strong> cylindrical phantom using MLEM algorithm
and <strong>the</strong> HS collimator as function <strong>of</strong> <strong>the</strong> iteration number. 2 decreased rapidly at early iterations.
Subsequently it declines slightly at late iterations. In this case, <strong>the</strong> feasible iteration number could be
determined as about 40 iteration for with attenuation and scatter correction (ACSC) and 30 iteration
for without ACSC. The values <strong>of</strong> 2 performed by AC and SC were small compared to those without
correction. The same tendency was observed in <strong>the</strong> results using UHR. The computation time for
image reconstruction was about 2 sec for one iteration.
Fig.6 shows <strong>the</strong> generated sinogram (projection data) from brain phantom and reconstructed
images using MLEM with and without ACSC for both collimators. The maximum counts in <strong>the</strong>
projection data <strong>of</strong> main window were 17805 and 1811 counts/pixel using HS and UHR, respectively.
The sensitivity <strong>of</strong> HS was about 10 times higher than that <strong>of</strong> UHR. The computation times for
generating <strong>of</strong> <strong>the</strong> sinograms were about 10 hr and 16 hr using HS and UHR, respectively. The values
<strong>of</strong> 2 using MLEM algorithm with and without ACSC are shown in Fig.7 as a function <strong>of</strong> <strong>the</strong> number
<strong>of</strong> iteration. The reconstructed images at each iteration were also shown. The feasible iteration
numbers were about 40 for HS and 50 for UHR when AC and SC were performed. Visual inspection
has con rmed that <strong>the</strong> stopping rule work well. It is evident that <strong>the</strong> performing <strong>of</strong> AC and SC
slows <strong>the</strong> iterative process down. Fig.8 shows <strong>the</strong> comparison <strong>of</strong> three algorithms on 2 with ACSC.
The number <strong>of</strong> iterations needed to reach a constant value were di erent for each algorithm. ASIRT
needed <strong>the</strong> largest number, MLEM <strong>the</strong> lowest number <strong>of</strong> iteration. The ASIRT required more than
100 iteration to produce a comparable result <strong>of</strong> MLEM and MSIRT. We observed almost equivalent
performance between MLEM and MSIRT. The similar results were obtained using HS.
Fig. 9 shows <strong>the</strong> count ratio <strong>of</strong> gray and white matter in ROIs as a function <strong>of</strong> <strong>the</strong> iteration
number using MLEM. By performing <strong>the</strong> AC and SC, <strong>the</strong> gray/white ratio was improved from 1.99
to 2.89 using HS and 2.89 to 3.82 using UHR at 80 iteration. In UHR collimator study, <strong>the</strong> estimated
gray/white values were nearly equal to <strong>the</strong> assumed value <strong>of</strong> 4.0, but a little underestimation (-4.5%)
was observed. The reasonable explanation for <strong>the</strong> underestimation is that modeling <strong>of</strong> distancedependent
blurring was not included in <strong>the</strong> reconstruction algorithms. Fig.10 shows <strong>the</strong> comparison
<strong>of</strong> algorithms on gray/white ratio using UHR collimator. All iterative reconstruction algorithms
were e ective in compensating for scatter and non-uniform attenuation distribution. The simulations
revealed <strong>the</strong> slow convergence property <strong>of</strong> ASIRT. It also makes little di erent on <strong>the</strong> results whe<strong>the</strong>r
we utilize MLEM or MSIRT for <strong>the</strong> image reconstruction.
5 Conclusion
We implemented three iterative reconstruction algorithms incorporation <strong>of</strong> scatter and attenuation
compensation. In order to investigate <strong>the</strong> convergence properties, <strong>the</strong> simulation SPECT system
using EGS4 was constructed. The simulation studies makes clear convergence properties <strong>of</strong> each
algorithm for two kinds <strong>of</strong> phantoms and collimators. In conclusion, <strong>the</strong>se methods are potential for
4

improvement <strong>of</strong> quantitative SPECT capability. EGS4 is powerful tool for investigating <strong>the</strong> properties
<strong>of</strong> reconstruction algorithms without actual phantom experiments using <strong>the</strong> radioactive isotopes.
Acknowledgment
We thank to Dr. Yuichiro Narita <strong>of</strong> Chiba Cancer Center for providing <strong>the</strong> projection program
and helpful suggestion for EGS4.
References
[1] L. Shepp and Y. Vardi, \Maximum likelihood reconstruction for emission tomography". IEEE
Trans. Med. Imaging MI-1(1982)113-122.
[2] K. Lange and R. Carson, \EM reconstruction algorithms for emission and transmission tomography",
J. Comput Assist Tomogr 8(1984)306-316.
[3] P. Gilbert, \Iterative methods for <strong>the</strong> three-dimensional reconstruction <strong>of</strong> an object from projections",
J. Theor. Biol. 36(1972)105-117.
[4] B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gullberg. \Comparison between ML-EM and WLS-CG
algorithms for SPECT image reconstruction", IEEE Trans Med Imaging MI-13(1994)601-609.
[5] S. Mastuoka, H. Shinohara, S. Yamamoto, Y. Niio, H. Shima, M. Yamada, et al., \Combined scatter
and attenuation correction for Tl-201 myocardial perfusion SPECT using OS-EM algorithm",
Nippon Acta Radiologica 58(1998)751-757.
[6] DM Titterington, \On <strong>the</strong> iterative image space reconstruction algorithm for ECT", IEEE Trans.
Med. Imaging MI-6(1987)52-56.
[7] W. R. Nelson, H. Hirayama, D. W. O. Rogers, \The EGS4 code system", Stanford Linear Accelerator
Center Report SLAC-265, 1985.
[8] A. P. Dempster, N. M. Laird, D. B. Rubin, \Maximum likelihood from incomplete data via <strong>the</strong>
EM algorithm", J. Roy Statis Soc B39(1977)1-38.
[9] K. Ogawa, Y. Harata, T. Ichihara, A. Kubo, S. Hashimoto, \A practical method for positiondependent
Compton-scatter correction in single photon emission CT", IEEE Trans. Med. Imag.
10(1991)408-412.
[10] T. Ichihara, H. Maeda, K. Yamakado, N. Motomura, K. Matsumura, K. Takeda, T. Nakagawa,
\Quantitative analysis <strong>of</strong> scatter- and attenuation-compensated dynamic single-photon emission
tomography for functional hepatic imaging with a receptor-binding radiopharmaceutical", Eur.
J. Nucl. Med. 24(1997)59-67.
[11] G. Salamon and Y. P. Huang,\Computed tomography <strong>of</strong> <strong>the</strong> brain", Springer-Verlag, Berlin
Heidelberg New York, 1980.
[12] H. Iida, Y. Narita, S. Eberl, \Simulation <strong>of</strong> Compton scatter in single photon-emission computedtomography",
Fifth EGS4 User's Meeting in Japan, KEK <strong>Proceedings</strong> 95-9, 33-46, 1995.
[13] Y. Narita, H. Iida, S. Eberl, et al., \Monte Calro evaluation <strong>of</strong> accuracy and noise properties <strong>of</strong> two
scatter correction methods for 201 Tl cardiac SPECT", IEEE Trans. on Nucl. Sci. 44(1997)2465-
2472.
[14] S. Maeda, K. Ogawa, \Quantitative assessment <strong>of</strong> scattered photons considering skull bone in
brain SPECT", Jpn. J. Nucl. Med. (Kaku-Igaku) 31(1994)431-439.
5

Table 1. Simulation parameters
Detector size 400 mm x 250 mm
Collimator geometry
Ultra high resolution (UHR) 1.0 mm x60mm
High sensitive (HS) 2.0 mm x35mm
Scintillator material and thickness NaI(Tl), 9.5mm
Energy windows
Main window 141 keV 10%
Sub window 120 keV 5%
Energy resolution 10%
Rotation radius 250 mm
Projection 128 x 128 matrix, 128 views over 360 degree
Pixel size 3.125 mm
6

Figure 1: Notation and coordinate systems.
Figure 2: Flowchart <strong>of</strong> three iterative algorithms.
7

Figure 3: Digital cylindrical and brain phantoms used in <strong>the</strong> simulation.
Figure 4: Simulated energy spectra using EGS4.
8

Figure 5: Progress <strong>of</strong> reconstruction for <strong>the</strong> cylindrical phantom using MLEM algorithm as a function <strong>of</strong> iteration
number.
Figure 6: The generated sinograms (projection data) from brain phantom and reconstructed images using
MLEM with and without ACSC for both collimators.
9

Figure 7: The values <strong>of</strong> 2 using MLEM algorithm with and without ACSC as a function <strong>of</strong> <strong>the</strong> number <strong>of</strong>
iteration.
Figure 8: Comparison <strong>of</strong> three iterative algorithms on 2 using UHR collimator as a function <strong>of</strong> <strong>the</strong> number <strong>of</strong>
iteration.
10

Figure 9: The values <strong>of</strong> gray/white matter counts ratio using MLEM algorithm with and without ACSC as a
function <strong>of</strong> <strong>the</strong> number <strong>of</strong> iteration.
Figure 10: Comparison <strong>of</strong> three iterative algorithms on gray/white matter counts ratio using UHR collimator
as a function <strong>of</strong> iteration.
11

Table 1 The radionuclides used in <strong>the</strong> measurement, and <strong>the</strong> photon energies emitted
from <strong>the</strong> radionuclides and <strong>the</strong> characteristic X-rays.
Radio Nuclide Energy Ratio
Am-241 26.3keV 2.40%
33.2keV 0.13%
59.5keV 35.90%
13.9keV (Np-L) 42.00%
Ba-133 81.0keV 34.10%
276.0keV 7.20%
31.0keV (Cs-K ) 23.1%
35.0keV (Cs-K ) 23.10%
Co-57 14.4keV 9.20%
122.0keV 85.60%
136.0keV 10.70%
Tc-99m 141.0keV 89.10%
18.4keV (Tc-K ) 8.10%
20.6keV (Tc-K ) 1.20%
φ
γ
Figure 1: The geometrical relationship <strong>of</strong> <strong>the</strong> radionuclide and <strong>the</strong> HP-Ge detector.
3

Figure 2: Aschematic illustration <strong>of</strong> <strong>the</strong> X-ray Tube (CIRCLEX6/1.2P18DE, Shimadzu).
4

StrippingMethodwithEGS4
AbsorptionSpectrum
insideHP-Ge
formono-energyphoton
NormalizationwithPhoto-Peak
(ComptonEscape,K-Escape&SumPeak)
Elimination<strong>of</strong>
Comptonescape,
K-escape
-EGS4-
NCASE500,000
AE0.52
AP0.001
ECUT0.52
X-raySpectrum
measuredwithHP-GeCrystal
Photo-Peak
Efficiency
Correctionwith
Photo-Peak
X-raySpectrum
correctedwithStrippingMethod
Figure 3: The ow diagram <strong>of</strong> <strong>the</strong> stripping method procedure using EGS4.
5

Efficiency ( % )
120
100
80
60
40
20
0
Co-57:14.4keV
Photo-Peak Efficiency inside HP-Ge Crystal Detector
Am-
Ba-133:31.0keV
Ba-133:35.0keV
Ba-133:53.2keV
Am-
6mmφ×10mm
6mmφ×5mm
0 20 40 60 80 100 120 140
Photon Energy ( keV )
Figure 4: The photon energy coe ciency inside <strong>the</strong> HP-Ge detector (6 mm 5 mm, 6 mm 10 mm).
Pulseheight(Counts/MeV/incident)
10 4
10 3
10 2
10 1
10 0
10 -1
10 -2
10 -3
AbsorptionspectruminsideHP-Ge
formono-energyphoton
0 20 40 60 80 100 120
Ba-133:81.0keV
110keV
PhotonEnergy(keV)
Figure 5: The absorption spectrum inside <strong>the</strong> HP-Ge detector for a mono-energy photon <strong>of</strong> 110 keV.
6
Co-57:122keV

2.0E+04
1.8E+04
1.6E+04
1.4E+04
1.2E+04
1.0E+04
8.0E+03
6.0E+03
4.0E+03
2.0E+03
0.0E+00
400
350
300
250
200
150
100
50
Birch&MarshallSimulation
90kV(2.5mmAl)
90kV(SiO2+...)
110kV(2.5mmAl)
110kV(SiO2+..)
0
0 20 40 60 80 100 120
PhotonEnergy(kev)
Figure 6: The simulated spectra <strong>of</strong> <strong>the</strong> X-ray tube at 90 kV and 110 kV.
Birch&Marshall
correction.(+)
correction.(-)
0 20 40 60 80 100 120
Photon Energy ( keV )
Figure 7: The observed X-ray spectra. Correction to <strong>the</strong> continuous X-ray by <strong>the</strong> stripping method produces a
spectrum from a radionuclide with multiple-energy photon radiation that is almost <strong>the</strong> same as that obtained
using <strong>the</strong> semi-empirical formula <strong>of</strong> Birch & Marshall.
7

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.242-249
Response <strong>of</strong> CdZnTe Detector
in Measurement <strong>of</strong> Diagnostic X-ray Spectra
S. Miyajima 1 , H. Sakuragi 2 and M. Matsumoto 2
1
Graduate School <strong>of</strong> Medicine, Course <strong>of</strong> Health Sciences, Osaka University
1-7 Yamadaoka, Suita, Osaka, 565-0871, Japan
2
School <strong>of</strong> Allied Health Sciences, Faculty <strong>of</strong> Medicine, Osaka University
1-7 Yamadaoka, Suita, Osaka, 565-0871, Japan
Abstract
We calculated <strong>the</strong> response functions <strong>of</strong> a CdZnTe detector to be employed in x-ray spectrometry
using LSCAT (Low energy photon SCATtering expansion for <strong>the</strong> EGS4 code). Incident energy <strong>of</strong>
x-rays was from 10 to 150keV. In <strong>the</strong> usercode, <strong>the</strong> Hecht equation was utilized to deal with <strong>the</strong>
e ects <strong>of</strong> trapping <strong>of</strong> charge carriers in a CZT crystal. Parameters in <strong>the</strong> Hecht equation, <strong>the</strong> mean
free path <strong>of</strong> charge carriers, were determined by comparing shapes <strong>of</strong> <strong>the</strong> peaks in <strong>the</strong> response
functions with <strong>the</strong> ones in measured -ray spectra (source: 241 Am, 133 Ba). Finally, we corrected
<strong>the</strong> measured x-ray spectra with <strong>the</strong> response functions. The results indicated a CdZnTe detector
is valid as a x-ray spectrometer with proper corrections.
1 Introduction
X-ray spectrometry is <strong>the</strong> measurement <strong>of</strong> energy distribution in x-rays emitted from an x-ray
tube. A High-Purity Germanium (HPGe) detector has usually been employed for its high e ciency
and excellent charge transport properties[1]. In x- or gamma-ray spectrometry, output pulse height
is not always proportional to <strong>the</strong> incident energy <strong>of</strong> x-rays because <strong>of</strong> escapes <strong>of</strong> <strong>the</strong> incident and
secondary x-rays. Therefore, corrections for detector response are required to obtain a real x-ray
spectrum we need to calculate <strong>the</strong> incident x-ray energies from <strong>the</strong> output <strong>of</strong> a detector <strong>the</strong> output
indicates energy deposited by <strong>the</strong> incident x-rays. To do this, response functions <strong>of</strong> a detector are
usually utilized to calculate a real x-ray spectrum from an output pulse height spectrum.
We employed a CdZnTe (CZT) detector as an x-ray spectrometer in this study. The CZT detector
can be operated at room temparature because it has a large band gap. As a result, <strong>the</strong> detector
doesn't need to be cooled by liquid nitrogen during measurement. It means a specroscopy system
with a CZT detector is relatively compact. However, charge transport properties in <strong>the</strong> CZT crystal
are poor because trapping <strong>of</strong> charge carriers is severe. For that reason, <strong>the</strong> e ects should be corrected
in addtion to <strong>the</strong> escape <strong>of</strong> incident and secondary x-rays.
In this study we analized a response <strong>of</strong> a CZT detector to monoenergetic x-rays to obtain parameters
in corrections. We calculated response functions with <strong>the</strong> parameters. To validate <strong>the</strong> response
functions, we corrected gamma-ray spectra and compared <strong>the</strong> results with <strong>the</strong> gamma-ray emission
rate <strong>of</strong> source. After that, we corrected x-ray spectra using <strong>the</strong> response functions.
2 Methods
A CdZnTe crystal in <strong>the</strong> detector (Amptek XR-100T) was a density <strong>of</strong> 5.86g/cm 3 and atomic
percentages <strong>of</strong> 45.0% (Cd), 5.0% (Zn), 50.0% (Te) respectively. The size was 3 3mm 2 with a
thickness <strong>of</strong> 2mm. It had a 0.25mm Be window on its face. Bias voltage was 2500V/cm (500V/0.2cm).
Incident x-rays were in pencil beams in both calculation and measurement.
1

2.1 Monte Carlo calculation
We calculated response functions <strong>of</strong> a CZT detector to monoenergetic x-rays with LSCAT (Low
energy photon SCATtering expansion for <strong>the</strong> EGS4 code)[2]. Incident energy <strong>of</strong> x-rays was from 10
to 150keV in 0.5keV increments. The followings were especially taken into account in <strong>the</strong> code
1. production <strong>of</strong> K-shell uorescence x-rays (K x-rays),
2. e ects <strong>of</strong> trapping <strong>of</strong> charge carriers.
Escape peaks <strong>of</strong> K x-rays in a spectrum are prominent for low energy x-rays such as diagnostic
x-rays because <strong>the</strong> photoelectric e ect is <strong>the</strong> most probable and <strong>the</strong> interactions tend to occur near a
detector surface. However, <strong>the</strong> default version <strong>of</strong> EGS4 deals with production <strong>of</strong> K x-rays in elements.
Therefore, we employed <strong>the</strong> test version <strong>of</strong> LSCAT (Low energy photon SCATtering expansion for
<strong>the</strong> EGS4 code), which had been developed at KEK, to deal with K x-rays in compounds. Now <strong>the</strong>
default version <strong>of</strong> LSCAT (kek_improve) can handle <strong>the</strong>m easily[3].
Such semiconductors as CZT have poor charge transport properties because <strong>of</strong> <strong>the</strong>ir relatively high
density <strong>of</strong> trapping centers. Since <strong>the</strong>y cause incomplete charge collection, peaks in a spectrum have
tails to <strong>the</strong> low energy side. Accordingly, we utilized <strong>the</strong> Hecht equation to take e ects <strong>of</strong> <strong>the</strong>m into
account in <strong>the</strong> code.
where
= e
D
(1 ; exp(;(D ; x)
:ratio <strong>of</strong> induced charge to initial charge,
x :distance from interaction site to cathode,
D :thickness <strong>of</strong> a crystal,
e :mean free path <strong>of</strong> electrons,
h :mean free path <strong>of</strong> holes.
e
)) + h
D
(1 ; exp(;x))
(1)
h
In this case, <strong>the</strong> induced charge due to energy deposition by an x-ray is equal to <strong>the</strong> initial charge
multiplied by . The parameters in <strong>the</strong> Hecht equation, mean free path <strong>of</strong> charge carriers, were
determined by comparing shapes <strong>of</strong> peaks (tails) in response functions with <strong>the</strong> ones in measured
gamma-ray spectra. And we determined <strong>the</strong> mean free path <strong>of</strong> electrons ( e) was 200 times larger
than that <strong>of</strong> holes ( h) in reference to literature on this subject to reduce <strong>the</strong> parameters in Monte
Carlo calculations, i.e. <strong>the</strong> parameter in <strong>the</strong> calculation was h only.
In <strong>the</strong> code, cut o energy was set at 5.0keV for photons (AP=0.005 in <strong>the</strong> PEGS4 input le) and
150.0keV for electrons (ECUT=0.150+0.511 in <strong>the</strong> EGS4 user code we did not transport electrons). To
consider <strong>the</strong> electron binding e ects in <strong>the</strong> Rayleigh and Compton scattering, options in <strong>the</strong> PEGS4
input les and <strong>the</strong> EGS4 user code were turned on (IRAYL=1, IBOUND=1, INCOH=1 in <strong>the</strong> PEGS4
input les, IRAYLR(I)=1, INCOHR(I)=1 in <strong>the</strong> EGS4 user code).
2.2 Experimental considerations
In measurement, we placed collimators in front <strong>of</strong> <strong>the</strong> detector (0.8mm for gamma-rays, 0.4mm
for x-rays, made from tungsten). We usually use collimators in x-ray spectrometry to reduce pulse
pileup. The pulse pileup causes distortion <strong>of</strong> <strong>the</strong> output spectrum which cannot be easily corrected.
Channel width was 0.1keV per channel in gamma-ray spectrometry and 0.5keV per channel in x-ray
spectrometry. The channel width for gamma-rays was smaller to avoid distortion due to <strong>the</strong> channel
width after FWHM (Full Width at Half Maximum) analysis, <strong>the</strong> gamma-ray data was converted to
data <strong>of</strong> 0.5keV per channel for correction procedures.
2

To compare measured peaks in gamma-ray spectra with <strong>the</strong> ones in response functions, we have to
remove distortion due to electric noise and statistical uctuations in number <strong>of</strong> charge carriers because
<strong>the</strong> response functions don't contain <strong>the</strong>se e ects. Therefore, we employed <strong>the</strong> unfolding method to
calculate a spectrum without this distortion. In <strong>the</strong> procedure, we regarded e ects <strong>of</strong> this distortion as
gaussian distribution based on measured FWHM. In <strong>the</strong> unfolding method, we used relations between
input and output as follows.
Z 1
M(E) =
where
S(E 0 ) :number <strong>of</strong> input x-rays with energy E 0 ,
0
R(EE 0 )S(E 0 )dE 0 (2)
R(EE 0 ) :response functions (matrix) probability <strong>of</strong> detection in channels corresponding
to energy E with incident energy E 0 ,
M(E) :number <strong>of</strong> output x-rays counted in channels corresponding to energy E.
We can obtain <strong>the</strong> input (S(E)) by solving <strong>the</strong> determinant(2). This determinant can be solved as
simultaneous equations.
2.3 Correction for spectra
We employed <strong>the</strong> stripping method to correct gamma- and x-ray spectra[4-6]. In <strong>the</strong> stripping
method, we assume counts in each channel consist <strong>of</strong> <strong>the</strong> following two components
1. counts due to photoelectric e ect without trapping,
2. counts due to contribution by incident x-rays with higher energies going through escapes <strong>of</strong>
secondary x-rays or trapping <strong>of</strong> charge carriers during charge transport.
In energy deposition in 2nd case, x-rays are counted on channels lower than <strong>the</strong> incident energy.
Procedures <strong>of</strong> <strong>the</strong> stripping method are as follows
1. remove counts due to 2. in spectrum,
2. divide <strong>the</strong> counts to be left with probability <strong>of</strong> full energy deposition without trapping (1.).
where
This procedure is represented by <strong>the</strong> following equation.
S(E) = M(E) ; P Emax
E 0 =E+1 R(EE0 )S(E 0 )
R(EE 0 )
S(E) :number <strong>of</strong> incident photons with energy E,
M(E) :number <strong>of</strong> output photons counted in channels corresponding to energy E,
Emax :maximum energy <strong>of</strong> a x-ray spectrum (determined by tube voltage),
R(EE 0 ) :response functions probability <strong>of</strong> detection in channels corresponding to energy
E with incident energy E 0 .
In this procedure, we assume counts in <strong>the</strong> highest energy <strong>of</strong> x-ray spectra don't contain counts
due to contribution from its higher energies, i.e. <strong>the</strong> M(Emax) is equal to <strong>the</strong> S(Emax).
3
(3)

2.4 Evaluation <strong>of</strong> results
First, to validate <strong>the</strong> calculated response functions, we corrected gamma-ray spectra <strong>of</strong> 241 Am
using <strong>the</strong>m and compared relative intensity <strong>of</strong> peaks in corrected spectra with <strong>the</strong> gamma-ray emission
rate <strong>of</strong> 241 Am. If <strong>the</strong> response functions are valid, corrected results are close to input data, i.e. source
data <strong>of</strong> Radio Isotopes. Next, we corrected measured x-ray spectra with <strong>the</strong> response functions. The
results were compared with corrected spectra measured with a HPGe detector.
3 Results
The results we obtained in this study were as follows
1. In <strong>the</strong> response functions calculated with <strong>the</strong> code, escape peaks <strong>of</strong> each element (Cd, Zn, Te)
and tails <strong>of</strong> each peak appeared (Fig.1). Parameters in <strong>the</strong> calculations were h = 0:20cm
( h =8:010 ;5 cm 2 =V in 2500V=cm), e =40:0cm ( e =1:610 ;2 cm 2 =V in 2500V=cm).
2. In gamma-ray spectra corrected with <strong>the</strong> response functions, relative counts <strong>of</strong> peaks were in
good agreement with <strong>the</strong> gamma-ray emission rate <strong>of</strong> source. At <strong>the</strong> same time, tails to <strong>the</strong> low
energy side <strong>of</strong> <strong>the</strong> peaks, due to trapping <strong>of</strong> charge carriers, also disappeared in spectra (Fig.2).
The results meant input spectra were calculated from output spectra and <strong>the</strong> response functions
were valid.
3. X-ray spectra corrected with <strong>the</strong> response functions were close to corrected spectra measured
with a HPGe detector (Fig.3).
4 Discussions
As you can see in Fig.4, tails in <strong>the</strong> response functions don't completely t <strong>the</strong> ones in measured
gamma-ray spectra. The discrepancies were more signi cant in<strong>the</strong> high energy region. We suppose
<strong>the</strong>re are problems in <strong>the</strong> assumptions made in <strong>the</strong> Hecht equation. In <strong>the</strong> Hecht equation, <strong>the</strong>
followings are assumed
1. trapped charges are not detrapped,
2. a uniform density <strong>of</strong> trapping centers in a crystal exists,
3. electric eld in a crystal is uniform.
Since presence <strong>of</strong> detrapping in a CZT crystal and models including <strong>the</strong> e ects are already published,
we should take <strong>the</strong> e ects into account in <strong>the</strong> code.
And <strong>the</strong> discrepancies in <strong>the</strong> high energy region <strong>of</strong> x-ray spectra must also be due to di erences
between calculated and measured responses. We believe <strong>the</strong> discrepancies must be smaller with improvements
made on <strong>the</strong> model related to <strong>the</strong> trapping <strong>of</strong> charge carriers.
5 Conclusions
We calculated response functions <strong>of</strong> a CdZnTe detector using LSCAT (Low energy photon SCATtering
expansion for <strong>the</strong> EGS4 code). Corrected spectra with <strong>the</strong> response functions were close to <strong>the</strong>
ones measured with a High Purity Germanium detector. A CdZnTe detector can be used in x-ray
spectrometry with proper corrections.
4

References
[1] T. R. Fewell and R. E. Shuping, \Photon energy distribution <strong>of</strong> some typical diagnostic x-ray
beams", Med. Phys. 4(3)(1977)187-197.
[2] Y. Namito and H. Hirayama, \LSCAT: Low-Energy Photon-Scattering Expansion for <strong>the</strong> EGS4
code (Inclusion <strong>of</strong> Electron Impact Ionization)", KEK Internal, 2000-4, 2000.
[3] H. Hirayama and Y. Namito, \Implementation <strong>of</strong> a General Treatment <strong>of</strong> Photoelectric-Related
Phenomena for Compounds or Mixtures in EGS4", KEK Internal, 2000-3, 2000.
[4] W. W. Seelentag and W. Panzer, \Stripping <strong>of</strong> x-ray bremsstrahlung spectra up to 300kVp on a
desk type computer", Phys. Med. Biol. 24(4) (1979)767-780.
[5] E. D. Castro et al., \The use <strong>of</strong> cadmium telluride detectors for <strong>the</strong> qualitative analysis <strong>of</strong> diagnostic
x-ray spectra", Phys. Med. Biol. 29(9)(1984)1117-1131.
[6] P. Pani, R. F. Laitano and R. Pellegrini, \Diagnostic x-ray spectra measurements using a silicon
surface barrier detector", Phys. Med. Biol. 32(9)(1987)1135-1149.
Relative Intensity
1
0.8
0.6
0.4
0.2
40keV
80keV
120keV
0
0 20 40 60 80 100 120
Energy [keV]
Figure 1: Response functions calculated with EGS4. Incident energy <strong>of</strong> x-rays are 40keV, 80keV and 120keV
respectively.
5

Relative Intensity
1
0.8
0.6
0.4
0.2
CZT corrected
CZT measured
0
0 10 20 30 40 50 60
Energy [keV]
Figure 2: A corrected gamma-ray spectrum compared with <strong>the</strong> measured one. Source was 241 Am. Tails <strong>of</strong> peaks
disapeared and relative intensity <strong>of</strong> peaks (26.3/59.5keV) agree well with gamma-ray emission rate <strong>of</strong> source.
6

Relative Intensity
Relative Intensity
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
CZT corrected
CZT measured
0 10 20 30 40 50 60 70 80
Energy [keV]
CZT corrected
HPGe corrected
0 10 20 30 40 50 60 70 80
Energy [keV]
Figure 3: (a) A corrected x-ray spectrum compared with <strong>the</strong> measured one. Tube voltage was 80kV. In <strong>the</strong>
corrected spectrum, low energy components are less than <strong>the</strong> ones in <strong>the</strong> measured spectrum.
(b) A corrected x-ray spectrum compared with a HPGe detectore. Tube voltage was 80kV.
7

Relative Intensity
Relative Intensity
1
0.8
0.6
0.4
0.2
Calculated
Measured
0
0 10 20 30 40 50 60 70 80
0.035
0.03
0.025
0.02
0.015
0.01
0.005
Energy [keV]
Figure 4: Di erence in tails between measured and calculated data.
0
0 20 40 60 80 100 120
Energy [keV]
CZT
HPGe
Figure 5: A corrected x-ray spectrum. Tube voltage was 120kV.
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.250-254
Evaluation <strong>of</strong> Response Functions <strong>of</strong>
16"x16"x4" Large-sized NaI Scintillation Detector
for Environmental Gamma-ray Survey
H. Itadzu, T. Iguchi, A. Uritani and J. Kawarabayashi
Department <strong>of</strong> Nuclear Engineering, Nagoya University
Furo-cho, Chikusa-ku, Nagoya, 464-8603, JAPAN
Abstract
Response functions <strong>of</strong> <strong>the</strong> 16"x16"x4" - large sized NaI detector, which is mainly used for high
sensitive gamma-ray survey in outdoor environment, have been calculated by using EGS4 code.
The calculated results are compared with <strong>the</strong> measured data for standard gamma-ray sources to
check <strong>the</strong>ir accuracy. Through <strong>the</strong> precise modeling <strong>of</strong> <strong>the</strong> detector structure in <strong>the</strong> calculation, <strong>the</strong>
agreement between both results has been improved up to around 15% relative deviation in 137 Cs
source spectrum. Based on this calculation model, <strong>the</strong> directional response matrix consisting <strong>of</strong>
24 energy groups x256 pulse height bins has been prepared to unfold gamma ray spectra from <strong>the</strong>
measured data. The unfolding results seem to be reasonable in a preliminary analysis on natural
background gamma-ray spectra.
1 Introduction
Wide area and rapid survey for environmental nuclear radiation is <strong>of</strong>ten needed in health physics
study[1], in <strong>the</strong> mineral resource search application[2] and/or sometimes in nuclear facility accidents[3].
For <strong>the</strong>se purposes, a mobile radiation survey system based on a large volume NaI scintillation detector
has already been developed and put to practical use. We have calculated response functions <strong>of</strong> a
16"x16"x4" large-sized NaI scintillation detector, which have not been established well, especially
directional response functions, by using <strong>the</strong> EGS4 code and veri ed an accuracy <strong>of</strong> <strong>the</strong> calculated
responses through comparison with experiments from <strong>the</strong> viewpoint <strong>of</strong> application to gamma-ray
spectrum unfolding.
2 Detector Speci cation and Calculation Model
The NaI detector used, is commercially available type GPX-1024 (Exploranium G.S. Ltd.). As
shown in Fig.1, it consists <strong>of</strong> four 4"x4"x16" NaI detector units arranged in parallel. Each NaI crystal
is hermetically sealed in a 0.5mm thick stainless steel container and attached with a photomultiplier
through an optical window (Fig. 2). The four components are packed into a ruggedized aluminum
case with an e ective thickness <strong>of</strong> 1.6mm, toge<strong>the</strong>r with some <strong>the</strong>rmal insulator and cushion materials.
In <strong>the</strong> EGS4 calculation, <strong>the</strong> detector structure was modeled as precisely as possible, except for
photomultipliers, that is, in a combinatorial geometry consisting <strong>of</strong> four kinds <strong>of</strong> regions, NaI crystal,
stainless steel cover, Aluminum case and air gap, as shown in Fig.3.
Twenty ve points <strong>of</strong> incident gamma-ray energy were selected between 0.005 MeV and 3.0 MeV
corresponding to <strong>the</strong> output signal gain <strong>of</strong> <strong>the</strong> detector system, while <strong>the</strong> pulse height distribution (or
deposited energy distribution inside <strong>the</strong> detector) obtained from <strong>the</strong> calculation was divided into 256
1

Figure 1: Appearance <strong>of</strong> GPX-1024.
Figure 2: Cross sectional view <strong>of</strong> each NaI scintillator
unit.
channels adjusting to <strong>the</strong> function <strong>of</strong> <strong>the</strong> Multi-channel analyzer. The above energy range includes
major gamma-rays produced from natural radioactive isotopes. This 25x256 response matrix was
prepared for a uniform parallel-beam gamma-ray incidence perpendicular to <strong>the</strong> 16"x16" detector
surface as a reference and also checked on <strong>the</strong> dependence <strong>of</strong> <strong>the</strong> gamma-ray beam incident angle to
<strong>the</strong> detector surface. In addition, some response functions for an isotropic point source were calculated
to compare with an experiment for standard gamma-ray sources, which were broadened to reproduce
<strong>the</strong> measured results <strong>of</strong> photoelectric peaks, according to an energy resolution (Gaussian) function
with an energy dependent relative FWHM (Full Width at Half Maximum),
p
+ E
R =
(1)
E
where E is <strong>the</strong> gamma-ray energy and <strong>the</strong> parameters and are experimentally determined.
Figure 3: Geometry for EGS4 calculation.
2

3 Results and Discussion
For standard gamma-ray sources such as 137 Cs and 60 Co, <strong>the</strong> directional response functions were
measured and compared with <strong>the</strong> calculated results. Fig. 4 shows an experimental arrangement to
measure <strong>the</strong> response function for a point source placed just above <strong>the</strong> 16"x16" detector surface, that
is, in <strong>the</strong> 0 degree incidence <strong>of</strong> gamma-rays. Fig. 5 gives an example <strong>of</strong> comparison results between
experiment and calculation for a 137 Cs(662 keV) gamma-ray source in <strong>the</strong> arrangement <strong>of</strong> Fig. 4.
By making <strong>the</strong> detector modeling more precise step by step, an agreement between both results has
reached up to within 15% relative deviation in <strong>the</strong> whole energy range. Fig. 6 illustrates ano<strong>the</strong>r
example <strong>of</strong> experimental arrangements to measure <strong>the</strong> response function in <strong>the</strong> just side ( or 90 degree)
incidence <strong>of</strong> gamma-rays. For this arrangement, <strong>the</strong> calculated response was also compared with <strong>the</strong>
measured one, as shown in Fig. 7, where good agreement is found in <strong>the</strong> energy range <strong>of</strong> a photoelectric
peak and compton continuum for <strong>the</strong> 137 Cs gamma-ray spectrum, while <strong>the</strong> discrepancy in <strong>the</strong> lower
energy region would be mainly due to <strong>the</strong> contribution <strong>of</strong> gamma-rays scattered from <strong>the</strong> experimental
room oor.
Figure 4: Experimental arrangement for <strong>the</strong> 0 degree
gamma-ray incidence.
Figure 6: Experimental arrangement for <strong>the</strong> 90 degree
gamma-ray incidence.
Figure 5: Comparison between experiment and calculation
in <strong>the</strong> 0 degree incidence <strong>of</strong> 137 Cs gamma-ray.
Figure 7: Comparison between experiment and calculation
in <strong>the</strong> 90 degree incidence <strong>of</strong> 137 Cs gamma-ray.
3

Figure 8: Comparison <strong>of</strong> calculated directional response
functions.
Figure 9: Preliminary unfolding result <strong>of</strong> natural
background gamma-ray spectrum.
Fig. 8shows a comparison <strong>of</strong> calculated directional responses corresponding to <strong>the</strong> incident angle
<strong>of</strong> uniform parallel-beam gamma-rays from 0 to 90 degrees. It is found that <strong>the</strong> directionality <strong>of</strong>
response functions is clearly appeared in <strong>the</strong> lower energy parts <strong>of</strong> pulse height distribution. This
means that <strong>the</strong> directional response functions <strong>of</strong> <strong>the</strong> present system should be precisely evaluated
and adequately applied to derive (or unfold) gamma-ray spectrum from measured data by considering
<strong>the</strong> directionality <strong>of</strong> gamma-ray elds <strong>of</strong> interest. Fig. 9 demonstrates a preliminary result <strong>of</strong>
natural background gamma-ray spectrum, which was derived from <strong>the</strong> measured data <strong>of</strong> environmental
gamma-rays through an analysis combining <strong>the</strong> present response matrix with a simple unfolding
method 'SAND-II'. The unfolded spectrum seems to be reasonable, where natural radioactive isotope
sources such as 40 K (1.461MeV), 214 Bi (1.765MeV), 208 Tl (2.615MeV) are clearly observed and
separated as gamma-ray peaks[4, 5].
4 Conclusion
We have calculated directional response functions and/or response matrices for a 16"x16"x4" -
large sized NaI detector by using <strong>the</strong> EGS4 code and checked <strong>the</strong>ir accuracy by comparing with <strong>the</strong>
measured responses for standard gamma-ray sources. The comparison results have shown that <strong>the</strong> calculated
responses could agree with <strong>the</strong> measured ones within 15% relative deviation( corresponding
to 3 )in 137 Cs source spectrum through <strong>the</strong> precise detector modeling in <strong>the</strong> calculation.
It has been also pointed out that <strong>the</strong> directional response functions should be precisely evaluated
and adequately applied to derive accurate gamma-ray spectra from measured data. For this purpose,
<strong>the</strong> EGS4 code is a powerful tool and will be used to make more detailed response matrices for our
NaI system.
References
[1] L. Travis et al., Nucl. Instr. and Meth. in Physics Research A 422(1999)144-147.
[2] M. Cruz et al, Fuel 77, No.13(1998)1427-1430.
4

[3] ICRU Report 53 1994.
[4] K. Saito, S. Moriuchi, JAERI 1306pp.6-7(1987).
[5] S. Minato, JCAC 32(1998)5.
5

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.255-263
Beam Dump for High Current Electron Beam at JNC
H. Takei and Y. Takeda 1
Japan Nuclear Cycle Development Institute (JNC)
4002 Narita, Oarai-machi, Ibaraki-ken 311-1393 Japan
Abstract
High current electron beams are required for transforming ssion products with gamma-rays.
Elemental technology to build a linac that can accelerate a high current beam in an e cient and
stable manner, is being developed at <strong>the</strong> Japan Nuclear Cycle development institute (JNC).
This paper presents <strong>the</strong> design and performance <strong>of</strong> a beam dump for a high current, low energy
beam (20 mA <strong>of</strong> a 10 MeV electron beam). A ring and disk (RD) structure was adopted to analyze
<strong>the</strong> condition <strong>of</strong> <strong>the</strong> beam in real-time, as well as to absorb <strong>the</strong> beam safely. The absorbed dose
rate for photons averaged over all directions is found to be 12.2 0.07 Gy/h using <strong>the</strong> EGS4 code
when <strong>the</strong> beam with average beam current <strong>of</strong>20mAenters into <strong>the</strong> beam dump.
The performance <strong>of</strong> <strong>the</strong> beam dump was evaluated using a beam <strong>of</strong> 7 MeV and an average
current <strong>of</strong> 0.84 mA. Comparison <strong>of</strong> 1 cm dose equivalent rate from <strong>the</strong> dose meter with that from
EGS4 code shows that <strong>the</strong> values from <strong>the</strong> EGS4 code at <strong>the</strong> beam energy <strong>of</strong> 7 MeV well reproduce
<strong>the</strong> experimental data.
1 Introduction
High current electron beams are required for transforming ssion products with gamma-rays.
Elemental technology to build a linac that can accelerate a high current beam in an e cient and
stable manner, is being developed at <strong>the</strong> Japan Nuclear Cycle development institute (JNC)[1].
The conceptual design <strong>of</strong> <strong>the</strong> accelerator was started in 1989. The test operation <strong>of</strong> <strong>the</strong> linac was
started aiming at <strong>the</strong> permitted average current <strong>of</strong> 10.5 mA, in October 1999, after many research
e orts. Main speci cation <strong>of</strong> <strong>the</strong> accelerator is shown in Table 1.
Table 1 Main speci cation <strong>of</strong> <strong>the</strong> JNC linac
Parameters Design values
Energy 10 MeV
Maximum Beam Current 100 mA
Average Beam Current 20 mA
Pulse Length 0.1 4 msec
Pulse Repetition 0.1 50 Hz
Duty Factor 0.001 20 %
Norm. Emittance 50 mm mrad
Energy Spread 0.5 %
estimated value by simulation
1 Guest Scientist from Paul Scherrer Institut (PSI), Switzerland
1

Since <strong>the</strong> beam from <strong>the</strong> JNC linac is a very high current, low energy beam, energy loss induced in
<strong>the</strong> material irradiated by <strong>the</strong> beam becomes very large, and resulting power density <strong>of</strong> heat generation
is also quite high.
Therefore, it is <strong>of</strong> utmost importance from <strong>the</strong> viewpoint <strong>of</strong> safety for <strong>the</strong> JNC beam dump to
be secured to dissipate and remove <strong>the</strong> generated heat e ciently. At <strong>the</strong> same time, shielding <strong>of</strong>
<strong>the</strong> radiation generated from <strong>the</strong> beam dump is also <strong>of</strong> major concern in order to minimize <strong>the</strong>
possible induction <strong>of</strong> radioactivity. Since <strong>the</strong> beam dump is installed on <strong>the</strong> beam line at about 10 m
downstream <strong>of</strong> <strong>the</strong> exit <strong>of</strong> <strong>the</strong> accelerator tube, it is also possible to utilize it as a beam monitor for
directly monitoring <strong>the</strong> condition <strong>of</strong> <strong>the</strong> beam.
2 Design
2.1 Conceptual Design
The conceptual design [2] <strong>of</strong> <strong>the</strong> JNC beam dump is based on <strong>the</strong> following four criteria:
(1) to disperse <strong>the</strong> beam by electromagnets disposed in front <strong>of</strong> <strong>the</strong> beam entry
(2) to stop <strong>the</strong> beam by absorbing it in spatially separated target blocks
(3) to minimize <strong>the</strong> possibility <strong>of</strong> <strong>the</strong> induction <strong>of</strong> radioactivity
(4) to add <strong>the</strong> function <strong>of</strong> a beam monitor for <strong>the</strong> high current beam.
The rst criterion is for making <strong>the</strong> current density <strong>of</strong> <strong>the</strong> beam smaller by spreading <strong>the</strong> beam
with quadrupole electromagnets. It is also assuring to avoid mishaps <strong>of</strong> <strong>the</strong> pin point beam hitting
<strong>the</strong> target and destroying it. The second criterion is for making <strong>the</strong> energy loss per unit volume <strong>of</strong> <strong>the</strong>
target smaller by absorbing <strong>the</strong> power <strong>of</strong> <strong>the</strong> spread beam in spatially distributed target. The third
criterion reduces <strong>the</strong> amount <strong>of</strong> material that is directly in <strong>the</strong> passage <strong>of</strong> <strong>the</strong> beam or near <strong>the</strong> beam
in order to reduce <strong>the</strong> possible induction <strong>of</strong> radioactivity. In particular, since <strong>the</strong> amount <strong>of</strong> cooling
water circulating to <strong>the</strong> heat exchanger tends to be large, care should be taken so that <strong>the</strong> cooling
water is not irradiated directly with <strong>the</strong> beam. The last criterion is to enable <strong>the</strong> direct monitoring
<strong>of</strong> <strong>the</strong> beam with average beam current <strong>of</strong> 20 mA. This is di cult with a conventional beam monitor.
It is especially important to grasp <strong>the</strong> situation immediately when <strong>the</strong> beam condition such as <strong>the</strong>
direction <strong>of</strong> <strong>the</strong> beam changes.
2.2 Target
It is a major feature <strong>of</strong> <strong>the</strong> JNC beam dump that <strong>the</strong> target for absorbing <strong>the</strong> beam is separated
into 22 plates. Each plate is made from Oxygen Free High-purity Copper (OFHC), and has thickness
<strong>of</strong> 5 cm. Fig. 1 shows <strong>the</strong> cross section <strong>of</strong> <strong>the</strong> beam dump including <strong>the</strong> plates.
The structure <strong>of</strong> <strong>the</strong> plates is such that 18 rings with each having slightly di erent inside diameter
are arranged on <strong>the</strong> upstream side and 4 disks having no hole are arranged on <strong>the</strong> downstream side.
This structure <strong>of</strong> <strong>the</strong> JNC beam dump will be hereafter referred to as Ring and Disk (RD) structure.
As described before, all <strong>the</strong> rings have di erent inside diameters which gradually decrease from
upstream to downstream. (The spread beam passes through inside this ring.) The frontmost ring has
<strong>the</strong> inside diameter <strong>of</strong> 19.6 cm and o<strong>the</strong>r rings have smaller diameters which successively decrease by
1.0 cm or 1.2 cm. The 18 rings are divided into two types according to <strong>the</strong> shape <strong>of</strong> <strong>the</strong> cross section
in a plane parallel to <strong>the</strong> beam axis direction (hereinafter referred to as Z-axis direction) in which <strong>the</strong>
beam travels. From No. 1toNo.10 ring, <strong>the</strong> cross section <strong>of</strong> <strong>the</strong> ring is a rectangular shape, that is,
<strong>the</strong> ring has equal thickness at <strong>the</strong> inside diameter and at <strong>the</strong> outside diameter. The cross section <strong>of</strong>
<strong>the</strong> remaining 8 rings is a wedge <strong>of</strong> shape having stepwisely smaller thickness at <strong>the</strong> inside diameter
compared to o<strong>the</strong>r portion. Fig. 2shows <strong>the</strong> typical cross sections <strong>of</strong> <strong>the</strong> rings. The two types <strong>of</strong> cross
2

enter into <strong>the</strong> beam dump. In Fig. 4, (1) shows <strong>the</strong> relation between energy and scattering angle, and
(2) shows <strong>the</strong> relation between energy and azimuth angle. As seen in Fig. 4, photons are localized in
<strong>the</strong> two regions, upper left and lower right regions. However, distribution is uniform with respect to
azimuth angle. Reason for <strong>the</strong> localization <strong>of</strong> photons in speci ed scattering angle lies in <strong>the</strong> di erence
<strong>of</strong> production process. The upper region <strong>of</strong> Fig. 4 (1) represents <strong>the</strong> photons produced by electrons
incident on <strong>the</strong> plates in <strong>the</strong> back scattering from <strong>the</strong> atomic nucleus. On <strong>the</strong> o<strong>the</strong>r hand, lower right
region represents photons which are produced by electrons traveling in <strong>the</strong> plates and which have
passed <strong>the</strong> lead shield. Therefore, energy <strong>of</strong> former photons is about 0.6 MeV, while energy <strong>of</strong> <strong>the</strong>
latter photons is about 2 MeV.
Fig. 5 shows energy spectra <strong>of</strong> photons falling in a speci ed range <strong>of</strong> scattering angle. In Fig. 5,
vertical axis represents photon uence, and solid angle is taken into account in (2). The scattering
angles set in <strong>the</strong> gure are 0 180 , 0 120 , 177.5 180 . Among <strong>the</strong>m, photons having <strong>the</strong>
scattering angle in 0 120 correspond to those photons in <strong>the</strong> lower right region <strong>of</strong> Fig. 4(1), and
photons having scattering angles in 177.5 180 correspond to those photons in <strong>the</strong> upper region
<strong>of</strong> <strong>the</strong> same gure. As can be seen from Fig. 5 (2), <strong>the</strong> number <strong>of</strong> photons per unit solid angle is
asymmetric with respect to scattering angle. The intensity <strong>of</strong> photons scattered in <strong>the</strong> direction devoid
<strong>of</strong> <strong>the</strong> lead shield, that is, in <strong>the</strong> backward direction, is higher than <strong>the</strong> intensity <strong>of</strong> photons scattered
in <strong>the</strong> forward direction. For example, <strong>the</strong> intensity <strong>of</strong> photons having scattering angle in 177.5
180 is as much as10 2 times higher than <strong>the</strong> intensity averaged over all directions.
From <strong>the</strong> above described result, when <strong>the</strong> beam with beam energy <strong>of</strong> 10.51 MeV and average
beam current <strong>of</strong>20mAenters into <strong>the</strong> beam dump, <strong>the</strong> absorbed dose rate for photons averaged over
all directions is found to be 12.2 0.07 Gy/h. Fig. 6 shows absorbed dose rate averaged over a
speci ed range <strong>of</strong> scattering angles. These values represent <strong>the</strong> absorbed dose rate at a distance <strong>of</strong> 1
m from <strong>the</strong> center <strong>of</strong> <strong>the</strong> beam dump, and were obtained by multiplying <strong>the</strong> value on <strong>the</strong> evaluating
sphere by 9.
When average beam current <strong>of</strong> accelerator is low, <strong>the</strong> absorbed dose rate in <strong>the</strong> direction <strong>of</strong> 180
from <strong>the</strong> beam dump may be substituted by <strong>the</strong> value for <strong>the</strong> scattering angle <strong>of</strong> 90 , and evaluation
performed accordingly. However, in <strong>the</strong> case <strong>of</strong> JNC accelerator where <strong>the</strong> average beam current is
high, it is important from <strong>the</strong> viewpoint <strong>of</strong> radiation protection to evaluate <strong>the</strong> dose rate for arbitrary
scattering angle. In <strong>the</strong> present study, <strong>the</strong> photons scattered backward from <strong>the</strong> JNC beam dump
were evaluated using <strong>the</strong> EGS4 code, and <strong>the</strong> value <strong>of</strong> 3100 Gy/h was obtained for <strong>the</strong> absorbed dose
rate.
4 Experimental Results and Discussion
4.1 General
In <strong>the</strong> test operation <strong>of</strong> <strong>the</strong> linac started in January 1999, beam current was increased aiming at
<strong>the</strong> permitted average current <strong>of</strong> 10.5 mA. In December <strong>of</strong> <strong>the</strong> same year, <strong>the</strong> linac was operated for
about 60 minutes with <strong>the</strong> average beam current <strong>of</strong>3.5mA (maximum beam current 100mA, pulse
width 1 msec, repetition frequency 35Hz). The nominal energy <strong>of</strong> <strong>the</strong> beam was 7.0 MeV as calculated
from <strong>the</strong> decrease <strong>of</strong> <strong>the</strong> high frequency energy.
During this test operation, a test was performed to determine <strong>the</strong> characteristics <strong>of</strong> <strong>the</strong> beam dump
for low current beam (<strong>the</strong> beam dump test). The average beam current in <strong>the</strong> beam dump test was
set to 0.84 mA (maximum beam current 100 mA, beam width 0.24 msec, repetition frequency 35Hz)
that allows electrons to be accelerated stably, since temperature <strong>of</strong> <strong>the</strong> plates need to be examined for
a long period.
4.2 Measurement <strong>of</strong> Dose Equivalent Rate
In order to measure <strong>the</strong> 1 cm dose equivalent rate during <strong>the</strong> beam dump test for comparison
with <strong>the</strong> result <strong>of</strong> <strong>the</strong> EGS4 code, lm badges (FB) and <strong>the</strong>rmoluminescence dosimeters (TLD) were
4

installed on <strong>the</strong> surface (at <strong>the</strong> locations <strong>of</strong> six black circles in Fig. 3) <strong>of</strong> <strong>the</strong> shield <strong>of</strong> <strong>the</strong> beam dump.
In <strong>the</strong> present test, one FB and a pair <strong>of</strong> two TLD was installed at each measuring point, and
irradiated by <strong>the</strong> beam for 172 minutes. As a result, two ndings were obtained. First, <strong>the</strong> most
<strong>of</strong> <strong>the</strong> energy <strong>of</strong> photons at each measuring point is equal to or greater than 80 keV. And second,
<strong>the</strong> three dose equivalents obtained at each measuring point were averaged, and shown in Fig. 7 as
1 cm dose equivalent rate. The error <strong>of</strong> <strong>the</strong> dose equivalent rate was obtained from <strong>the</strong> error <strong>of</strong> FB
50 %, <strong>the</strong> error <strong>of</strong> TLD 5 %, and <strong>the</strong> uctuation <strong>of</strong> <strong>the</strong> three measured values. When <strong>the</strong> measured
value exceeded <strong>the</strong> measuring range <strong>of</strong> TLD, <strong>the</strong> value <strong>of</strong> FB was used. Especially, since<strong>the</strong>value for
<strong>the</strong> scattering angle <strong>of</strong> 176 exceeded <strong>the</strong> measuring range <strong>of</strong> FB, <strong>the</strong> upper bound <strong>of</strong> FB (2 Sv) was
used. In addition, 1 cm dose equivalent rate was calculated using <strong>the</strong> EGS4 code for each measuring
point for average beam current <strong>of</strong> 0.84 mA, and shown in <strong>the</strong> same gure. Here, <strong>the</strong> computational
conditions for <strong>the</strong> EGS4 code are as follows.
(1) The beam energies are 7.0 MeV and 10.51 MeV.
(2) In order to adjust <strong>the</strong> maximum beam current for each module obtained from <strong>the</strong> EGS4 code so
as to coincide with <strong>the</strong> measured value, two cases for <strong>the</strong> density distribution <strong>of</strong> <strong>the</strong> current are
considered, that is, <strong>the</strong> distribution \3 ", and <strong>the</strong> Gaussian distribution with 1/5 <strong>of</strong> <strong>the</strong> beam
radius adopted as <strong>the</strong> standard deviation (hereafter, this distribution is referred to as \5 ").
(3) The photons at each measuring point are, considering <strong>the</strong> size <strong>of</strong> <strong>the</strong> pair <strong>of</strong> dosimeter, those
falling in <strong>the</strong> range <strong>of</strong> 5 cm on <strong>the</strong> shield centered at <strong>the</strong> dosimeter, except in <strong>the</strong> case <strong>of</strong> 0 ,
where <strong>the</strong> range 15 cm is used.
(4) The photon detection e ciency <strong>of</strong> each dosimeter is set to 1, since <strong>the</strong> measured dose equivalent
rate includes error <strong>of</strong> more than 50 % and <strong>the</strong> object <strong>of</strong> <strong>the</strong> present measurement istoevaluate
<strong>the</strong> performance <strong>of</strong> <strong>the</strong> beam dump.
Comparison <strong>of</strong> 1 cm dose equivalent rate from <strong>the</strong> dose meter with that from <strong>the</strong> EGS4 code shows
that <strong>the</strong> values from <strong>the</strong> EGS4 code at <strong>the</strong> beam energy <strong>of</strong> 7 MeV well reproduce <strong>the</strong> experimental
data. Especially, under <strong>the</strong> condition <strong>of</strong> \7.0 MeV, 5 ", <strong>the</strong> two seem to be in agreement within a
factor <strong>of</strong> about 2. For more detailed comparison, energy distribution <strong>of</strong> photons needs to be obtained.
5 Conclusion
A beam dump at JNC, employing <strong>the</strong> Ring and Disk structure, has been designed to absorb <strong>the</strong>
beam (200 kW <strong>of</strong> 10 MeV electron) safely and to analyze <strong>the</strong> beam condition in real-time. The beam
could be stopped at <strong>the</strong> inner edge <strong>of</strong> <strong>the</strong> rings which are cooled by water. The absorbed dose rate
for photons averaged over all directions is found to be 12.2 0.07 Gy/h using <strong>the</strong> EGS4 code when
<strong>the</strong> beam with average beam current <strong>of</strong>20mAenters into <strong>the</strong> beam dump.
The performance <strong>of</strong> <strong>the</strong> beam dump was evaluated using a beam <strong>of</strong> 7 MeV and an average current<strong>of</strong>
0.84 mA. Comparison <strong>of</strong> 1 cm dose equivalent rate from <strong>the</strong> dosimeter with that from EGS4 code shows
that <strong>the</strong> values from <strong>the</strong> EGS4 code at <strong>the</strong> beam energy <strong>of</strong> 7 MeV well reproduce <strong>the</strong> experimental
data. Especially, under <strong>the</strong> condition <strong>of</strong> \7.0 MeV, 5 ", <strong>the</strong> two seem to be in agreement within a
factor <strong>of</strong> about 2.
References
[1] S. Toyama et al., \Transmutation <strong>of</strong> long-lived Fission Product ( 137 Cs, 90 Sr) by a Reactor-
Accelerator System", Proceeding <strong>of</strong> 2nd <strong>International</strong> Symposium on Advanced Energy Research
(1990).
5

[2] H. Takei and Y. Takeda, \Conceptual Design <strong>of</strong> Beam Dump for High Power Electron Beam",
<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> Sixth EGS4 Users' Meeting in Japan, KEK <strong>Proceedings</strong> 96-10, November
1996.
[3] W. R. Nelson, H. Hirayama and D. W. .O Rogers, \The EGS4 Code System", SLAC-Report-265,
December 1985.
[4] A. F. Bielajew and D. W. O. Rogers, \PRESTA: The Parameter Reduced Electron-Step Transport
Algorithm for electron monte carlo transport", Nucl. Instr. and Meth. B18(1987)165.
Figure 1: JNC beam dump in cross-section.
6

Figure 4: The relation <strong>of</strong> <strong>the</strong> energy, scattering angle, and azimuth angle <strong>of</strong> 1.4*10 4 photons that pass through
<strong>the</strong> evaluating sphere.
Figure 5: Energy spectra <strong>of</strong> photons falling in a speci ed range <strong>of</strong> scattering angle.
8

Figure 6: Absorbed dose rate at a distance <strong>of</strong> 1 m from <strong>the</strong> center <strong>of</strong> <strong>the</strong> beam dump.
Figure 7: Comparison <strong>of</strong> 1 cm dose equivalent rate from <strong>the</strong> dose meter with that from <strong>the</strong> EGS4 code.
9

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.264-271
Variation <strong>of</strong> Dose Distribution by Detectors for Narrow Beam
T. Fujisaki, H. Saitoh 1 , T. Inada, S. Abe, M. Fukushi 1 and K. Fukuda 1
Ibaraki Prefectural University <strong>of</strong> Health Sciences
4669-2, Ami, Ami-Machi, Ibaraki 300-0394 Japan
1 Tokyo Metropolitan University <strong>of</strong> Health Sciences
7-2-10, Higashi-Ogu, Arakawa-Ku, Tokyo 116-8551 Japan
Abstract
Percentage depth dose (PDD) is <strong>the</strong> essential parameter for <strong>the</strong> absorbed dose determination.
Since precise measurement is required for <strong>the</strong> narrow beam especially, several kinds <strong>of</strong> detectors are
commonly used to measure dose distribution for narrow beam. However, <strong>the</strong> variation <strong>of</strong> response
caused by kinds <strong>of</strong> <strong>the</strong> detectors has not been investigated precisely.
In this study, PDDswere measured using several kinds <strong>of</strong> detectors, such as ionization chambers,
silicon diode detectors and lms. Fur<strong>the</strong>rmore, <strong>the</strong> absorbed dose <strong>of</strong> <strong>the</strong>se detection materials in
water was calculated using Monte Carlo simulation.
As a result, it was shown that <strong>the</strong> response <strong>of</strong> ionization chambers (air-gas) was higher than
diode detectors (silicon) and a lm (photoemulsion). Therefore, <strong>the</strong> depth dose curves changed by
kinds <strong>of</strong> <strong>the</strong> detector (materials).
1 Introduction
Percentage depth dose (PDD) is <strong>the</strong> essential parameter for <strong>the</strong> absorbed dose determination.
Since precise measurement is required for <strong>the</strong> narrow beam especially, several kinds <strong>of</strong> detectors,
such as ionization chambers, silicon diode detectors and lms, are commonly used to measure dose
distribution[1, 2,3,4].
Fur<strong>the</strong>rmore, <strong>the</strong> absorbed dose <strong>of</strong> <strong>the</strong>se detection materials in water was calculated using Monte
Carlo simulation. The variation <strong>of</strong> response caused by kinds <strong>of</strong> <strong>the</strong> detectors was investigated.
2 Methods
2.1 Measurements
The experiments were carried out at <strong>the</strong> IPU in Ibaraki, using <strong>the</strong> 10 MV X-ray beam from a
linear accelerator (Mitsubishi Electric, EXL-15SP). Four di erent ionization chambers, two di erent
silicon diode detectors and a photographic lm detector were used
1. a 30001 standard chamber (PTW-Freiburg),
2. a IC-10 standard waterpro<strong>of</strong> chamber (Wellho er Dosimetrie),
3. a IC-04 small volume waterpro<strong>of</strong> chamber (Wellho er Dosimetrie),
4. a PPC-05 markus shape waterpro<strong>of</strong> chamber (Wellho er Dosimetrie),
5. a EDD-5 entrance and exit dose p-Si photon detector (Scanditronix Medical),
6. a EDD-2 risk organ monitoring p-Si photon detector (Scanditronix Medical)
1

References
[1] C. F. Serago, P. V. Houdek, G. H. Hartmann, D. S. Saini, M. E. Serago and A. Kaydee, \Tissue
maximum ratios (and o<strong>the</strong>r parameters) <strong>of</strong> small circular 4, 6, 10, 15 and 24 MV x-ray beams for
radiosurgery", Phys Med Biol 37(1992)1943-1956.
[2] P. Francescon, S. Cora, C. Cavedon, P. Scalchi, and S. Reccanello, \Use <strong>of</strong> a new type <strong>of</strong> radiochromic
lm, a new parallel-plate micro-chamber, MOSFETs, and TLD 800 microcubes in dosimetry
<strong>of</strong> small beams", Med Phys 25(1998)503-511.
[3] C. McKerracher and D. I. Thwaites, \Assesment <strong>of</strong> new small- eld detectors against standard- eld
detectors for practical stereotactic beam data acquisition", Phys Med Biol 44(1999)2143-2160.
[4] IAEA: The use <strong>of</strong> plane parallel ionization chambers in high energy electron and photon beams
An international code <strong>of</strong> practice for dosimetry, IAEA, No. 381, 1997.
[5] W. R. Nelson, H. Hirayama and D. W. O. Rogers, \The EGS4 code system", , SLAC report-265,
1985.
[6] A. F. Bielajew and D. W. O. Rogers, \PRESTA, The \Parameter Reduced Electron Transport
Algo-rithm" for electron Monte Carlo transport", National Research Council <strong>of</strong> Canada report
PIRS-0042, 1987.
[7] <strong>International</strong> Commission on Radiation Units and Measurements (ICRU): Tissue Substitutes in
Radiation Dosimetry and Measurement, Report 44 <strong>of</strong> <strong>the</strong> ICRU, 1989.
[8] R. Mohan, C. Chui, and L. Lid<strong>of</strong>sky, \Energy and angular distributions <strong>of</strong> photons from medical
linear accelerators", Med Phys 12(1985)592-597.
3

Table 1 Physical parameters <strong>of</strong> <strong>the</strong> ionization chambers and silicon detectors
(courtesy <strong>of</strong> <strong>the</strong> manufacturers).
ionization chamber
Type Active Outer electorode Inner electorode
volume Material Thick Inner Material Radius Length
(cm 3 ) (mm) radius (mm) (mm)
(mm)
30001 0.6 PMMA 0.45 3.05 Al 0.5 21.2
IC 10 0.14 C-552 0.4 3.0 C-552 0.5 3.8
IC 04 0.03 C-552 0.4 2.0 C-552 0.5 2.1
PPC 05 0.04 Front window: C-552
Collecting electrode: diameter 10 mm, PPE, graphite
diode detector
Active volume Build-up cap Detector
Type (mm) Material Thick Material Thick <strong>of</strong><strong>the</strong>
(mm) Si chip(mm)
EDD-5 2.5x2.5x0.06 t Polystyrene 2.5 p-type Si 0.50 0.02
EDD-2 1.5 0:06 t Polyuretan 0.1 p-type Si 0.50 0.02
Epoxy plastic 0.3
4

φ
Figure 1: Geometrical arrangement <strong>of</strong> Monte Carlo simulation for deposit energy sampling. The incident
photons impinged vertically on a concentric circular cylindrical water phantom model (element and relative
amount <strong>of</strong> atoms in <strong>the</strong> compound by weight H 11.2 % O 88.8 %, density 1.0 g/cm 3 ) <strong>of</strong> 40 cm diameter and
50 cm thickness.
5

Mdepth/Mrefdepth=10
Mdetector/MIC-10
1.50
1.25
1.00
0.75
0.50
1.050
1.025
1.000
0.975
0.950
5×5cm2
IC-10
EDD-5
EDD-2
0 5 10 15 20
1.50
1.25
1.00
0.75
0.50
Depthinwater(cm)
(A) (B)
5×5cm2
0 5 10 15 20
Depthinwater(cm)
EDD-5
EDD-2
Mdepth/Mrefdepth=10
1.050
1.025
1.000
0.975
0.950
(C) (D)
Mdetector/MIC-10
1×1cm2
0 5 10 15 20
Depthinwater(cm)
IC-10
EDD-5
EDD-2
1×1cm2
0 5 10 15 20
Depthinwater(cm)
EDD-5
EDD-2
Figure 3: Relative depth dose curves normalized at 10 cm depth using diode detectors and IC-10 ionization
chamber. Lower column shows <strong>the</strong> ratio <strong>of</strong> diode detectors to ionization chamber.
Mdepth/Mrefdepth=10
1.50
1.25
1.00
0.75
0.50
5×5cm2
30001
XV-2
0 5 10 15 20
Depthintoughwaterphantom(cm)
Mdetector/M30001
1.100
1.075
1.050
1.025
1.000
0.975
0.950
0.925
0.900
(A) (B)
5×5cm2
0 5 10 15 20
Depthintoughwaterphantom(cm)
Figure 4: Relative depth dose curves normalized at 10 cm depth using XV-2 lm and 30001 ionization chamber.
(B) shows <strong>the</strong> ratio <strong>of</strong> lm to ionization chamber.
7

Cdepth/Crefdepth=10
Cmed/Cair
1.50
1.25
1.00
0.75
0.50
1.100
1.050
1.000
0.950
0.900
5×5cm2
air
si
photoemul
Cdepth/Crefdepth=10
1.50
1.25
1.00
0.75
1×1cm2
air
si
photoemul
0.50
0 5 10 15 20
0 5 10 15 20
(A)
Depthinwater(cm)
(B)
Depthinwater(cm)
5×5cm2
si
photoemul
Cmed/Cair
1.100
1.050
1.000
0.950
1×1cm2
si
photoemul
0.900
0 5 10 15 20
0 5 10 15 20
Depthinwater(cm)
(C) (D)
Depthinwater(cm)
Figure 5: The calculated depth dose curves normalized at 10 cm depth using air-gas, silicon and photoemulsion.
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.272-279
Returning Electron Simulation
for a Klystron Collector Using EGS4
Z. Fang, S. Fukuda 1 , S. Yamaguchi 1 , and S. Anami 1
The graduate university for advanced studies (Soken-Dai)
1 High energy accelerator research organization (KEK)
1-1, Oho, Tsukuba-shi, Ibaraki, 305-0801, Japan
Abstract
The process <strong>of</strong> electron backscattering in a klystron collector has been calculated using EGS4.
A program to simulate <strong>the</strong> returning electrons from <strong>the</strong> klystron collector has been developed
and its evaluation achieved. The e ects <strong>of</strong> <strong>the</strong> collector shape, i.e. its diameter and length, are
discussed and physical phenomena are clari ed. The dependence <strong>of</strong> <strong>the</strong> returning electrons on
various materials is also discussed in this paper.
1 Introduction
For a klystron collector, various e orts were made to understand power dissipation, cooling
method, collector potential depression and so on. Though <strong>the</strong> roles <strong>of</strong> secondary electrons and
backscattered electrons on <strong>the</strong> collector surface were suggested regarding abnormal collector heating,
less attention had been paid to <strong>the</strong> returning electrons from a collector. Recently, UHF klystrons
at KEK have shown a strong oscillation without any driving power in <strong>the</strong> input cavity, and it was found
that this oscillation was caused by returning electrons. Recently, <strong>the</strong> EGS4 Monte Carlo method[1,2]
has enabled us to simulate electrons interacting with <strong>the</strong> collector material in <strong>the</strong> energy range from
a few keV to several hundred keV this energy range corresponds to <strong>the</strong> applied voltage <strong>of</strong> a klystron.
Thus, a simulation <strong>of</strong> <strong>the</strong> returning electrons from <strong>the</strong> klystron collector has been attempted by designing
a program using <strong>the</strong> EGS4.
In this paper, prior to klystron applications, <strong>the</strong> EGS4 results are compared with experimental data
to check <strong>the</strong> accuracy in chapter 2. We have successfully performed a simulation on <strong>the</strong> returning
electrons from <strong>the</strong> klystron collector. Descriptions <strong>of</strong> <strong>the</strong> calculation method and <strong>the</strong> application
results to <strong>the</strong> klystron collector are given in chapter 3.
2 Comparison Between Backscattering Simulations and Experiments
Concerning <strong>the</strong> klystron collector, we are interested in electrons in <strong>the</strong> energy range from a few
keV to several hundred keV. Many scientists, such as E. J. Sternglass[3] and G. Neubert[4], had
measured backscattered electrons in this energy range. The experimental concept for backscattered
electrons is shown in Fig.1. Generally, a backscattering coe cient is de ned as <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> amount
<strong>of</strong> backscattered electrons to that <strong>of</strong> incident electrons. The angle dependence <strong>of</strong> <strong>the</strong> backscattering
coe cient for copper[4] is shown in Fig.2. The energy distribution <strong>of</strong> backscattered electrons[3] is
shown in Fig.3.
For this decade, an electron backscattering process could be simulated using <strong>the</strong> EGS4 code. Before
applying EGS4 to a klystron, it is necessary to con rm <strong>the</strong> code validity by comparing <strong>the</strong> calculation
1

with experiments for <strong>the</strong> fundamental process. This was applied for <strong>the</strong> case <strong>of</strong> a copper plate thicker
than 1mm.
It is well-known experimentally that <strong>the</strong> backscattering coe cients are essentially independent <strong>of</strong>
<strong>the</strong> primary energy[3] a simulation reproduced this successfully. For normal incidence on copper,
<strong>the</strong> backscattering coe cient is known to be about 0.3, and a simulation gave <strong>the</strong> same value. Fig.2
gives <strong>the</strong> simulation results <strong>of</strong> <strong>the</strong> backscattering coe cient as a function <strong>of</strong> <strong>the</strong> incident angle. The
calculated energy distributions <strong>of</strong> backscattered electrons are shown in Fig.3. The simulation results
<strong>of</strong> backscattered electrons agree well with <strong>the</strong> experiment results. From <strong>the</strong>se studies, it is concluded
that <strong>the</strong> EGS4 code is su ciently reliable to be applied to backscattered electrons from a klystron
collector.
3 Returning Electrons From a Klystron Collector
3.1 Simulation method
In <strong>the</strong> klystron <strong>the</strong> electron beam emitted from a gun is focused by external magnetic elds
are transported in <strong>the</strong> drift tube. The focusing magnetic eld decreases rapidly at <strong>the</strong> entrance <strong>of</strong>
<strong>the</strong> collector and <strong>the</strong> beam diverges in <strong>the</strong> collector due to <strong>the</strong> space-charge force. After <strong>the</strong> beam
bombards <strong>the</strong> collector surface, some <strong>of</strong> electrons are backscattered, and secondary electrons are also
created. Since <strong>the</strong> energy <strong>of</strong> <strong>the</strong> secondary electrons is less than 50eV, we could neglect <strong>the</strong>se e ects.
Some <strong>of</strong> <strong>the</strong> backscattered electrons have a chance to go back to <strong>the</strong> drift tube directly, or undergo
a few successive collisions with <strong>the</strong> collector wall. Some <strong>of</strong> <strong>the</strong>m are re ected by <strong>the</strong>rapidly varying
magnetic eld due to its mirror e ect, and electrons which are not re ected can be focused again by
<strong>the</strong> magnetic eld in <strong>the</strong> drift tube and transferred to <strong>the</strong> gun direction. These are called returning
electrons, and are considered to be harmful since <strong>the</strong>y can cause instabilities. Here, we de ne <strong>the</strong>
returning electron coe cient as <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> number <strong>of</strong> returning electrons to <strong>the</strong> number <strong>of</strong>
incident electrons.
The simulation <strong>of</strong> returning electrons from a klystron collector is divided into three steps:
1. a beam trajectory calculation due to <strong>the</strong> space-charge force in <strong>the</strong> collector up to <strong>the</strong> collector
wall,
2. a calculation <strong>of</strong> backscattered electrons on <strong>the</strong> collector surface using <strong>the</strong> EGS4 Monte-Carlo
method and associated track calculation in <strong>the</strong> collector, and
3. a plotting routine <strong>of</strong> <strong>the</strong> trajectories after <strong>the</strong> simulation.
The programs <strong>of</strong> step (1) and step (3) have been written by FORTRAN 90.
In step (1), <strong>the</strong> initial conditions <strong>of</strong> <strong>the</strong> beam at <strong>the</strong> entrance <strong>of</strong> <strong>the</strong> collector are calculated rst.
Here, because we assume <strong>the</strong> case <strong>of</strong> no driving rf power in an input cavity, <strong>the</strong> electrons have a
constant kinetic energy corresponding to <strong>the</strong> applied voltage. A uniform-density beam is assumed
and beam rotation due to <strong>the</strong> focusing magnetic eld is derived by <strong>the</strong> Bush <strong>the</strong>orem, <strong>the</strong> angularmomentum
conservation law in <strong>the</strong> electromagnetic eld. The beam is divided into a large number
<strong>of</strong> rays, each trajectory <strong>of</strong> which was calculated by solving <strong>the</strong> equation <strong>of</strong> motion numerically. In
this calculation, space-charge forces, relativistic e ects, self- eld and external magnetic eld e ects
were included. The nal data in this step were saved in memory to be made use <strong>of</strong> in <strong>the</strong> next
EGS4 application. The second step program was made by constructing a so-called \user code" using
MORTRAN. Using <strong>the</strong> data calculated in <strong>the</strong> previous step, backscattered processes are calculated
for each ray. Some electrons are absorbed in <strong>the</strong> collector material and some are backscattered after
bombarding <strong>the</strong> surface. The tracks <strong>of</strong> <strong>the</strong> backscattered electrons are traced by solving an equation
<strong>of</strong> motion including a magnetic eld until <strong>the</strong>y hit <strong>the</strong> wall again or until <strong>the</strong>y go back to <strong>the</strong> drift
tube. Parts <strong>of</strong> <strong>the</strong>m might bebackscattered or absorbed in <strong>the</strong> next collision <strong>the</strong>se are repeated until
returning electrons are completed to be calculated. In second step, <strong>the</strong> space-charge force is neglected.
2

Usually 1,000,000 electrons are employed for a calculation to obtain good statistics. After carrying
out simulations for all <strong>of</strong> <strong>the</strong>se incident electrons, <strong>the</strong> information concerning <strong>the</strong> returning electrons
is saved in memory, including <strong>the</strong>ir coe cient and energy distribution, and is used to plot trajectories
in <strong>the</strong> nal step. This program is executed using a personal computer with a clock <strong>of</strong> 333MHz it
takes 2 hours for a simulation.
3.2 Simulation results
A typical collector shape used in this simulation is shown in Fig.4 D t is <strong>the</strong> diameter <strong>of</strong> <strong>the</strong>
drift tube: D c and L c are <strong>the</strong> diameter and length <strong>of</strong> <strong>the</strong> collector, respectively. Returning electrons
have been calculated based on <strong>the</strong> various shapes <strong>of</strong> a collector made <strong>of</strong> a copper material. The
results, including <strong>the</strong> actual klystron dimensions, are given in table 1 <strong>the</strong> relative error in this table is
reduced from <strong>the</strong> statistical error <strong>of</strong> <strong>the</strong> number <strong>of</strong> <strong>the</strong> returning electrons. The energy distributions <strong>of</strong>
returning electrons corresponding to <strong>the</strong> actual collector shapes are shown in Fig.5. In this gure, <strong>the</strong>
energy <strong>of</strong> <strong>the</strong> returning electrons is normalized by <strong>the</strong> incident-beam energy at <strong>the</strong> collector entrance,
and a few <strong>of</strong> <strong>the</strong> returning electrons have a higher energy than <strong>the</strong> incident beam, since some are
accelerated by <strong>the</strong> space-charge force. It has been clari ed that <strong>the</strong> number <strong>of</strong> returning electrons
strongly depends upon <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> drift-tube diameter to <strong>the</strong> collector diameter. It has also been
clari ed that <strong>the</strong> length <strong>of</strong> <strong>the</strong> collector has a large e ect on <strong>the</strong> returning electrons. These tendencies
are given in Fig.6 (a) shows <strong>the</strong> returning electron coe cient as a function <strong>of</strong> <strong>the</strong> collector length, L c
(b) shows <strong>the</strong> returning electron coe cient as a function <strong>of</strong> <strong>the</strong> collector diameter, D c.
In order to analyze <strong>the</strong> features <strong>of</strong> returning electrons from <strong>the</strong> collector, a sketch <strong>of</strong> three di erent
typical collector shapes is shown in Fig.7, where <strong>the</strong> shaded line on <strong>the</strong> collector boundary indicates
<strong>the</strong> collector surface bombarded by <strong>the</strong> incident beam. From Fig.6 <strong>the</strong> contributions to <strong>the</strong> returning
coe cient can be divided into two parts: one from <strong>the</strong> cylindrical surface <strong>of</strong> <strong>the</strong> collector and ano<strong>the</strong>r
from <strong>the</strong> cone shaped surface <strong>of</strong> <strong>the</strong> collector. The former contribution seems to come mainly from
backscattering <strong>of</strong> <strong>the</strong> beam edge parts, since <strong>the</strong> coe cients remain constant for large Lc. This also
means that one collision is predominant for <strong>the</strong> returning electrons. This may be directly shown by
some arti cial setting <strong>of</strong> <strong>the</strong> boundary <strong>of</strong> EGS4, which we are planning to do. It is natural that
if <strong>the</strong> cone-shaped part <strong>of</strong> <strong>the</strong> collector is located near to <strong>the</strong> drift tube, a fairly large number <strong>of</strong>
direct backscattering electrons contribute to <strong>the</strong> returning electrons. For designing a suitable collector
with small returning electron coe cients, a suitable ratio <strong>of</strong> <strong>the</strong> drift-tube diameter to <strong>the</strong> collector
diameter should be determined for an acceptable backscattering coe cient. If a longer collector shape
can be chosen, only this diameter ratio determines <strong>the</strong> number <strong>of</strong> returning electrons. When a longer
collector size is not allowed for some manufacturing reason, compromising between <strong>the</strong> two factors
mentioned above is necessary by investigating <strong>the</strong> tendency, like Fig.6. A similar analysis is applicable
to a collector <strong>of</strong> o<strong>the</strong>r microwave tube devices, a beam dump <strong>of</strong> <strong>the</strong> accelerator, a secondary electron
monitor (SEM) and a Farad cup, if unwanted returning electrons are desired to be eliminated.
Interesting features can be obtained by changing <strong>the</strong> collector material. Figure 8 shows <strong>the</strong> returning
electron coe cient from a collector made <strong>of</strong> various materials, and Fig.9 gives <strong>the</strong> energy
distribution <strong>of</strong> returning electrons from a collector made <strong>of</strong> various materials. Obviously, a smaller
number <strong>of</strong> returning electrons is expected from low atomic-number materials. Using an aluminum or
its alloy is possible for <strong>the</strong> collector material. Ano<strong>the</strong>r application is, for example, to use SiC as <strong>the</strong>
collector material. Since <strong>the</strong> range in material for this electron energy region is very small, making
a coating on <strong>the</strong> collector surface using <strong>the</strong> sputtering technique is also possible. If a manufacturing
limitation prevents a suitable size <strong>of</strong> <strong>the</strong> collector, <strong>the</strong> material choice may be important.
4 Conclusion
Asimulation code for applying EGS4 to calculate returning electrons from <strong>the</strong> klystron collector
has been developed after an evaluation <strong>of</strong> <strong>the</strong> electron backscattering process returning electrons
3

were successfully calculated. The returning electron coe cient and energy distributions are shown
with various collector shapes. It is shown that <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> drift-tube diameter to <strong>the</strong> collector
diameter plays an important role concerning <strong>the</strong> number <strong>of</strong> returning electrons. The procedure used
to design a collector with small returning electron coe cients is also presented. Interesting features
<strong>of</strong> returning electrons concerning various materials have been investigated, and <strong>the</strong> possibility to use
o<strong>the</strong>r materials instead <strong>of</strong> well-used copper material is also presented. These simulation results had
been applied to a study <strong>of</strong> <strong>the</strong> oscillation <strong>of</strong> a UHF klystron caused by returning electrons <strong>the</strong> results
agreed with <strong>the</strong> experiment [5].
References
[1] W. R. Nelson, H. Hirayama and D. W. O. Rogers, \The EGS4 code system", SLAC-report-265,
1985.
[2] W. R. Nelson and Y. Namito, \The EGS4 code system: solution <strong>of</strong> gamma-ray and electron
transport problems", SLAC-PUB-5193, February, 1990.
[3] E. J. Sternglass, \Backscattering <strong>of</strong> kilovolt electrons from solids", Phy. Rev. Vol. 95, No.
2(1954)345-358.
[4] G. Neubert and S. Rogaschewski, \Backscattering coe cient measurements <strong>of</strong> 15 to 60 keV
electrons for solids at various angles <strong>of</strong> incidence", Phys. Stat. Sol. (a) 59(1980)35-41.
[5] Z. Fang et al., \Simulation <strong>of</strong> returning electrons from a klystron collector", to be presented in
<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> 20th international linac conference, California, USA, August 2000.
4

Figure1:Sketch<strong>of</strong>electronbackscatteringonaplate
Figure2:Back-scatteringcoefficientasfunction<strong>of</strong><strong>the</strong>incidentangleonacoppersurface.
RelativeNo.
(Incidentenergy<strong>of</strong>electrons,60keV;Experimentdata,reference4)
1.2
1
0.8
0.6
0.4
0.2
0
Incidentelectrons
θ
Material
Back-scatteringCoefficient
1
0.8
0.6
0.4
0.2
0
EGS4
experiment
experiment
EGS4
Angledistribution<strong>of</strong>
back-scatteredelectrons
0 30 60 90
Incident degrees
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
E/Eo
Figure3:Energydistributions<strong>of</strong>back-scatteredelectronsfromacoppersurface.
(Incidentenergy<strong>of</strong>electrons,32keV;Experimentdata,reference3)
5

Electron
beam
Figure4:Typicalcollectorshape
Table1:Returningelectroncoefficientfordifferentdimensions<strong>of</strong>acoppercollector.
Dt(cm) Dc(cm) Lc(cm) Returningelectroncoefficient Relativeerror
10
13 62.4 0.00665 1.2%
23 92.4 0.00174 2.4%
23 122.4 0.00136 2.7%
7 23 122.4
0.00081 3.5%
5
Fraction(%)
0.06
0.05
0.04
0.03
0.02
0.01
0
Dt
Dc
EnergyDistribution<strong>of</strong>ReturningElectrons
0.00023 6.6%
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
E/E0
Figure5:Energydistributions<strong>of</strong>returningelectronsfordifferentdimensions<strong>of</strong>acoppercollector.
6
Lc
#1
#1A
#2

Returningcoefficient(%)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 50 100 150 200 250 300
Lc(cm)
(a) (b)
Figure6:Returningelectroncoefficientasfunction<strong>of</strong><strong>the</strong>collectorlength(Lc)anddiameter(Dc).
Collector(a)
Dc(13cm)
Dc(23cm)
Dc(30cm)
Dc(40cm)
Collector(b)
Figure7:Sketch<strong>of</strong>threedifferenttypicalcollectorshapes.
Returningcoefficient(%)
0.5
0.4
0.3
0.2
0.1
0
Incident
electronbeam
7
Lc(122.4cm)
Lc(182.4cm)
Lc(262.4cm)
0 10 20 30 40 50
Dc(cm)
Collector(c)

Returningelectroncoefficient(%)
0.3
0.25
0.2
0.15
0.1
0.05
0
ReturningCoefficient(%)
Carbon Aluminum Iron Copper Tungsten Lead
Figure8:Returningelectroncoefficientasafunction<strong>of</strong><strong>the</strong>collectormaterial.
Fraction(%)
0.03
0.025
0.02
0.015
0.01
0.005
0
EnergyDistribution<strong>of</strong>ReturningElectrons
Carbon
Aluminum
Iron
Copper
Tungsten
Lead
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
E/E0
Figure9:Returningelectronenergydistributionasfunction<strong>of</strong><strong>the</strong>collectormaterial.
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.280-285
Direct Measurement <strong>of</strong> Electron-Tracks
Using a Charge Coupled Device
S. Kitamoto 12 , M. Ohta 1 , T. Okada 1 , T. Kohmura 1 ,
K. Mori 1 , H. Awaki 23 , K. Tachibana 3
1
Department <strong>of</strong> Earth and Space Science, Graduate School <strong>of</strong> Science, Osaka University
1-1, Machikaneyama, Toyonaka, Osaka, 560-0043, Japan
2
CREST Japan Science and Technology Corporation (JST)
4-1-8 Honmachi, Kawaguchi, Saitama 332, Japan
3
Department <strong>of</strong> Physics, Faculty <strong>of</strong> Science, Ehime University, Matsuyama, 790-8577, Japan
Abstract
We present two-dimensional projections <strong>of</strong> various electron tracks in silicon. Acharge-coupleddevice
(CCD) was exposed to -rays (976 keV and 1048 keV) from 207 Bi radio isotope. The incident
angle <strong>of</strong> <strong>the</strong> -rays was set to be a grazing incidence <strong>of</strong> 13 deg. The -rays deposit charge in
<strong>the</strong> pixels according to <strong>the</strong>ir tracks. Thus <strong>the</strong> obtained images show two-dimensional projections
<strong>of</strong> <strong>the</strong> -ray tracks. This experiment isuseful for diagnosis <strong>of</strong> CCDs. We also show a thickness
measurement <strong>of</strong> <strong>the</strong> depletion layer <strong>of</strong> a CCD.
1 Introduction
Charge coupled devices (CCDs) as a X-ray detector are now widely used. As well as its imaging
capability, aCCD has many advantages as a X-ray detector. If a CCD is used as a photon counting
and <strong>the</strong> incident X-ray intensity is enough low soastoavoidamultiple photon detection, a CCD has
a good energy resolution [1,2]. A CCD also can measure polarization <strong>of</strong> X-ray photons by analyzing
<strong>the</strong> charge cloud distribution produced by a single X-ray[3]. In <strong>the</strong> X-ray astronomy, now a CCD is
one <strong>of</strong> a standard focal plane detector <strong>of</strong> X-ray telescopes[1,4,5].
2 Motivation <strong>of</strong> this work
In order to deduce <strong>the</strong> maximum capability <strong>of</strong> CCDs, <strong>the</strong> measurement <strong>of</strong><strong>the</strong>internal structure
<strong>of</strong> <strong>the</strong> CCD, such as <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> depletion layer, is important. Also understanding <strong>of</strong> <strong>the</strong>
behavior <strong>of</strong> electrons in a CCD is required. In gure 1, a schematic illustration <strong>of</strong> a cross section <strong>of</strong> a
front illuminated CCD and a behavior <strong>of</strong> electrons are shown.
A front illuminated CCD has various gate structures on <strong>the</strong> top <strong>of</strong> <strong>the</strong> CCD, which acts as a
dead layer for X-ray detection. X-rays, which penetrate <strong>the</strong> dead layer, are absorbed by Si due to a
photo-electric interaction and <strong>the</strong>n a photo-electron is created. The photo-electron ionizes surrounding
atoms and produces a number <strong>of</strong> electron-hole pairs. The number <strong>of</strong> <strong>the</strong> electron has an information
on <strong>the</strong> energy <strong>of</strong> <strong>the</strong> incident X-ray. However, <strong>the</strong> behavior <strong>of</strong> <strong>the</strong> electrons is complicated, because <strong>the</strong>
internal structure <strong>of</strong> a CCD is complicated. The electrons created near <strong>the</strong> boundary <strong>of</strong> <strong>the</strong> pixels are
divided into two or more number <strong>of</strong> pixels. Fur<strong>the</strong>rmore, if electrons are created in <strong>the</strong> channel-stop,
only a part <strong>of</strong> <strong>the</strong> electrons will be detected as a signal[6,7]. Although electric eld is strong in <strong>the</strong>
depletion layer and <strong>the</strong> di usion <strong>of</strong> <strong>the</strong> electrons is small, <strong>the</strong> electric eld is weak below <strong>the</strong> depletion
1

3 Experiments
For a -ray source, 207 Bi radio isotope is selected. 207 Bi is a conversion electron source and emits
mono-energetic -rays. The measured spectrum with a windowless Si(Li) detector is shown in gure
3. Two peaks by -rays (976 keV and 1048 keV) are clearly seen. Some -rays are also emitted. Since
<strong>the</strong> range <strong>of</strong> <strong>the</strong> -rays are roughly 2mm, signi cant fraction <strong>of</strong> <strong>the</strong> -rays will run straightly in Si
while it has enough energy.
Figure 3: The energy spectrum <strong>of</strong> 207 Bi obtained by a windowless Si(Li) detector. Two peaks at 976 keV and
1048 keV are by mono-energetic electrons.
The used CCD is a front illuminated CCD produced by HAMAMATSU K.K . The pixel size is 12
m square and <strong>the</strong> number <strong>of</strong> pixels are 512 512. The CCD is cooled down to ;100 o C using LN2.
Ashutter is installed on <strong>the</strong> front <strong>of</strong> <strong>the</strong> 207 Bi source. The size <strong>of</strong> <strong>the</strong> -ray source is less than 0.5mm.
Aschematic illustration <strong>of</strong> <strong>the</strong> experimental setup is shown in gure 4 and <strong>the</strong> pictures are shown in
gure 5 and gure 6. The incident angle <strong>of</strong> <strong>the</strong> -ray is ranging from 12 deg to 14 deg according to
<strong>the</strong> position <strong>of</strong> <strong>the</strong> imaging area <strong>of</strong> <strong>the</strong> CCD. 300 images with an exposure time <strong>of</strong> 50 sec are obtained.
4 Electron Tracks
One example <strong>of</strong> <strong>the</strong> CCD image is shown in gure 7. -rays were exposed from right side <strong>of</strong>
<strong>the</strong> gure. Many tracks can be seen. Since <strong>the</strong> 207 Bi emits -rays as well as -rays, we extracted
<strong>the</strong> candidates <strong>of</strong> -ray events. The horizontal straight lines with di use image at <strong>the</strong> left end were
picked up. Six examples <strong>of</strong> <strong>the</strong> extracted images are shown in gure 8. The straight and thin tracks
correspond to <strong>the</strong> electrons from <strong>the</strong> depletion layer and <strong>the</strong> di use image corresponds to <strong>the</strong> eld free
region below <strong>the</strong> depletion layer.
From <strong>the</strong>se data we can deduce <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> depletion layer and also measure <strong>the</strong> di usion <strong>of</strong>
<strong>the</strong> electron as a function <strong>of</strong> <strong>the</strong> depth from <strong>the</strong> surface. Here we show <strong>the</strong> results <strong>of</strong> <strong>the</strong> measurement
<strong>of</strong> depletion layer thickness. First we extracted an favorable events straight thin track events with
3

[9] A. Owens et al., X-ray Spectrometry 476(1997)924.
[10] M. W. Bautz, S. Kissel, G. Prigozhin, S. Jones, T. Isobe, H. Manning, M. Pivovaro , G. Ricker,
and J. Woo, SPIE <strong>Proceedings</strong> 2808(1996)170.
[11] R. Hartmann., et al., Nucl. Instrum. Meth. A 377(1996)191.
[12] K. Mori, M. Shouh, H. Katayama, S. Kitamoto S., et al., Nucl. Instrum. Meth. A. (2000)in press.
Figure 6: A picture <strong>of</strong> <strong>the</strong> experimental setup. The CCD and <strong>the</strong> -ray source are installed in a vacuum
chamber.
Figure 7: One example <strong>of</strong> <strong>the</strong> CCD image. The -ray was exposed from right side.
5

Figure 8: Six examples <strong>of</strong> images <strong>of</strong> <strong>the</strong> -ray events. The pixel size is 12 m.
Figure 9: Average length <strong>of</strong> straight-thin region <strong>of</strong> <strong>the</strong> -ray tracks as a function <strong>of</strong> <strong>the</strong> position on <strong>the</strong> imaging
area <strong>of</strong> <strong>the</strong> CCD. Best t expected curve is also plotted.
6

Table 1 List <strong>of</strong> Monte Carlo simulations and its parameters for gas bremsstrahlung production.
Author Organization code maximum target AE AP pressure gas
(date) electron length (MeV) (MeV) (atm) material
energy
G.Tromba Sincrotrone
& A.Rindi[3] Trieste EGS4 10GeV 1m 1.0 0.01 1.0 air
(1990)
J.C.Liu[4] SLAC EGS4 10GeV 1m 1.511 0.1 1.0 air
(1994)
Ferrari
et.al [1] INFN FLUKA 1GeV 1,10m 10.0 0.01 1.0, 0.1 air
(1993)
N.E.Ipe &
A.Fasso[5] SLAC FLUKA 7GeV 15m 10.0 0.01 1.0, 0.1 air
(1994)
2 Calculations
Sensitivity analyses were carried out at
1. <strong>the</strong> number <strong>of</strong> interactions,
2. several AE values ranging from 0.521 to 10 MeV under 1.0 and 0.1 atm,
3. several gas pressure values ranging from 1 to 10 ;3 atm under <strong>the</strong> straight section lengths <strong>of</strong> 1m,
19m, and 40m, and
4. several stored electron energy, to investigate its dependence on <strong>the</strong> energy spectrum and <strong>the</strong>
emission angle distribution <strong>of</strong> <strong>the</strong> gas bremsstrahlung.
The option <strong>of</strong> <strong>the</strong> true angular distribution <strong>of</strong> <strong>the</strong> emitted photons[6] is employed in all calculations
with double precision. The calculated photon energy spectra and photon emission angle distributions
are given in
1. Fig.1 for <strong>the</strong> number <strong>of</strong> interactions,
2. Fig.2 and Fig.3 for several AE values ranging from 0.521 to 10 MeV under 1.0 and 0.1 atm,
3. Figs.4 to 9 for several gas pressure values ranging from 1 to 10 ;3 atm under <strong>the</strong> straight section
lengths <strong>of</strong> 1m, 19m, and 40m, and
4. Fig.10 for several stored electron energy, respectively.
As shown in Fig.1, <strong>the</strong> gas bremsstrahlung generated within single interactions between <strong>the</strong> electrons
and 0.1205 g/cm 2 air molecules is about 60 % <strong>of</strong> that generated within multi-interactions. The
gas bremsstrahlung is nearly saturated within triple or more interactions. As shown in Figs.2, 3, AE
value dependence is apparent on <strong>the</strong> intensity <strong>of</strong> gas bremsstrahlung generation, while <strong>the</strong> energy
spectrum and <strong>the</strong> emission angle distribution are independent <strong>of</strong>AEvalues under 0.01205 g/cm 2 (0.1
atm). Figure 4 shows that <strong>the</strong> energy spectrum is independent <strong>of</strong> gas pressure under <strong>the</strong> length <strong>of</strong>
straight section <strong>of</strong> 1 m, while as shown in Fig.5, although gas pressure dependence is apparent on <strong>the</strong>
emission angle distribution, its dependence becomes less for a gas pressure below 0.01205 g/cm 2 (0.1
atm). However, as shown in Figs. 6, 7, 8, and 9, gas pressure dependence is apparent on both <strong>the</strong>
intensity <strong>of</strong> energy spectrum and <strong>the</strong> emission angle distribution under <strong>the</strong> lengths <strong>of</strong> straight section
<strong>of</strong> 19 mand40 m. Moreover, <strong>the</strong> longer <strong>of</strong> straight section, <strong>the</strong> tendency <strong>of</strong> <strong>the</strong> dependence is more
apparent. The calculation with su cient accuracy is no longer expected under <strong>the</strong> gas pressure <strong>of</strong> 0.1
atm with <strong>the</strong> AE value <strong>of</strong> 10 MeV for SPring-8. Figure 10 shows that <strong>the</strong> emission angle distribution
2

strongly depend on <strong>the</strong> stored electron energy, especially <strong>the</strong> extreme directivity is recognized in stored
electron energy <strong>of</strong> 8 GeV.
The e ective doses <strong>of</strong> anterior-posterior irradiation geometry as a function <strong>of</strong> <strong>the</strong> radius <strong>of</strong> <strong>the</strong>
surface <strong>of</strong> <strong>the</strong> photon uence crossing are shown in Fig. 11 with depending on gas pressure with <strong>the</strong>
path length <strong>of</strong> 16.54m at 40 m from <strong>the</strong> center <strong>of</strong> <strong>the</strong> straight sections, allowing multi interaction
<strong>of</strong> electron. Figure 12 shows <strong>the</strong> angular distributions <strong>of</strong> <strong>the</strong> gas bremsstrahlung as a functions
<strong>of</strong> <strong>the</strong> number <strong>of</strong> interactions. As shown in both gures, <strong>the</strong> e ective dose strongly depends on
<strong>the</strong> calculational gas pressure and <strong>the</strong> e ect <strong>of</strong> <strong>the</strong> multi interaction is negligible small in angular
distribution at <strong>the</strong> pressure <strong>of</strong> 0.001 atm.
Figure 13 shows <strong>the</strong> relations between <strong>the</strong> angular distributions and electron path length that
depends on <strong>the</strong> gas pressure, indicating <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> emissions within 0.1 mradian to total emissions
in <strong>the</strong> vertical axis. As shown in this gure, <strong>the</strong> ratio can be on one curve. Moreover, <strong>the</strong> curve indicates
that <strong>the</strong> ratio is focused to <strong>the</strong> constant value below <strong>the</strong> electron path length <strong>of</strong> 10 ;2 g/cm 2 .
3 Conclusions
The simulations <strong>of</strong> gas bremsstrahlung at SPring-8 beamlines were performed as <strong>the</strong> functions
<strong>of</strong> <strong>the</strong> interactions, AE values, and residual gas pressures to get su cient accuracy <strong>of</strong> <strong>the</strong> intensity
and angular distribution <strong>of</strong> <strong>the</strong> emission. As <strong>the</strong> results, <strong>the</strong> simulations under <strong>the</strong> recommendations
<strong>of</strong> Ferrari et al. have some problems for <strong>the</strong> conditions <strong>of</strong> SPring-8 beamlines. The spectrum <strong>of</strong> gas
bremsstrahlung is independent <strong>of</strong> <strong>the</strong> gas pressure, however <strong>the</strong> angular distribution <strong>of</strong> photon emission
depends on <strong>the</strong> pressure strongly. In order to correct <strong>the</strong> defect, it is clari ed that <strong>the</strong> path length
<strong>of</strong> stored electron must be set to be less than 10 ;2 g/cm 2 . This means that <strong>the</strong> simulation conditions
must be set to be less than 0.1 atm <strong>of</strong> air in case <strong>of</strong> <strong>the</strong> straight section <strong>of</strong> 1 m and 0.0025 atm for 40
m. Moreover, it is clari ed that <strong>the</strong> simulations <strong>of</strong> gas bremsstrahlung with su cient accuracy can be
performed under <strong>the</strong> path length <strong>of</strong> less than 10 ;2 g/cm 2 without considering <strong>the</strong> AE (lower cut o
energy for electron and threshold energy <strong>of</strong> M ller scattering to minimize any angular de ection) and
<strong>the</strong> restriction <strong>of</strong> single interaction <strong>of</strong> stored electron with residual gas molecules.
References
[1] A. Ferrari, M. Pellicioni, and P. R. Sala, \Estimation <strong>of</strong> uence rate and absorbed dose rate due
to gas bremsstrahlung from electron storage rings", Nucl. Instrum. Methods B83(1993)518-524.
[2] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, \The EGS4 CODE system", SLAC-265 (1985).
[3] G. Tompa and A. Rindi, \Gas Bremsstrahlung from Electron Storage rings: A Monte Carlo
Evaluation and Some Useful Formula", Nucl.Instum. Methods A292(1990)700-705.
[4] J. C. Liu et al., \Gas Bremsstrahlung and Associated Photon-Neutron Shielding Calculations for
Electron Storage Rings", SLAC-Pub-6532 (1994).
[5] N. E. Ipe and A. Fasso, \Gas bremsstrahlung considerations in <strong>the</strong> shielding design <strong>of</strong> <strong>the</strong> Advanced
Photon Source synchrotron radiation", Nucl. Instrum. Methods A351(1994)534-544.
[6] A. F. Bielajew et al., National Research Council <strong>of</strong> Canada, Internal Report PIRS-0203 (1989).
3

x10 –15
Photons(Ep*dN/dEp)[e –1 m –1 at10 –9 Torr]
6.0
5.0
4.0
3.0
2.0
10 0
INT3–INT5
INT2
INT1
10 1
10 2
10 3
PhotonEnergy(MeV)
10 4
Fig.1 Gas bremsstrahlung spectra depending on <strong>the</strong>
number<strong>of</strong><strong>the</strong>interactionsgeneratedbyEGS4resulting
from8GeVelectronandinteractingwith0.1205g/cm 2 air.
(INT1; single interactions, INT2; double interactions,
INT3,4,5;tripleormoreinteractions.)
Photon(Ep*dN/dEp)[e –1 m –1 at10 –9 Torr]
10 –14
10 –15
10 –2.0
–16
10
AP;0.1MeV
AE(0.521–10MeV)
AP;0.01MeV
AE(0.521MeV)
0.0
10
2.0
10
PhotonEnergy(MeV)
0.1atm
Fig.3 Gas bremsstrahlung spectra depending on lower
cut<strong>of</strong>fenergyforelectron,AE,andlowercut<strong>of</strong>fenergyfor
photon,AP,allowingonlysingleinteraction<strong>of</strong>electronwith
residualgas<strong>of</strong>0.01205g/cm 2 air.
4
Photon(Ep*dN/dEp)[e –1 m –1 at10 –9 Torr]
[x10 –15 ]
6.0
5.0
4.0
3.0
2.0
0.0
10
0.621MeV
1.0
10
1.511MeV
0.561MeV
0.521MeV
2.0
10
PhotonEnergy(MeV)
1atm,AE
10.0MeV
3.0
10
Fig.2 Gasbremsstrahlungspectradependingonlower
cut <strong>of</strong>f energy for electron, AE, allowing only single
interaction<strong>of</strong>electronwithresidualgas<strong>of</strong>0.1205g/cm 2
air.
Photon(Ep*dN/dEp)[e –1 m –1 at10 –9 Torr]
10 –14
10 –15
10 –2 10 –16
single–interaction
10 0
10 2
Energy(MeV)
:1atm
:0.1atm
:0.01atm
:0.001atm
Fig.4 Gas bremsstrahlung spectra depending on gas
pressurewith<strong>the</strong>pathlength<strong>of</strong>1mandAE<strong>of</strong>10MeV,
allowingonlysingleinteraction<strong>of</strong>electron.

Photon(sr –1 e –1 m –1 at10 –9 Torr)
10 –5
10 –6
single–interaction
:1atm
:0.1atm
:0.01atm
:0.001atm
10
0 0.1 0.2
–7
EmissionAngle(mradian)
Fig.5 Angular distributions depending on gas pressure
with<strong>the</strong>pathlength<strong>of</strong>1mandAE<strong>of</strong>10MeV,allowing
onlysingleinteraction<strong>of</strong>electron.
Photon(sr –1 e –1 m –1 at10 –9 Torr)
10 –5
10 –6
10 –7
multiinteraction
singleinteraction
:1atm
:0.1atm
:0.01atm
:0.001atm
0 0.1 0.2
Emissionangle(mrad.)
Fig.7 Angular distributions depending on gas pressure
with<strong>the</strong>pathlength<strong>of</strong>19mandAE<strong>of</strong>10MeV,allowing
only single interaction <strong>of</strong> electron and multi interaction
within1atm.
5
Photon(Ep*dN/dEp)[e –1 m –1 at10 –9 Torr]
10 –14
10 –2
10 –15
10 0
singleinteraction
multiinteraction
10 2
:1atm
:0.1atm
:0.01atm
:1atm
Energy(MeV)
Fig.6 Gas bremsstrahlung spectra depending on gas
pressurewith<strong>the</strong>pathlength<strong>of</strong>19mandAE<strong>of</strong>10MeV,
allowing only single interaction <strong>of</strong> electron and multi
interaction.
Photon(Ep*dN/dEp)[e –1 m –1 at10 –9 Torr]
10 –14
10 –2
10 –15
singleinteraction
multiinteraction
10 0
10 2
:1atm
:0.1atm
:0.01atm
:0.001atm
:1atm
Energy(MeV)
Fig.8 Gas bremsstrahlung spectra depending on gas
pressurewith<strong>the</strong>pathlength<strong>of</strong>40mandAE<strong>of</strong>10MeV,
allowing only single interaction <strong>of</strong> electron and multi
interaction.

Figure 9: Angular distributions depending on gas
pressure with <strong>the</strong> path length <strong>of</strong> 40 m and AE <strong>of</strong> 10
MeV, allowing only single interaction <strong>of</strong> electron and
multi interaction within 1 atm.
Figure 11: The e ective dose distributions as a function
<strong>of</strong> radial scoring area due to gas bremsstrahlung
in anterior-posterior irradiation geometry at 40 m
from <strong>the</strong> center <strong>of</strong> <strong>the</strong> straight section, allowing multiinteractions
and AE <strong>of</strong> 10 MeV. (The full circles indicate
<strong>the</strong> calculations with <strong>the</strong> gas pressure <strong>of</strong> 0.001
atm, open circles 0.01 atm, open triangle 0.1 atm,
and Open squares 1 atm)
6
Figure 10: Angular distribution depending on stored
electron energy with <strong>the</strong> path length <strong>of</strong> 1 m and gas
pressure <strong>of</strong> 0.1 atm, allowing only single interaction
<strong>of</strong> electron.
Figure 12: Angular distributions depending on <strong>the</strong>
allowing number <strong>of</strong> interactions generated by EGS4
resulting from 8 GeV electron and interacting with
0.00482 g/cm 2 air. (INT1: single interactions, INT2
double interactions, INT3,4 triple or more interactions)

Photonemittionratio(

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.293-298
Study on Spatial Distribution <strong>of</strong> Electromagnetic Shower
Around a Lead Block Irradiated by 700-MeV Bremsstrahlung
S. Oki, Y. Takashima 1 , M. Yamakage, H. Kobayakawa
K. Yoshida 2 , K. Goto 2
Dept. <strong>of</strong> Materials Processing Eng., Graduate School <strong>of</strong> Engineering,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
1 Institute for Molecular Science, Myodaiji, Okazaki, 444-8585, Japan
2 Hiroshima Synchrotron Radiation Center, Hiroshima University,
2-313 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan
Abstract
We measured electromagnetic showers around a Pb block set on a photon beam line extended
from a straight section <strong>of</strong> a storage ring by using thin NaI(Tl) scintillation counter. We also
performed simulations <strong>of</strong> <strong>the</strong> experiment by using EGS4 Monte Carlo code and compared with <strong>the</strong>
experimental results. We apply <strong>the</strong> calculation to evaluate <strong>the</strong> dose equivalent <strong>of</strong> electromagnetic
shower and neutrons generated in a Pb shielding block irradiated by 1-GeV bremsstrahlung.
1 Introduction
Electron storage rings constructed for sources <strong>of</strong> synchrotron radiation usually have some straight
sections in which insertion devices are installed to generate intense light. Gas bremsstrahlung, whichis
produced by interaction <strong>of</strong> circulating electrons with residual gas in <strong>the</strong> straight section passes through
a beam line and <strong>the</strong>n cause electromagnetic shower in a shielding block. There are many studies for
shielding <strong>the</strong> bremsstrahlung by measuring <strong>the</strong> electromagnetic shower behind shielding blocks. In a
facility <strong>of</strong> small storage ring, we usually work near <strong>the</strong> ring or beamlines in which <strong>the</strong> shielding blocks
for <strong>the</strong> bremsstrahlung are constructed so that it is needed to investigate <strong>the</strong> distribution <strong>of</strong> radiations
all around <strong>the</strong> shielding blocks.
The study <strong>of</strong> spatial distribution <strong>of</strong> <strong>the</strong> electromagnetic shower around <strong>the</strong> shielding block is
necessary to estimate <strong>the</strong> radiation dose in order to make e ective shields for radiations. We measured
energy deposition <strong>of</strong> electromagnetic shower in a thin NaI(Tl) scintillation counter positioned around
a small Pb block and compare <strong>the</strong> results with calculations performed by using EGS4 Monte Carlo
code.
2 Experiment
The measurementwas performed at Hiroshima Synchrotron Radiation Center (HiSOR), Hiroshima
University. The storage ring is <strong>of</strong> a racetrack type and consists <strong>of</strong> two long straight sections <strong>of</strong> 8.24
mandtwo bending magnets <strong>of</strong> 2.7 tesla. The electron energy is 700 MeV and <strong>the</strong> stored current just
after injection was about 100 mA.
Experimental set up is shown in Figure 1. Gas bremsstrahlung produced in a vacuum duct <strong>of</strong> <strong>the</strong>
straight section passed through a sapphire exit window and injected intoa5cm 5cm 2cmlead
block which was set in <strong>the</strong> air. NaI(Tl) scintillation counter was used to detect <strong>the</strong> electromagnetic
shower from <strong>the</strong> lead block. The diameter and <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> NaI(Tl) was 2.45 cm and 1.8 mm,
respectively. We calibrated <strong>the</strong> counter by using a 137 Cs standard radiation source. The detection
1

Figure 1: Experimental set up is schematically shown.
Figure 2: Geometry <strong>of</strong> <strong>the</strong> Pb block and NaI(Tl) counter used in EGS4 calculation.
angles were 60 ,75,90, 105 ,120 and <strong>the</strong> distance from <strong>the</strong> lead block to <strong>the</strong> NaI(Tl) counter was
23 cm. A lead collimater <strong>of</strong> 2.0 cm diameter was set in front <strong>of</strong> <strong>the</strong> NaI(Tl) detector.
The intensity <strong>of</strong> <strong>the</strong> gas bremsstrahlung is normalized by <strong>the</strong> absorbed energy in <strong>the</strong> grass dosimeter,
1.6 cm 1.6 cm 0.15 cm, set behind <strong>the</strong> sapphire window in order to compare <strong>the</strong> data <strong>of</strong> <strong>the</strong>
experiment and <strong>the</strong> simulation.
3 Simulation using EGS4
We performed simulation <strong>of</strong> our experiment by using EGS4 Monte Carlo code. Figure 2 shows
<strong>the</strong> geometry used in our calculation.
We sampled photon energy uniformly between 0.1 MeV to 700 MeV. A weight for <strong>the</strong> calculation <strong>of</strong>
electromagnetic cascade caused by a photon <strong>of</strong> each energy is decided by <strong>the</strong> following bremsstrahlung
cross section <strong>of</strong> complete screening [1, 2].
kdk =4 r 0Z(Z +1) dk
k
1+( E
E 0
) 2 ; 2
3
E
E 0
1
; ln (183Z 3 )+ 1
9
E
E 0
(1)
where is ne structure constant, r 0 is <strong>the</strong> classical electron radius, Z is e ective atomic number <strong>of</strong>
residual gas, k is photon energy and E 0 is <strong>the</strong> electron energy circulating in <strong>the</strong> storage ring. The
radius <strong>of</strong> bremsstrahlung was assumed to be 1cm.
Figure 3(a)-(e) shows <strong>the</strong> measured and <strong>the</strong> calculated pulse hight distribution <strong>of</strong> energy deposition
<strong>of</strong> electrons, positrons and photon in <strong>the</strong> NaI(Tl) counter at <strong>the</strong> detection angle <strong>of</strong> 60 ,75 ,90 , 105 ,
2

120 , respectively. One incident photon <strong>of</strong> bremsstrahlung causes electromagnetic shower in <strong>the</strong> Pb
target and a number <strong>of</strong> electrons, positrons and photons are generated. Some <strong>of</strong> <strong>the</strong>se particles enter
<strong>the</strong> NaI(Tl) counter and deposit <strong>the</strong>ir energy.
10 8
10 7
10 6
10 5
10 4
10 3
107
106
105
104
103
(a)
Experiment
EGS4
0 1 2 3 4 5
102
0 1 2 3 4 5
10 7
10 6
10 5
10 4
10 3
10 2
(e)
0 1 2 3 4 5
10 8
10 7
10 6
10 5
10 4
10 3
10 7
10 6
10 5
10 4
10 3
10 2
(b)
Experiment
EG S4
0 1 2 3 4 5
(d)
0 1 2 3 4 5
Figure 3: Energy deposition <strong>of</strong> electromagnetic shower in <strong>the</strong> NaI(Tl) counter. The detection angle are (a)60 ,
(b)75 , (c)90 , (d)105 and (e)120 . Closed circles and open squares show <strong>the</strong> experimental and calculated
results, respectively.
The peaks near 0.8 keV in Figure 3(a),(b),(c) agree with <strong>the</strong> energy <strong>of</strong> <strong>the</strong> minimum ionization
loss <strong>of</strong> electrons in NaI(Tl) <strong>of</strong> 1.8 mm thick. The data <strong>of</strong> calculations give good agreement with <strong>the</strong>
experiment.
4 Radiation shielding for 1-GeV bremsstrahlung
There is a plan to construct a small synchrotron radiation facility inNagoya University. The electron
energy, current and circumference <strong>of</strong> <strong>the</strong> storage ring are 1 GeV, 300 mA and 36 m, respectively.
The storage ring is planed to have 6.40 m straight sections.
3

We calculated energy deposition <strong>of</strong> electromagnetic shower in water placed around a Pb shielding
block irradiated by 1-GeV bremsstrahlung generated in <strong>the</strong> straight section in order to evaluate <strong>the</strong>
dose equivalent for various thicknesses <strong>of</strong> <strong>the</strong> Pb shielding block. In <strong>the</strong> calculation, we sampled <strong>the</strong>
energy <strong>of</strong> bremsstrahlung between 100 MeV to 1 GeV. The atomic number <strong>of</strong> residual gas in <strong>the</strong>
storage ring was assumed to be 10.
The dose equivalent H is expressed as
H = DQ: (2)
D is <strong>the</strong> average energy deposition in water with unit mass. D was evaluated at <strong>the</strong> depth <strong>of</strong> 1 cm from
<strong>the</strong> surface <strong>of</strong> <strong>the</strong> water. Q is quality factor and equal to 1 for photons, electrons and positrons[3].
Figure 4 shows <strong>the</strong> dose equivalent <strong>of</strong> electromagnetic shower in water which was placed at 1 m
from <strong>the</strong> Pb block for one incident photon. The cross section <strong>of</strong> <strong>the</strong> Pb blocks was 10 cm 10cm.
The calculation was performed for three thicknesses <strong>of</strong> Pb blocks. Open diamonds, open squares and
crosses are <strong>the</strong> results for <strong>the</strong> thickness <strong>of</strong> 5 cm, 10 cm and 15 cm, respectively.
Figure 5(a)-(c) show spatial distribution <strong>of</strong> <strong>the</strong> dose equivalent <strong>of</strong> electromagnetic shower for one
week <strong>of</strong> running time. In this calculation, we assumed that <strong>the</strong> electron current was constant <strong>of</strong> 300
mA and <strong>the</strong> storage ring worked 40 hours in a week.
High energy photons generate neutrons in <strong>the</strong> shielding block by photo-nuclear reactions[3]. We
calculated neutron yield caused by giant resonance in <strong>the</strong> Pb shielding block. The neutron yield Y is
expressed by <strong>the</strong> following equation[4],
Y = N 0
A
(k) =
Z Emax
Eth
dl
dk
m
1+ (k2 ;k 2 m )2
k 2 ; 2
(k)dk (3)
(4)
where N 0 is Avogadro constant, is <strong>the</strong> density <strong>of</strong> Pb block, A is <strong>the</strong> mass number <strong>of</strong> Pb, Emax =40
MeV is maximum photon energy for giant resonance and Eth = 6:7 MeV is <strong>the</strong> threshold energy
dl
for giant resonance. is di erential track length calculated by EGS4. (k) is <strong>the</strong> cross section <strong>of</strong>
dk
one neutron production by giant resonance. m, km and ; are <strong>the</strong> maximum cross section <strong>of</strong> giant
resonance ( 639 mb), <strong>the</strong> photon energy for m ( 13.4 MeV) and half width <strong>of</strong> <strong>the</strong> cross section ( 4.07
MeV), respectively. The dose equivalent D is
D = YH
(5)
2 4 r
where r is <strong>the</strong> distance from <strong>the</strong> Pb block.
Figure 6 shows <strong>the</strong> result <strong>of</strong> our calculation <strong>of</strong> <strong>the</strong> dose equivalent <strong>of</strong> neutrons caused by giant
resonance at 1 m from <strong>the</strong> Pb block. Open squares and open diamonds show <strong>the</strong> results for 1 GeVand
0.7-GeV bremsstrahlung, respectively. The dose equivalent increases with <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> Pb
block and saturate at 10 cm.
In this calculation, we do not consider <strong>the</strong> absorption <strong>of</strong> neutrons in <strong>the</strong> Pb block so that <strong>the</strong> dose
equivalent is constant for <strong>the</strong> thicknesses over 10 cm.
5 Conclusion
We measured electromagnetic shower using NaI(Tl) scintillation counter placed around a Pb block
irradiated by 700-MeV gas bremsstrahlung at HiSOR. We performed simulation <strong>of</strong> <strong>the</strong> experiment by
using EGS4 Monte Carlo code. The simulation gave good agreement with <strong>the</strong> experiment.
We evaluated <strong>the</strong> dose equivalent <strong>of</strong> electromagnetic shower and neutrons caused by 1-GeV bremsstrahlung
in order to estimate <strong>the</strong> thickness <strong>of</strong> a shielding Pb block. Pb block <strong>of</strong> 10 cm 10 cm
15 cm is needed to restrict dose equivalent under 1mSv/w. The dose equivalent <strong>of</strong> neutrons are <strong>the</strong>
same order as that <strong>of</strong> electromagnetic shower for <strong>the</strong> 15 cm thick Pb block.
4

Figure 4: Calculated results <strong>of</strong> dose equivalent <strong>of</strong>
electromagnetic shower at 1 m from Pb block irradiated
by 1-GeV bremsstrahlung. The cross section <strong>of</strong>
<strong>the</strong> blocks is 10 cm 10 cm and <strong>the</strong> thickness is 5
cm (open diamonds), 10 cm (open squares) and 15
cm (crosses).
Figure 5: Spatial distribution in horizontal plane <strong>of</strong>
dose equivalent <strong>of</strong> electromagnetic shower around a
Pb block irradiated by 1-GeV bremsstrahlung calculated
by using EGS4. The size <strong>of</strong> <strong>the</strong> Pb blocks are
(a)10 cm 10 cm 5 cm, (b)10 cm 10 cm 10
cm and (c)10 cm 10 cm 15 cm.
5

Figure 6: Calculated results <strong>of</strong> dose equivalent by neutrons generated in Pb block caused by giant resonance.
The cross section <strong>of</strong> <strong>the</strong> Pb block is10cm 10 cm. Open squares and open diamonds show <strong>the</strong> data for 1-GeV
and 0.7-GeV bremsstrahlung.
References
[1] A. Rindi, "Gas bremsstrahlung from electron storage rings", Health Physics 42(1982)187.
[2] H. Hirayama, S. Ban, and S. Miura, "Investigations <strong>of</strong> electromagnetic cascades produced in
lead by 2.5-GeV bremsstrahlung", Nucl. Sci. Eng. 96(1987)66.
[3] T. Nakamura, "Radiation Physics and Accelerator Safety Engineering" (in Japanese), (Chijinshokan,
Tokyo, 1995)
[4] S. S. Dietrich and B. L. Berman, "Atlas <strong>of</strong> photoneutron cross section obtained with monoenergetic
photons", Atomic Data and Nuclear Table 38(1988)199.
6

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.299-307
Support <strong>of</strong> Low Energy X-ray Polarization with EGS4
K. Asamura, S. Gunji, Y. Inoue, T. Suzuki, T. Maeda, and H. Sakurai
Department <strong>of</strong> Physics, Yamagata University,
Yamagata 990-8560, Japan
Abstract
In X-ray astronomy, itisvery important to detect polarization <strong>of</strong> X rays from stellar objects.
There is, however, no e ective polarimeter with high sensitivity for polarization. So we have been
developing some types <strong>of</strong> X-ray polarimeters. For <strong>the</strong> design, computer simulation program is necessary,
which is capable <strong>of</strong> simulating interaction between polarized low energy X rays and material.
From <strong>the</strong> thirst, we have improved EGS4 (Electron Gamma-ray Simulation Version.4)[1][2][3] program
capable <strong>of</strong> simulating <strong>the</strong> interaction with <strong>the</strong> polarized X rays lower than few hundred keV.
Using <strong>the</strong> EGS4 program, we investigated <strong>the</strong> manner <strong>of</strong> polarized X rays for gas detector. As <strong>the</strong>
results <strong>of</strong> <strong>the</strong> simulation with <strong>the</strong> program, we recognized that <strong>the</strong> shape <strong>of</strong> electron cloud depends
on <strong>the</strong> polarization direction <strong>of</strong> <strong>the</strong> incident Xray.
1 Introduction
X-ray astronomy has progressed through <strong>the</strong> observation <strong>of</strong> stellar objects by <strong>the</strong> energy spectrum,
time variability, and <strong>the</strong> image. Detectors capable <strong>of</strong> obtaining <strong>the</strong> three information have been
continuously developed. On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> observation for <strong>the</strong> polarization has been rarely
carried out or <strong>the</strong> development <strong>of</strong> polarimeter has not been much advanced in spite <strong>of</strong> <strong>the</strong> importance.
So we have been developing some types <strong>of</strong> polarimeters sensitive to <strong>the</strong> energy range from 10 keV to a
few hundred KeV[4][5][6]. The performance <strong>of</strong> polarimeters is expressed by <strong>the</strong> parameter <strong>of</strong> Minimum
Detectable Polarization (MDP) as shown in <strong>the</strong> below equation.
MDP = 429
S AF
s S A + B
MDP : Minimum Detectable Polarization [%]
B : Background Count
S : Signal Counting Rate [cm ;2 sec ;1 ]
: Detection E ciency
A : Geometrical Area [cm 2 ]
F : Modulation Factor
T : Observation Time [sec]
In <strong>the</strong> equation, <strong>the</strong> modulation factor represents <strong>the</strong> ability for <strong>the</strong> determination <strong>of</strong> <strong>the</strong> polarization
<strong>of</strong> <strong>the</strong> incident Xrays. Though it can be recognized from this equation that it is important to improve
<strong>the</strong> modulation factor and <strong>the</strong> detection e ciency simultaneously, it is in general very di cult. So <strong>the</strong>
optimization <strong>of</strong> <strong>the</strong> performance by computer simulation is necessary for <strong>the</strong> design <strong>of</strong> <strong>the</strong> polarimeter.
As <strong>the</strong> three interactions <strong>of</strong> photoabsorption, Rayleigh scattering, and Compton scattering are
dominant for low energy X rays, we have developed EGS4 (Electron Gamma-ray Simulation version.4)
program capable <strong>of</strong> simulating <strong>the</strong> three interactions for <strong>the</strong> polarized X rays lower than few hundred
keV. In this paper, we will describe <strong>the</strong> detail <strong>of</strong> <strong>the</strong> developed EGS4 program and <strong>the</strong> application <strong>of</strong>
<strong>the</strong> EGS4 program for a gas detector.
1
T
(1)

2 Improvement for EGS4
2.1 Support <strong>of</strong> polarization
Applying new formulae for photoabsorption, Rayleigh scattering, and Compton scattering to
support polarized X rays, we have developed EGS4 program.
2.1.1 Compton scattering
We used <strong>the</strong> following equation for Compton scattering cross section.
d
d
/ [ k
k0
+ k0
k ; 2sin2 cos 2 ] (2)
where k0, k, , and are incident X-ray energy, scattered X-ray energy, zenith angle, and azimuthal
angle, respectively. As <strong>the</strong> k and are calculated by <strong>the</strong> original EGS4 code <strong>of</strong> subroutine COMPT, <strong>the</strong>
azimuthal angle is determined according to <strong>the</strong> above equation by Monte Carlo method. Moreover
<strong>the</strong> polarization vector <strong>of</strong> scattering X ray is determined according to <strong>the</strong> following equation by Monte
Carlo method.
d
d k
d
d ?
/ kc
k0
/ kc
k0
+ k0
; 2 + 4(1 ; sin
kc
2 cos 2 ) (3)
+ k0
; 2 (4)
kc
The polarization vector <strong>of</strong> scattered Xray has "parallel" vector or "vertical" vector. The vertical
vector is perpendicular to <strong>the</strong> polarization vector <strong>of</strong> incident Xray and <strong>the</strong> direction <strong>of</strong> <strong>the</strong> scattered
Xray. The parallel vector is perpendicular to <strong>the</strong> vertical vector and <strong>the</strong> direction <strong>of</strong> <strong>the</strong> scattered X
ray. The direction <strong>of</strong> <strong>the</strong> two vectors is shown in Fig.1. As <strong>the</strong> polarization vector for <strong>the</strong> scattered X
vertical
polarization
vector
x
polarization vector
z
θ
ϕ
scattered X ray
parallel
polarization
vector
y
incident X ray
Figure 1: The two polarization vector <strong>of</strong> scattered X rays.
ray is determined in <strong>the</strong> above method, multiple Compton scattering for polarized X rays is supported
in <strong>the</strong> developed EGS4 program.
2.1.2 Rayleigh scattering
We used following equation for Rayleigh Scattering cross section. As <strong>the</strong> zenith angle is determined
by subroutine PHOTON in <strong>the</strong> original EGS4 code, <strong>the</strong> azimuthal angle is determined by Monte Carlo
method according to this equation.
d
d / 1 ; 2sin2 cos 2
As shown in Fig.2, <strong>the</strong> polarization vector <strong>of</strong> <strong>the</strong> scattered X ray hasonly"parallel" vector.
2

2.1.3 Photoabsorption
x
z
ϕ
incident X ray
scattered X ray
parallel
polarization
vector
y
polarization vector
Figure 2: The manner <strong>of</strong> Rayleigh scattering.
We used <strong>the</strong> following equation for <strong>the</strong> cross section <strong>of</strong> photoabsorption.
d
d
/ 2 sin 2 (1 ; 2 ) 0:5 cos 2
(1 ; cos ) 4 ; (1 ; (1 ; 2 ) 0:5 )cos 2
2(1 ; 2 ) 0:5 (1 ; cos ) 3
+ (1 ; (1 ; 2 ) 0:5 ) 2
4(1 ; 2 )(1 ; cos
where is <strong>the</strong> speed <strong>of</strong> <strong>the</strong> photoelectron divided by light speed. Both <strong>the</strong> zenith angle and
are determined by in subroutine PHOTO <strong>of</strong> <strong>the</strong> original EGS4 code. According to this equation,
<strong>the</strong> azimuthal angle is determined by Monte Carlo method. After photoabsorption with K-shell
electron occurs, characteristic X ray or Auger electron is emitted. The probability is determined
with uorescence yield. According to <strong>the</strong> following semi-empirical equation <strong>the</strong> uorescence yield was
determined by Monte Carlo method.
!k
1 ; !k
1
4
3
=0:015 + 0:0327Z ; 0:64 10 ;6 Z 3
where !k and Z are <strong>the</strong> uorescence yield and atomic number <strong>of</strong> material, respectively. The emitted
direction for Auger electron and uorescence photon was assumed to be isotropical. The polarization
vector <strong>of</strong> <strong>the</strong> uorescence photon is determined at random.
2.2 Algorithm <strong>of</strong> <strong>the</strong> developed EGS4 program
The developed EGS4 programming codes written with Fortran consist <strong>of</strong> <strong>the</strong> EGS4 codes in which
polarization is supported, user codes, interface subroutines, CERN Library developed in CERN, and
CLICOM Library developed in Univ. <strong>of</strong> Tokyo[10]. They are as follows.
original EGS4 codes
ANNIH, BHABHA , COMPT , EDGSET , ELECTR , HATCH , MOLLER , MSCAT,PAIR,
PHOTO , PHOTON , SHOWER , and UPHI
User code
egs4main (This is <strong>the</strong> main program) , usr ana , ure ausgab , and usr howfar
interface subroutines
usr where, usr dnear, usr step, usr geomread, usr hatchsetup, usr prehatch,
usr iausfl, usr incident, and hbook read
Libraries
CERN Library and CLICOM Library
3

egs4main.f
EGS4
setup
PRESTA
setup
Do loop
histograms
save
hbook_end
to CERN
lib
usr_geomread
input geometry
file
usr_hatchsetup usr_prehatch
hatch PEGS4 data
edgset
init_usr_incident
usr_IAUSFL
hbook_read
usr_incident
usr_ana
PRESTA
_dnear
MSCAT
annih
bhabha
moller
brems
from user
to CERN
lib
shower
electr photon
compt
pair
photo
UPHI
Original EGS4 Codes
getene
_info
etc
EGS4 Common
Block
howfar
usr_dnear
usr_step
where
ausgab
Figure 3: Algorithm for <strong>the</strong> developed EGS4 program.
The developed EGS4 program runs according to <strong>the</strong> Algorithm chart shown in Fig.3. This EGS4
program is controlled by <strong>the</strong> main program egs4main. Through <strong>the</strong> main program, <strong>the</strong> following
initialization is carried out.
1. The dimension <strong>of</strong> simulated detector is handed to EGS4 Common Block through usr geomread
<strong>of</strong> interface subroutine.
2. The used material in detector is handed to EGS4 Common Block through usr hatchsetup and
usr prehatch <strong>of</strong> interface subroutines.
3. The information <strong>of</strong> <strong>the</strong> direction, <strong>the</strong> position, and <strong>the</strong> energy for incident Xrays is handed to
EGS4 Common Block through ini usr incident <strong>of</strong> interface subroutine.
4. The histograms <strong>of</strong> energy spectrum for each parts <strong>of</strong> <strong>the</strong> detector are de ned through hbook read
<strong>of</strong> interface subroutine.
5. The setup <strong>of</strong> PRESTA is carried out to simulate tracks for low energy electron in accuracy.
After <strong>the</strong>m, actual simulations are carried out through usr incident <strong>of</strong> interface subroutine and
shower <strong>of</strong> <strong>the</strong> original EGS4 code. The usr ana <strong>of</strong> user program makes histograms <strong>of</strong> energy spectrum
for each part <strong>of</strong> detector, using <strong>the</strong> information <strong>of</strong> <strong>the</strong> deposited energy calculated in EGS4 code. The
energy spectrum for each parts are saved in <strong>the</strong> end <strong>of</strong> simulation.
4

2.3 How to run <strong>the</strong> program
Before running <strong>the</strong> program, you must prepare for two les called geometry le and histogram
le. Fig.4 (a) and (b) are examples <strong>of</strong> <strong>the</strong> geometry le and <strong>the</strong> geometry. Each row corresponds
a)
1 23 0.0 0.0 2.0 7.0 3.0 4.0 0.514 0.001
1 18 0.0 0.0 5.0 7.0 3.0 2.0 0.514 0.001
shape
Material No.
center position <strong>of</strong>
<strong>the</strong> region
lengths <strong>of</strong> x,y,and z
ECUT
PCUT
b)
central position <strong>of</strong> region 2
(0.0 , 0.0 , 5.0)
region 2
material No.18
region 1
material No.23
x
z
3cm
7cm
central position <strong>of</strong> region 1
(0.0 , 0.0 , 2.0)
Figure 4: Fig(a) shows an example <strong>of</strong> geometry le. Fig(b) shows geometry that is represented by <strong>the</strong> example
<strong>of</strong> geometry le.
to <strong>the</strong> dimension for one part <strong>of</strong> <strong>the</strong> detector. The number in <strong>the</strong> rst column shows <strong>the</strong> shape <strong>of</strong>
<strong>the</strong> part. For instance, <strong>the</strong> number <strong>of</strong> 1 corresponds to a rectangular parallelepiped. The shapes <strong>of</strong>
sphere and column are also supported with <strong>the</strong> number <strong>of</strong> 2 and 3. The number in <strong>the</strong> second column
corresponds to kind <strong>of</strong> material. For example, <strong>the</strong> number <strong>of</strong> 23 is a plastic scintillator. The numbers
from <strong>the</strong> third column to <strong>the</strong> fth column correspond to <strong>the</strong> center position <strong>of</strong> <strong>the</strong> part. In <strong>the</strong> case
that <strong>the</strong> shape is rectangular parallelepiped, <strong>the</strong> numbers from <strong>the</strong> sixth number to <strong>the</strong> eighth number
correspond to <strong>the</strong> lengths <strong>of</strong> three sides. The ninth number and <strong>the</strong> tenth number correspond to cut
<strong>of</strong> energies for electron and photon, respectively. The following is an example <strong>of</strong> histogram le. With
this le, <strong>the</strong> histogram for each part <strong>of</strong> <strong>the</strong> detector is de ned.
a)
1 100 100 0.0 0.1 Plastic
1 200 100 0.0 0.1 Argon 1 atm
0
Comments
Number <strong>of</strong> bins
histogram ID No.
histogram dimension
maximum and minimum energy
0.001
2cm
4cm
0.0
0.1 0.0
0.1
ID:100 Plastic ID:200 Argon 1 atm
Figure 5: Fig(a) shows an example <strong>of</strong> histogram le. Fig(b) shows histograms correspond to <strong>the</strong> example <strong>of</strong>
histogram le.
One row corresponds to a histogram for one part <strong>of</strong> <strong>the</strong> detector. The rst column shows <strong>the</strong>
dimension <strong>of</strong> histogram. In <strong>the</strong> case <strong>of</strong> <strong>the</strong> histogram for energy spectrum, <strong>the</strong> number <strong>of</strong> 1 should
be written. The number in <strong>the</strong> second column is identi cation number <strong>of</strong> histogram. The number
in <strong>the</strong> third column shows <strong>the</strong> number <strong>of</strong> bins in x axis. The fourth and fth numbers correspond
to minimum value and maximum value in x axis. In <strong>the</strong> sixth column, <strong>the</strong> comment is written. The
number <strong>of</strong> 0 in <strong>the</strong> third row is a mark which shows <strong>the</strong> end <strong>of</strong> <strong>the</strong> de nition. If users want to only
obtain <strong>the</strong> information about energy spectrum <strong>of</strong> each parts in <strong>the</strong> detector, you do not have to rewrite
any program or recompile it. It is only required for users to carry out <strong>the</strong> below procedure.
%egsanl
Input geometry file: ?test.geo
5
b)
y

Input PEGS data file: ? material.dat
kind <strong>of</strong> particle e:-1 gamma:0 e:1 ? 0 ! 0 means X ray.@
x center:? 0.0
y center: ? 0.0 ! position to injection <strong>the</strong> particles
z center: ? 0.85
x range: ? 0.0
y range: ? 0.0 ! range <strong>of</strong> <strong>the</strong> incident particles
z range: ? 0.0
x direction: ? 0.0
y direction: ? 0.0 ! vector <strong>of</strong> incident direction
z direction: ?-1.0
Polarization vector x: ? 1.0
Polarization vector y: ? 0.0 ! polarization vector <strong>of</strong> incident X ray
Polarization vector z: ? 0.0
incident energy [MeV]: ? 0.1
Do you make histogram (Y/N): ?Y
idim: 1 ? @temp.his ! temp.his is histogram filename.
Input initial random number: ? 12345679
Number <strong>of</strong> particle: ? 10000 ! number <strong>of</strong> injected particles
----Simulation is started---input
HBK filename: ? temp.hbk ! histogram data is saved in temp.hbk file
By this procedure, <strong>the</strong> histograms are saved in <strong>the</strong> le <strong>of</strong> temp.hbk. Users can check <strong>the</strong> results with
<strong>the</strong> program <strong>of</strong> dis45[10].
2.4 Tests <strong>of</strong> <strong>the</strong> program
By obtaining several histograms, we checked <strong>the</strong> developed EGS4 program. Preparing for a
geometry le for plastic scintillator, we had simulations by injecting 30 keV X rays polarized parallel
to x axis from <strong>the</strong> direction <strong>of</strong> -z axis. Fig.6 shows <strong>the</strong> distribution for direction <strong>of</strong> scattered X
rays by Compton scattering for <strong>the</strong> original EGS4 code and <strong>the</strong> developed EGS4 code. In this Figure,
<strong>the</strong> x axis and y axis correspond to <strong>of</strong> <strong>the</strong> azimuthal angle and number <strong>of</strong> events, respectively. As
shown in this gure, <strong>the</strong> maxima for number <strong>of</strong> events are observed at <strong>the</strong> azimuthal angle <strong>of</strong> 90
and 270 . The results are consistent with <strong>the</strong> equation for <strong>the</strong> cross section <strong>of</strong> Compton scattering.
We also had similar simulation for Rayleigh scattering, and obtained <strong>the</strong> similar results to Compton
counts counts
azimuthal angle azimuthal angle
< in original EGS4 case > < in new EGS4 case>
Figure 6: The distribution <strong>of</strong> azimuthal angle for scattered X rays by Compton scattering. The left and <strong>the</strong>
right gures correspond to simulation for <strong>the</strong> original EGS4 code and <strong>the</strong> developed EGS4 code.
scattering. At second, using <strong>the</strong> same geometry le, we investigated <strong>the</strong> distribution <strong>of</strong> <strong>the</strong> azimuthal
angle for emitted photoelectrons by photoabsorption. The results for <strong>the</strong> original EGS4 code and <strong>the</strong>
developed EGS4 code are shown in Fig.7. From <strong>the</strong> equation <strong>of</strong> <strong>the</strong> cross section for photoabsorption,
<strong>the</strong> maxima <strong>of</strong> number <strong>of</strong> events are expected to be at 0 and 180 . So <strong>the</strong> distribution in this gure is
consistent with <strong>the</strong> equation <strong>of</strong> <strong>the</strong> cross section for photoabsorption. Finally, we had two simulations
6

counts
counts
azimuthal angle
azimuthal angle
< in original EGS4 case > < in new EGS4 case>
Figure 7: The distribution <strong>of</strong> azimuthal angle for emitted photoelectrons by photoabsorption. The left and <strong>the</strong>
right gures correspond to simulation for <strong>the</strong> original EGS4 code and <strong>the</strong> developed EGS4 code.
to check <strong>the</strong> program for uorescence yield. For one simulation, preparing for a geometry le <strong>of</strong> a
detector made <strong>of</strong> lead (Z=82), X rays with <strong>the</strong> energy <strong>of</strong> 100 keV were injected to <strong>the</strong> detector. For
<strong>the</strong> o<strong>the</strong>r one, preparing for a geometry le <strong>of</strong> a detector made <strong>of</strong> argon gas (Z=18) at 2 atm, X rays
with <strong>the</strong> energy <strong>of</strong> 20 keV were injected to <strong>the</strong> detector. For each case, <strong>the</strong> uorescence yields were
calculated from <strong>the</strong> results <strong>of</strong> <strong>the</strong> simulations. In table.1, <strong>the</strong> uorescence yields for each case are
summarized. As shown in this table, <strong>the</strong> results <strong>of</strong> <strong>the</strong> simulations have good agreements with <strong>the</strong>
data for <strong>the</strong> experiment.
Table 1: The comparison <strong>of</strong> uorescence yields obtained from <strong>the</strong> simulations with <strong>the</strong>m from <strong>the</strong> data for <strong>the</strong>
experiment.
lead argon gas
Simulation 97% 11%
Experiment 95% 8 10%
3 Application to Gas Counter
Wehave been developing an X-ray polarimeter in use <strong>of</strong> Gas Proportional Counter with MicroStrip,
sensitive to <strong>the</strong> energy range from 20 keV to 40 keV[7][8][9]. Fig.8 shows <strong>the</strong> schematic view <strong>of</strong> <strong>the</strong>
MSGC as X-ray polarimeter. As incidentXrays come to <strong>the</strong> chamber, <strong>the</strong> X ray is photoabsorbed and
Figure 8: Schematic view <strong>of</strong> <strong>the</strong> MSGC as X-ray polarimeter.
7

8
We would like to thank Dr. Y.Namito in KEK for o ering <strong>of</strong> <strong>the</strong> valuable references.
Acknowledgements
We haveimproved EGS4 code to simulate polarized X rays with low energies by applying formulae
for cross sections <strong>of</strong> photoabsorption, Compton scattering, and Rayleigh scattering in consideration
<strong>of</strong> X-ray polarization. Moreover, uorescence yields for K-shell were also supported in <strong>the</strong> code. The
code is written with Fortran and users do not have to recompile <strong>the</strong> code even if geometry <strong>of</strong> <strong>the</strong>
detector is changed. We had computer simulation with this code to investigate <strong>the</strong> characteristics
<strong>of</strong> <strong>the</strong> MSGC polarimeter developed by us. Consequently, we con rmed that <strong>the</strong> shape <strong>of</strong> electron
cloud depend on <strong>the</strong> polarization direction <strong>of</strong> <strong>the</strong> incident Xray. Therefore it is possible to detect <strong>the</strong>
polarization by using MSGC. In <strong>the</strong> future we will use EGS4 to develop a X-ray polarimeter.
4 Conclusion
Figure 9: The x axis and y axis correspond to <strong>the</strong> extension <strong>of</strong> electron cloud for 22keV polarized X rays and <strong>the</strong>
number <strong>of</strong> events, respectively. The solid line and <strong>the</strong> dashed line correspond to <strong>the</strong> extension for <strong>the</strong> directions
<strong>of</strong> x axis and y axis, respectively.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
[cm]
0
50
100
150
counts
200
250
300
350
400
450
500
photoelectron is emitted. Then <strong>the</strong> photoelectron ionizes gas molecule and electron cloud is created.
Since <strong>the</strong> photoelectron tends to be emitted to <strong>the</strong> same direction as <strong>the</strong> polarization vector <strong>of</strong> <strong>the</strong>
incident Xray, <strong>the</strong> shape <strong>of</strong> electron cloud extends to <strong>the</strong> polarization direction <strong>of</strong> <strong>the</strong> incident Xray
on <strong>the</strong> average. Then it is drifted on <strong>the</strong> several anode strips, keeping <strong>the</strong> shape <strong>of</strong> <strong>the</strong> electron cloud.
In <strong>the</strong> case that <strong>the</strong> polarization vector <strong>of</strong> <strong>the</strong> incident Xrayis perpendicular to <strong>the</strong> anode strips, <strong>the</strong>
number <strong>of</strong> anode strips with charge signal is more than that in <strong>the</strong> case that it is parallel to <strong>the</strong>m.
Thus it is in principle possible to detect <strong>the</strong> polarization by counting anode strips with charge signal.
To check <strong>the</strong> principle, injecting 22keV polarized X rays parallel to x axis to argon gas at 1 atm, <strong>the</strong>
extension <strong>of</strong> electron cloud for <strong>the</strong> two directions <strong>of</strong> x and y is simulated. Fig.9 shows <strong>the</strong> di erence
<strong>of</strong> <strong>the</strong> length <strong>of</strong> electron cloud.

References
[1] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, \The EGS4 code system", SLAC-265, Stanford
Linear Accelerator Center, 1985.
[2] Y. Namito, S. Ban, and H. Hirayama,\Implementation <strong>of</strong> lineary-polarized photon scattering into
<strong>the</strong> EGS4 code", Nucl. Instruum. and Meth. A 332(1994)489-494.
[3] Y. Namito, S. Ban, and H. Hiramaya, \LSCAT: Low-Energy Photon-Scattering Expansion for
<strong>the</strong> EGS4 code (Inclusion <strong>of</strong> Electron Impact Ionization)", KEK Internal 2000-4(2000).
[4] H. Tomita, S. Sano, H. Sakurai, M. Noma, S. Gunji, and E. Takase, \Basic Performance <strong>of</strong> Unitized
Compton Scattering Type Polarimeter" IEEE Trans. Nucl. Sci. Vol.43 No.3(1996)1527-
1532.
[5] H. Sakurai, S. Saito, M. Noma, S. Gunji, M. Tsukahara, and T. Tamura, \New Type <strong>of</strong> Imaging
X{ray Detector Using a Capillary Plate" <strong>Proceedings</strong> <strong>of</strong> SPIE(San Diego) Vol.3114 (1997) pp481-
487.
[6] T. Tamura, H. Sugeno, H. Sakurai, M. Noma, S. Gunji, and P. Gertenbort, \An application <strong>of</strong>
microstrip gas proportional counter for a X-ray polarimeter" IEEE Conf. Rec. 1(1995)234-237.
[7] A. Oed, \Position-Sensitive Detector with Microstrip Anode for Electron Multiplication with
Gases", Nucl. Inst. and Meth. A263(1988)351-359.
[8] H. Sugeno, Y. Takamura, H. Sakurai, M. Noma, S. Gunji, and P. Gertenbort, \A Study <strong>of</strong> <strong>the</strong> Rise
Time in a MicroStrip Gas Proportional Counter for <strong>the</strong> Development <strong>of</strong>anX{rayPolarimeter",
IEEE Trans. Nucl. Sci. Vol.44 No.3(1997)979-984.
[9] T. Tanimori et al., \Development <strong>of</strong> Imaging Microstrip Gas Chamber with 5cm 5cm area based
on Multi-Chip Module Technology", INS-Rep., pp1143 May 1996.
[10] Private communication with Dr.T. Takahashi in ISAS.
9

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.308-315
Unfolding <strong>of</strong> <strong>the</strong> Measured Spectra and Determination
<strong>of</strong> Correction Factors <strong>of</strong> a Free Air Ionization Chamber
Using EGS4 Simulations
G. H. Yoo 1 , K. J. Chun 2 and S. H. Ha 2
1
Department <strong>of</strong> Electrical Engineering, Daebul University,
Young-Arm Kun, Chonnam, S.Korea
2
Ionizing Radiation Group, Divison <strong>of</strong> Chemical Metrology and Materials Evaluation
Korea Research Institute <strong>of</strong> Standards and Science, S. Korea
Abstract
The responses <strong>of</strong> NaI detector and HPGe detector for incident photons up to 662 keV were
calculated using EGS4 simulations. The calculated spectra were normalized to <strong>the</strong> measured spectra
after being smoo<strong>the</strong>d using cubic spline t at highest energies, and were unfolded. The unfolded
one <strong>of</strong> a measured spectrum with NaI detector at a distance 100 cm away from <strong>the</strong> Cs-137 source
shows that <strong>the</strong> measured one was contributed remarkably from <strong>the</strong> surrounding materials at low
energy region. The measured spectra obtained by HPGe detector with a maximum energies 63 keV
and 83 keV were also unfolded. No signi cant di erence is seen in <strong>the</strong> shapes <strong>of</strong> spectra between
<strong>the</strong> measured and <strong>the</strong> unfolded ones. In a free air ionization chamber <strong>of</strong> 24 cm 24 cm 46
cm, a ratio <strong>of</strong> loss <strong>of</strong> ionizations and a ratio <strong>of</strong> secondary ionizations were calculated at incident
photon energy from 10 keV to 300 keV in 10 keV steps using EGS4 simulations. The ratio <strong>of</strong> loss
<strong>of</strong> ionization to <strong>the</strong> total ionization which shows no applicable value up to 130 keV <strong>of</strong> incident
photon energy, rises up from 130 keV to 220 keV and slightly decreases between 220 keV and 260
keV and <strong>the</strong>n increases again up to 300 keV. On <strong>the</strong> o<strong>the</strong>r hands, <strong>the</strong> ratio <strong>of</strong> secondary ionizations
decreases monotonously with <strong>the</strong> increase <strong>of</strong> photon energy.
1 Introduction
Generally, <strong>the</strong> radiation spectrum that we measure from <strong>the</strong> detector is much di erent from <strong>the</strong>
one that arrives at <strong>the</strong> detector from <strong>the</strong> radiation source. We call <strong>the</strong> former one a measured spectrum
and <strong>the</strong> latter one a real spectrum. Photon beam radiated from <strong>the</strong> source interact with <strong>the</strong> atoms
<strong>of</strong> <strong>the</strong> materials while <strong>the</strong>y are traveling through <strong>the</strong> medium to <strong>the</strong> detector, and inside <strong>the</strong> detector
before <strong>the</strong>y are measured. Thus <strong>the</strong> measured energy spectrum can be signi cantly di erent from <strong>the</strong>
one radiated from <strong>the</strong> source due to <strong>the</strong> contribution <strong>of</strong> <strong>the</strong> scattered photon. While <strong>the</strong> characteristics
and limitations <strong>of</strong> <strong>the</strong> radiation measurement system make itvery di cult to measure a real spectrum,
it is also possible to obtain a spectrum very close to <strong>the</strong> real one by using a s<strong>of</strong>tware in which all <strong>the</strong>
characteristics <strong>of</strong> measurement system are considered.[1,2,3,4] One <strong>of</strong> <strong>the</strong> most powerful tools currently
known so far is a computer simulation using EGS4 code.[5] Using this code, we can calculate an energy
absorption spectrum for <strong>the</strong> NaI or HPGe detectors for <strong>the</strong> incident photon beam with <strong>the</strong> energy
ranging from a few keV to hundreds <strong>of</strong> GeV. The energy spectrum thus calculated at many di erent
values <strong>of</strong> energy can <strong>the</strong>n be compared with <strong>the</strong> measured spectrum through an interpolation in order
to simulate <strong>the</strong> real spectrum, which is called unfolding <strong>of</strong> <strong>the</strong> measured spectrum.
In this paper, <strong>the</strong> results <strong>of</strong> unfolding procedure <strong>of</strong> <strong>the</strong> spectrum measured by 3 in. 3 in. NaI
detector at 100 cm away from <strong>the</strong> Cs-137 source and that by 9 mm 5 mm HPGe detector at 100
cm away from <strong>the</strong> X-ray generator are presented.[4,6] The result <strong>of</strong> <strong>the</strong> calculations <strong>of</strong> a ratio <strong>of</strong> loss
1

<strong>of</strong> ionizations and a ratio <strong>of</strong> secondary ionizations for a free air ionization chamber when <strong>the</strong> incident
photon beam is applied is also presented.[7,8,9] The dimension <strong>of</strong> <strong>the</strong> inner volume <strong>of</strong> <strong>the</strong> free air
chamber used in this calculation is 24 cm 24 cm 46 cm and <strong>the</strong> incident photon energy ranges
from 10 keV to 300 keV.
2 Unfolding <strong>of</strong> <strong>the</strong> Measured Spectrum
2.1 Unfolding <strong>of</strong> spectrum measured with NaI detector
A gamma-ray spectrum was measured by 3 in. 3 in. NaI detector at 100 cm away from
<strong>the</strong> Cs-137 source and analyzed. [Fig.1] The photon beam emitted from Cs-137 are mostly 662 keV
gamma-rays with small portion <strong>of</strong> 32 keV X-ray, but <strong>the</strong> measured spectrum shows a strong peak at
662 keV with a broad background at low energy region.[4] The strong peak around 662keV appears to
be contributed by 662 keV photons. A pulse height distributions which were calculated using EGS4
code with incident photon energy 662 keV are redistributed using a Gaussian distribution function with
a FWHM (full wave half maximum) 7 %. [Fig.1.(A)] After <strong>the</strong> highest energy peak was normalized
to <strong>the</strong> measured peak, <strong>the</strong> normalization result is compared with <strong>the</strong> measured spectrum. The result
shows an excellent agreement in shape for <strong>the</strong> calculated and measured one at <strong>the</strong> photon energies
above 450 keV. This explains that <strong>the</strong>re was no o<strong>the</strong>r incident photons with energy above 450 keV
except 662 keV photons from <strong>the</strong> Cs-137. On <strong>the</strong> o<strong>the</strong>r hand, in low energy regions below 450 keV, <strong>the</strong>
spectrum does not match well with <strong>the</strong> measured one. The result <strong>of</strong> measured strength subtracted by
<strong>the</strong> calculated one using EGS4 code at 662 keV is shown in Fig.1(B). The remaining part is considered
to be contributed by <strong>the</strong> secondary scattered photons from <strong>the</strong> surrounding materials. Divided <strong>the</strong>
normalized intensity by <strong>the</strong> detecting ratio at 662 keV, <strong>the</strong> unfolded intensity at 662 keV could be
obtained. This unfolded strength at 662 keV is considered as an intensity <strong>of</strong> <strong>the</strong> photons which arrived
at <strong>the</strong> detector with that energy.
To unfold <strong>the</strong> remaining strength, pulse height distributions at 11 energies were calculated at
incident photon energies from 50 keV to 500 keV. [Fig.1.(C)] The simulated spectra for <strong>the</strong> o<strong>the</strong>r
energies were obtained by <strong>the</strong> interpolation method. The calculated spectra were redistributed using a
Gaussian distribution function with a FWHM 7% except <strong>the</strong> highest energy peaks. The highest energy
peaks were not redistributed because <strong>of</strong> <strong>the</strong> convenience <strong>of</strong> normalizing <strong>the</strong> peaks to <strong>the</strong> remaining
spectrum. With <strong>the</strong> same method as was applied at 662keV peak, <strong>the</strong> intensity <strong>of</strong> <strong>the</strong> highest energy
<strong>of</strong> a calculated spectrum at next energy was normalized to that <strong>of</strong> <strong>the</strong> highest energy <strong>of</strong> a remaining
spectrum. Starting from <strong>the</strong> highest energy, <strong>the</strong> whole spectrum <strong>of</strong> a calculated one was multiplied by
<strong>the</strong> same normalization factor and was subtracted from <strong>the</strong> remaining spectrum. Then <strong>the</strong> unfolded
intensity at<strong>the</strong> highest energy can be obtained by dividing <strong>the</strong> intensity <strong>of</strong> a measured peak at that
energy by a peak detecting ratio. This process was repeated in a descending order down to zero energy.
The unfolded spectrum is shown in Fig.1.(D). The results show that 68% <strong>of</strong> whole strength are from
<strong>the</strong> Cs-137 source, and 32% are contributed by <strong>the</strong> surrounding materials.
2.2 Unfolding <strong>of</strong> spectrum measured with HPGe detector
The continuous energy X-rays produced by a X-ray generator with maximum energies 63 keV
and 82 keV, were measured by using a HPGe detector (9 mm diameter, 5 mm thickness and 5.23
g/cm 3 density for Ge crystal, 0.5 mm thick Be window, and 1 cm thick Al case), and was analyzed
using <strong>the</strong> same unfolding method as that <strong>of</strong> Cs-137 gamma-ray. However, in this procedure <strong>the</strong>
Gaussian distribution function was not applied to <strong>the</strong> simulated spectrum because <strong>of</strong> a very good
resolution <strong>of</strong> about 0.5 keV, which is less than <strong>the</strong> energy bin used in <strong>the</strong> calculation.[Fig.2] Due to
<strong>the</strong> secondary scattered photons coming from <strong>the</strong> surrounding materials, <strong>the</strong> measured spectrum has
di erent energy distribution from <strong>the</strong> one emitted from <strong>the</strong> source. The spectra measured by HPGe
detector with maximum energies at 63 keV and 82 keV are shown in Fig.3. The unfolding procedure
has been performed to obtain <strong>the</strong> simulated spectra using EGS4 code with <strong>the</strong> incident photon energies
2

from 5 keV to 85 keV in 5 keV step and several <strong>of</strong> <strong>the</strong>m are given in Fig.2. Since <strong>the</strong>re is no signi cant
peak in <strong>the</strong> measured spectra at <strong>the</strong> high energy region, like 662 keV peak in a spectrum by NaI
detector, <strong>the</strong> intensity <strong>of</strong> <strong>the</strong> highest energy <strong>of</strong> a calculated spectrum was normalized to <strong>the</strong> intensity
<strong>of</strong> <strong>the</strong> highest energy <strong>of</strong> a measured spectrum, and was subtracted from <strong>the</strong> measured spectrum. The
o<strong>the</strong>r steps are <strong>the</strong> same as in NaI detector. The unfolded spectra which were arrived at <strong>the</strong> detector
are given in Fig.3.(C) and Fig.3.(D).
3 Determination <strong>of</strong> correction factors <strong>of</strong> a Free Air Ionization Chamber
using EGS4 Simulations
Free air ionization chamber plays an important role in a measurement <strong>of</strong>gammaray exposure. An
air lled ionization chamber is well matched to this application because an exposure is expressed in
terms <strong>of</strong> <strong>the</strong> amount <strong>of</strong> ionization charge created in air. One <strong>of</strong> <strong>the</strong> quantities to describe an exposure
is kerma (kinetic energy released in material). [6,7,8,9] [Fig.4.(A)] Kerma is a sum <strong>of</strong> transferred
kinetic energy to <strong>the</strong> charged particles per unit mass at a point <strong>of</strong>interest by radiation. It is expressed
as
K = dEtr
dm
where unit is 1Gy=1J=kg
=
I
v o
W
e
1
1 ; g
Ki where I : ionization current (A)
W
e
v : sensitive volume (cm 3 )
: required energy to make an ion pair (33:97 eV=pair)
o : speci c gravity <strong>of</strong> dried air at STP (1:293 10 ;3 )
K i = K sc K e K a K s K p K l K h
where K sc = secondary scattered photo inization factor(e4)
K e = loss <strong>of</strong> ionization correction factor(e5)
K a = diminishing factor due to air between <strong>the</strong> de ning plane
and collector
K s = ion recombination correction factor
K p = polarity e ect <strong>of</strong> collecting electrons
K l = diaphragm penetration correction factor
K h = humidity correction factor:
As we see from <strong>the</strong> above equation, <strong>the</strong>re are several parameters to be determined to calculate kerma.
Among <strong>the</strong> parameters, we calculated a ratio <strong>of</strong> loss <strong>of</strong> ionizations (K e) and a ratio <strong>of</strong> secondary
ionizations (K sc) for a free air ion chamber composed <strong>of</strong> 24 cm 24 cm 46 cm, at photon's incident
energies from 10 keV to 300 keV with 10 keV steps for <strong>the</strong> 0.1 mm diameter beam using EGS4
simulations.
3.1 1 Determination <strong>of</strong> a ratio <strong>of</strong> loss <strong>of</strong> ionizations
As X-ray beam passes through <strong>the</strong> inner volume <strong>of</strong> a free air chamber occupied by air, <strong>the</strong>y
collide with air particles and make various kinds <strong>of</strong> interactions. Some <strong>of</strong> <strong>the</strong>m ionize air particles
by photo-absorption or Compton scattering and produce pairs <strong>of</strong> free electron (recoiled electron) and
positive ion. The recoiled electron has kinetic energy almost equivalent to one which X-ray loses
in <strong>the</strong> rst interaction subtracted by <strong>the</strong> binding energy <strong>of</strong> <strong>the</strong> recoiled electron to <strong>the</strong> atom. These
recoiled electrons interact with air particles and ionize <strong>the</strong>m until <strong>the</strong>y lose all <strong>the</strong> energy <strong>the</strong>y possess.
3

Theoretically, all <strong>the</strong> electrons produced in <strong>the</strong> volume can be collected by applying a high voltage
between <strong>the</strong> top and bottom plates surrounding <strong>the</strong> volume. However, some <strong>of</strong> <strong>the</strong> recoiled electrons
happen to hit <strong>the</strong> plates <strong>of</strong> a chamber before losing all <strong>the</strong> kinetic energies. This phenomenon causes a
loss <strong>of</strong> ionization current and should be corrected by <strong>the</strong>oretical calculation. In this study, <strong>the</strong> incident
photons with energy from 10 keV to 300 keV have been used in this simulation in 10 keV step. The
photons entered into <strong>the</strong> volume through a 0.1 mm diameter hole and passed 46 cm distance before
<strong>the</strong>y reach <strong>the</strong> guard strips in <strong>the</strong> backside. The sensitive volume (0.1 mm diameter, 10 cm long)
locates in <strong>the</strong> middle <strong>of</strong> <strong>the</strong> chamber, 18 cm away from front wall and 12 cm away from <strong>the</strong> side walls.
[Fig.4.(A)] We tried to trace all <strong>the</strong> electrons and photons that were produced in <strong>the</strong> volume until <strong>the</strong>y
lose all <strong>the</strong>ir energies or go out <strong>of</strong> <strong>the</strong> volume completely. The ratio <strong>of</strong> energy absorbed from ionized
electrons in <strong>the</strong> plates <strong>of</strong> a chamber to <strong>the</strong> total energy absorbed in <strong>the</strong> air inside <strong>the</strong> chamber, which
is de ned as a ratio <strong>of</strong> loss <strong>of</strong> ionization was obtained and <strong>the</strong> results are given in Fig.4.(B). In <strong>the</strong>
incident photon energy below 130 keV, <strong>the</strong> ratio is negligible, in o<strong>the</strong>r words, no electrons with <strong>the</strong>
energy less than 130 keV produced by primary scattering process could reach <strong>the</strong> plates. The ratio
exhibits increase starting from 130 keV up to 220 keV, slight decrease up to 260 keV and ano<strong>the</strong>r
increase up to 300 keV.
3.2 Determination <strong>of</strong> a ratio <strong>of</strong> secondary ionization
Besides <strong>the</strong> interactions described in section 3.1, some <strong>of</strong> <strong>the</strong> primarily scattered photons collide
with air particles again and ionize <strong>the</strong>m outside <strong>of</strong> <strong>the</strong> sensitivevolume. This process is called secondary
ionization, and thus <strong>the</strong> electrons produced in this process should not be taken into count and <strong>the</strong>
contribution due to it should be corrected. To do this, we followed <strong>the</strong> photon's track in EGS4
simulations and summed <strong>the</strong> energies transferred from <strong>the</strong> photon to <strong>the</strong> air particles when it occurred
outside <strong>the</strong> sensitive volume. The relative ratio <strong>of</strong> this energy to <strong>the</strong> total energy absorbed by air
particles inside <strong>the</strong> chamber was calculated for <strong>the</strong> incident photon energies from 20 keV to 300 keV
in 10 keV steps. The results are given in Fig.4.(C). In <strong>the</strong> photon energy below around 20 keV, <strong>the</strong>
ratio is about 0.8% and <strong>the</strong> ratio decreases monotonously as <strong>the</strong> photon energies goes up to 300 keV,
yielding <strong>the</strong> ratio <strong>of</strong> 0.2% at 300 keV.
4 Summaries
Monte Carlo simulation using EGS4 was used in unfolding process and in determining <strong>the</strong> correction
factors <strong>of</strong> free air ionization chamber. For <strong>the</strong> spectrum measured by NaI detector at 100 cm away
from <strong>the</strong> Cs-137, <strong>the</strong> calculations smoo<strong>the</strong>d with Gaussian distribution and cubic spline show that
<strong>the</strong> measured spectrum was contributed strongly by <strong>the</strong> surrounding materials at low energies. For
<strong>the</strong> spectrum measured by HPGe detector at 100 cm away from <strong>the</strong> X-ray generator, <strong>the</strong> pulse height
distributions obtained with EGS4 simulations were normalized to <strong>the</strong> measured spectra without curve
t because <strong>of</strong> a good energy resolution <strong>of</strong> X-ray. The comparison explains that <strong>the</strong> energy spectrum <strong>of</strong>
<strong>the</strong> incident photons is also continuous like <strong>the</strong> measured ones. In a free air ionization chamber composed
<strong>of</strong> a parallel plate with a distance between <strong>the</strong> two plates, 24 cm, <strong>the</strong> loss <strong>of</strong> ionizations to <strong>the</strong>
total ionization is negligible up to 130 keV <strong>of</strong> incident photon energy. Whereas, <strong>the</strong> ratio <strong>of</strong> secondary
ionizations which are dominant at low energy decreases monotonously as <strong>the</strong> energy increases. At
incident photon energies lower than 290 keV, <strong>the</strong> ratio <strong>of</strong> secondary ionizations is larger than <strong>the</strong> ratio
<strong>of</strong> loss <strong>of</strong> ionizations. At energies higher than 290 keV, <strong>the</strong> ratio <strong>of</strong> loss <strong>of</strong> ionizations is dominant.
References
[1] Radiation Quantities and Units, ICRU Report 33 (1980).
[2] <strong>International</strong> Organization for Standardization, X and gamma reference radiations for calibrating
dosimeters and doserate meters and for determining <strong>the</strong>ir response as a function <strong>of</strong> photon energy.
4

Part 1 : Characteristics <strong>of</strong> <strong>the</strong> radiations and <strong>the</strong>ir methods <strong>of</strong> production, Revision <strong>of</strong> ISO 4037:
1979,ISO/DIS 4037-1,(1994).
[3] National Institute <strong>of</strong> Standards Technology, Criteria for <strong>the</strong> Operation <strong>of</strong> Federally-Owned <strong>Second</strong>ary
Calibration Laboratories(Ionizing Radiation), NIST SP 812 (1991).
[4] G. F. Knoll, \Raidation detection and measurement", John Wiley and Sons, 1989.
[5] W. R. Nelson, H. Hirayama and D. W. O. Rogers, \The EGS4 Code System", SLACX-265,
Stanford Linear Accelerator Center, 1985.
[6] S. M. Seltzer, Nucl. Instr. Meth, 188(1981)133-151.
[7] F. H. Attix, \Introduction to radiological physics and radiation dosimetry", John Wiley and Sons
(1986).
[8] A. R. S. Marsh and T. T. Williams, \50 kV Primary Standard <strong>of</strong> Exposure: Design <strong>of</strong> Free-Air
Chamber", NPL Report RS (Ext) 54 (1982).
[9] M. Boutillon, \Volume recombination parameter in ionization chambers", Phys. Med. Biol.
43(1998)2061-2072.
5

Figure 1: (A) A spectrum measured with a NaI(3"x3") detector at 100 cm away from a radiation source Cs-137
is compared with a spectrum obtained using EGS4 simulations for 662keV incident photons. (B) Measured
strength subtracted by <strong>the</strong> simulated strength. A small portion <strong>of</strong> <strong>the</strong> strength above 430 keV were neglected
in <strong>the</strong> unfolding process. (C) Calculated spectra for a NaI (3 in. X 3 in.) detector using EGS4 code at di erent
incident photon's energies. (D) Unfolded energy spectrum <strong>of</strong> photons that arrived at <strong>the</strong> detector. The number
<strong>of</strong> 4.5 10 5 means <strong>the</strong> number <strong>of</strong> <strong>the</strong> incident photons that arrived at <strong>the</strong> detector with 662 keV from Cs-137
and 2.14 10 5 means <strong>the</strong> number <strong>of</strong> photons scattered from <strong>the</strong> surrounding materials. The numbers in <strong>the</strong>
paren<strong>the</strong>sis mean <strong>the</strong> relative strengths.
6

Figure 2: Calculated spectra using EGS4 code for <strong>the</strong> HPGe detector at di erent incident photon's energies.
Totally, 17 spectra obtained at <strong>the</strong> energies from 5keV to 85keV in 5keV steps were used for interpolation.
Figure 3: (A) Measured spectrum with a HPGe detector for <strong>the</strong> continuous X-rays <strong>of</strong> energies upto 63 keV.
(B) Measured spectrum with <strong>the</strong> same HPGe detector for <strong>the</strong> continuous X-rays <strong>of</strong> energies upto 82 keV. (C)
Unfolded spectrum for measured spectrum (A). (D) Unfolded spectrum for measured spectrum (B).
7

Figure 4: (A) Diagram for <strong>the</strong> free air ionization chamber. Incident photon beams pass through <strong>the</strong> 0.1mm
diameter hole. The energies used in this simulation are from 10 kev to 300 keV in 10 keV step. (B) A ratio <strong>of</strong>
loss <strong>of</strong> ionizations to <strong>the</strong> total air ionizations inside <strong>the</strong> chamber. (C) A ratio <strong>of</strong> air ionizations by <strong>the</strong> secondary
scattered photons to <strong>the</strong> total air ionizations.
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.316-323
Simulation <strong>of</strong> Ionization and Scintillation Signals
in a Liquid Ionization Drift Chamber
T. Shimoyama, E. Shibamura 1 , M. Miyajima
Department <strong>of</strong> Applied Physics, Fukui University
3-9-1, Bunkyo, Fukui-shi, 910-8507, Japan
1 College <strong>of</strong> Health Science, Saitama Pref. University
820, San-nomiya, Koshigaya-shi, Saitama-ken, 343-8540, Japan
Abstract
In order to search for double beta-decay events under existence <strong>of</strong> many background events,
We have simulated double beta-decay events <strong>of</strong> 136 Xe in liquid xenon ionization drift chamber by
EGS/PRESTA Monte Carlo code to construct data-sets for analyzing <strong>the</strong> position resolution <strong>of</strong>
vertex point from ionization and scintillation signals, which are observed with collecting charges
and scintillation photons generated by two beta-particles in liquid xenon. The ionization drift
chamber is a single gridded ionization chamber with a segmented collector <strong>of</strong> 200 50 42mm 3 in
size.
The position resolutions, which are calculated with <strong>the</strong> drift time and <strong>the</strong> position <strong>of</strong> electron
swarms formed by two beta-particles, were Y0 =1:501 0:004mm and Z0 =0:1249 0:005,
Y2 = 0:1231 0:003mm and Z2 = 0:0747 0:002mm, respectively. The same, which are
calculated with <strong>the</strong> number <strong>of</strong> photoelectrons observed at each photo-multiplier, were Y0 =
9:92 0:06mm and Z0 = 8:56 0:05, Y2 = 9:58 0:05mm and Z2 = 8:44 0:05mm,
respectively.
1 Introduction
In <strong>the</strong> double beta decay, <strong>the</strong>re are two main decaychannels, (A Z) ! (A Z+2)+e1+e2+ e1+ e2
(2 2 mode) and (A Z) ! (A Z +2)+e1 + e2 (2 0 mode). Two-neutrino decay (2 2 ) can be
understood by <strong>the</strong> second order weak intaraction. In neutrinoless decay (2 0 ), a neutrino emitted at
single beta decay is absorbed by o<strong>the</strong>r nucleon and <strong>the</strong> nucleon decays by emitting an electron. This
decay will be possible if neutrino is massive Majorana neutrino and/or right-handed current exists.[1]
Fur<strong>the</strong>rmore, this decay violates <strong>the</strong> law <strong>of</strong> lepton number coservation. So <strong>the</strong>re must be physics
beyond <strong>the</strong> standard model.
In double beta-decay searches, we can only observe two emitted beta rays at a decay, <strong>of</strong> which
<strong>the</strong> transition energy is normally low. Therefore, we have to look for double beta-decay events under
existence <strong>of</strong> many background events, which are due to environmental radiation, cosmic rays and so
on.
We have proposed a liquid xenon ionization drift chamber equipped with a daughter identi cation
system by laser uorescence to search for double beta decay events <strong>of</strong> 136 Xe.[2] Liquid xenon will be
used for <strong>the</strong> following several reasons:
1. <strong>the</strong> W-value <strong>of</strong> 15:6eV [3] is <strong>the</strong> smallest among liquid inert gases, so we can expect larger signal
sizes with a relatively good energy resolution.
2. electrons in liquid xenon moves with relatively large mobility and <strong>the</strong> drift velocity is almost
constant <strong>of</strong>about3mm= sec under <strong>the</strong> electric eld <strong>of</strong> 3kV=cm or higher[4, 5], so we can expect
<strong>the</strong> ionization chamber will be operated as an drift chamber.
1

3. <strong>the</strong> scintillation, whichisvery fast phenomena, can be used as <strong>the</strong> trigger signal <strong>of</strong> events because
that is observable with ionization at <strong>the</strong> same time.[6]
4. <strong>the</strong> daughter ions <strong>of</strong> 136 Xe are expected to be stable in liquid xenon and move slowly under an
electric elds.[7]
The detector previously proposed is a semi-cylindrical gridded ionization chamber. Segmented
electrodes xed at <strong>the</strong> inside surface <strong>of</strong> <strong>the</strong> outermost cylinder collect electrons liberated by two beta
rays and determine <strong>the</strong> sum energy <strong>of</strong> two beta rays and <strong>the</strong> position <strong>of</strong> <strong>the</strong> decay from <strong>the</strong> drift time
<strong>of</strong> <strong>the</strong> electron swarm from <strong>the</strong> segment position. The daughter ion drifts toward <strong>the</strong> central electrode
and will be observed near <strong>the</strong> electrode with photo-multiplier tubes xed above <strong>the</strong> chamber by <strong>the</strong>
laser uorescence.
Here, we describe <strong>the</strong> results <strong>of</strong> simulation <strong>of</strong> ionization and scintillation signals on a di erent
type <strong>of</strong> <strong>the</strong> liquid xenon ionization drift chamber for comparison to <strong>the</strong> previous detector. In order
to calculate <strong>the</strong> signal sizes which we can obtain in <strong>the</strong> detector, we construct data-sets composed <strong>of</strong>
<strong>the</strong> energy deposition <strong>of</strong> two beta rays emitted at a double beta decay simulated with EGS/PRESTA
code. From two data-sets <strong>of</strong> which one is for 2 2 mode and <strong>the</strong> o<strong>the</strong>r is for 2 0 mode, we calculated
distances between <strong>the</strong> vertex point <strong>of</strong> a double beta decay and <strong>the</strong> point determined by <strong>the</strong> ionization
and scintillation signals to estimate <strong>the</strong> beam size for laser shot. We also calculated detection e ciencies
and e ective volumes <strong>of</strong> <strong>the</strong> detector to <strong>the</strong> both mode, and energy spectra on a triggering level
by observation <strong>of</strong> scintillation photons.
2 Detector
The detector used in this simulation is a plane parallel liquid xenon single gridded ionization drift
chamber equipped with a daughter identi cation system by laser uorescence. The schematic drawing
is shown in Fig.1 without <strong>the</strong> daughter identi cation system. The laser beam to identify daughter ions
is shot to a X-direction. The volume <strong>of</strong> <strong>the</strong> chamber is 200 50 42mm 3 . The collector electrode,
which collects electron swarms liberated by two beta rays, locates at <strong>the</strong> bottom and is segmented
into 20 strips <strong>of</strong> 2mm 200mm with a pitch <strong>of</strong> 2:5mm. The Frish grid is an array <strong>of</strong> gold plated
tungsten wires <strong>of</strong> 100 m in diameter. The grid is located at 2mm above <strong>the</strong> collector and <strong>the</strong> wires
are strung with a spacing <strong>of</strong> 1mm parallel to Y -direction. The cathode, which collect <strong>the</strong> daughter
ions, situates at 40mm above <strong>the</strong> grid. In order to observe <strong>the</strong> scintillation (VUV) and uorescence
(visible) photons, two di erent types <strong>of</strong> photo-multiplier tube (PMT), <strong>of</strong> which 10 PMTs <strong>of</strong> 12:5mm
in diameter are for VUV photons and 4 PMTs <strong>of</strong> 50mm in diameter are for visible photons, are
xed just above <strong>the</strong> cathode. The scintillation signals are used to trigger <strong>the</strong> circuit for drift time
measurements and also used to roughly estimate <strong>the</strong> position <strong>of</strong> a daughter ion in a double beta decay
event. The sum energy <strong>of</strong> two beta rays is measured with <strong>the</strong> total ionization yields collected at each
segmented electrode. The position <strong>of</strong> <strong>the</strong> daughter ion is accurately determined from <strong>the</strong> distribution
<strong>of</strong> ionization yields on <strong>the</strong> several segments and <strong>the</strong> electron drift times.
3 Simulation model
The detector medium is liquid xenon <strong>of</strong> 100% enriched 136 Xe which is <strong>the</strong> double beta decay
source. The density <strong>of</strong>liquidis3:06g=cm 3 and <strong>the</strong> total weight 1:24kg. The chamber is divided into
two volumes, <strong>of</strong> which one is active and drift space <strong>of</strong> electron swarms and <strong>the</strong> o<strong>the</strong>r is <strong>the</strong> dead
volume between <strong>the</strong> collector and <strong>the</strong> grid. The whole volume <strong>of</strong> detector is divided into 200 50 42
cells and <strong>the</strong> energy deposition due to two beta rays in each cell is simulated by EGS4code.At each
event <strong>of</strong> <strong>the</strong> double beta decays, <strong>the</strong> coordinates <strong>of</strong> <strong>the</strong> vertex point, <strong>the</strong> number <strong>of</strong> cells in which any
energy deposition exists, and an assembly that <strong>the</strong> position <strong>of</strong> a cell and <strong>the</strong> energy deposition into
<strong>the</strong> cell are all memorized into a data-set. The source <strong>of</strong> double beta decays is uniformly distributed
2

inside <strong>the</strong> whole volume. Then, we produced two data-sets <strong>of</strong> which one is for 2 0 decays and <strong>the</strong>
o<strong>the</strong>r is for 2 2 decays.
3.1 2 0 decay
The sum energy <strong>of</strong> two betarays emitted through this mode is equal to <strong>the</strong> Q-value <strong>of</strong> 2:479MeV .
Then, one electron with <strong>the</strong> kinetic energy T1 in unit <strong>of</strong> electron mass is generated according to <strong>the</strong>
distribution function <strong>of</strong> Eq.1[8] and <strong>the</strong> energy <strong>of</strong> <strong>the</strong> o<strong>the</strong>r is given by <strong>the</strong> sum energy <strong>of</strong> 2:479MeV .
The distribution function <strong>of</strong> <strong>the</strong> single electron in 2 0 decay isgiven by
F (T1) =(T1 +1) 2 (T0 +1; T1) 2 (1)
where T1 is kinetic energy in unit <strong>of</strong> <strong>the</strong> electron mass energy, T0 is Q-value in <strong>the</strong> same unit. In
simulation <strong>the</strong> two electrons are assumed to emit simply back-to-back.
3.2 2 2 decay
In 2 2 decay, <strong>the</strong> distribution function <strong>of</strong> single electron and <strong>the</strong> sum energy are given by
F1(T1) =(T1 +1) 2 h
6
(T0 ; T1) (T0 ; T1) 2 i
+8(T0 ; T1)+28
(2)
F (T )=(T 4 +10T 3 +40T 2 +60T +30)T (T0 ; T ) 5 (3)
where T1 is <strong>the</strong> kinetic energy <strong>of</strong> single electron, T0 <strong>the</strong> Q-value, and T <strong>the</strong> sum-energy <strong>of</strong> emitted
electrons. T1, T0, T are all given in unit <strong>of</strong> electron mass energy. One electron with kinetic energy
<strong>of</strong> T1 is generated according to Eq.2 [8] and <strong>the</strong> o<strong>the</strong>r electron is generated to satisfy <strong>the</strong> distribution
function <strong>of</strong> <strong>the</strong> sum energy T given by Eq.3.The two electrons are assumed to emit back-to-back.
4 Ionization and Scintillation Signals
In order to get signal sizes from <strong>the</strong> data-sets mentioned above, <strong>the</strong> energy deposition in every cell
is converted to <strong>the</strong> number <strong>of</strong> electrons and photons by using <strong>the</strong> W-value (15:6eV ) for ionization and
<strong>the</strong> Ws-value (16:3eV ) for scintillation. However, <strong>the</strong> number <strong>of</strong> photons emitted under <strong>the</strong> electric
eld <strong>of</strong> operation is reduced to almost 1=3. Then, we use an estimated value <strong>of</strong> 50eV=photon to get
<strong>the</strong> number <strong>of</strong> photons.
4.1 Ionization signals
In order to properly operate <strong>the</strong> drift chamber, <strong>the</strong> electric eld between <strong>the</strong> grid and <strong>the</strong> collector
is so kept 2 to 3 times stronger than one between <strong>the</strong> grid and <strong>the</strong> cathode that <strong>the</strong> grid does not
capture even a fraction <strong>of</strong> electron swarms. Therefore, <strong>the</strong> drift velocity <strong>of</strong> electrons between <strong>the</strong> grid
and <strong>the</strong> collector is slightly larger than that between <strong>the</strong> cathode and <strong>the</strong> grid. Here, we used drift
velocities <strong>of</strong> 2:1mm= sec and 1:9mm= sec, respectively, to calculate rise times <strong>of</strong> ionization signals at
<strong>the</strong> collector segments. The total number <strong>of</strong> electrons collected at <strong>the</strong> collector was calculated event
by event and was again converted to <strong>the</strong> energy. The total energy deposition in <strong>the</strong> active volume
is shown in Fig.2 in <strong>the</strong> case <strong>of</strong> 2 0 decay mode. The spectrum in <strong>the</strong> case <strong>of</strong> 2 2 decay events
is also shown in Fig.3. The position <strong>of</strong> an event on Y -direction was determined from <strong>the</strong> centroid <strong>of</strong>
<strong>the</strong> charge distribution spread over several collector segments. Then, <strong>the</strong> distance between <strong>the</strong> vertex
point and <strong>the</strong> position <strong>of</strong> events was calculated. The displacement <strong>of</strong> <strong>the</strong> position from <strong>the</strong> vertex
point isshown in Fig.4 in <strong>the</strong> case <strong>of</strong> 2 0 decay mode. The position <strong>of</strong> every event on Z-direction
was calculated from <strong>the</strong> drift time when 90% <strong>of</strong> electrons reached to <strong>the</strong> collector and <strong>the</strong> drift time
was converted to <strong>the</strong> distance from <strong>the</strong> collector. The displacement <strong>of</strong><strong>the</strong> position determined with
<strong>the</strong> drift time from <strong>the</strong> vertex point is plotted in Fig.5 in <strong>the</strong> case <strong>of</strong> 2 0 decay events. In <strong>the</strong> case
<strong>of</strong> 2 2 decay events, <strong>the</strong> displacement onY -direction is shown in Fig.6 and <strong>the</strong> same on Z-direction
is shown in Fig.7.
3

4.2 Scintillation signals
The VUV sensitive PMT observes scintillation photons. The energy deposition in every cell is
converted to <strong>the</strong> number <strong>of</strong> photoelectrons at every PMT, using <strong>the</strong> solid angle subtended by every
PMT to every cell and assuming <strong>the</strong> quantum e ciency <strong>of</strong> all <strong>the</strong> PMT is 10%. Since this calculation
generates fractional gures in <strong>the</strong> number <strong>of</strong> photoelectrons, we obtained its integral number, assuming
<strong>the</strong> fractional photoelectron number shows an expected value in Poisson distribution. The histograms
<strong>of</strong> <strong>the</strong> displacement on <strong>the</strong> position determined with <strong>the</strong> number <strong>of</strong> photoelectrons at every PMT from
<strong>the</strong> vertex point are shown in Fig.8 to 11 for <strong>the</strong> both cases <strong>of</strong> decay modes.
5 Results and Discussions
We can estimate <strong>the</strong> e ciencies for detection <strong>of</strong> double beta decay events in <strong>the</strong> both decay
modes. Firstly, we blur <strong>the</strong> spectrum shown in Fig.1 with uctuations due to electronic noise <strong>of</strong>
<strong>the</strong> preampli er, rise time e ect in shaping circuit, shielding ine ciency <strong>of</strong> <strong>the</strong> grid and ionization
straggling. Assuming <strong>the</strong> energy resolution is determined from <strong>the</strong> total width due to those e ects,
<strong>the</strong> detection e ciency, which is de ned as a ratio <strong>of</strong> <strong>the</strong> number <strong>of</strong> counts detected with <strong>the</strong> energy
interval inside 2 FWHM at <strong>the</strong> peak to <strong>the</strong> total events, is plotted as a function <strong>of</strong> <strong>the</strong> energy
resolution in Fig.12 in <strong>the</strong> case <strong>of</strong> 2 0 decay mode. We expect <strong>the</strong> detection e ciency <strong>of</strong> about 84%
with a plausible resolution <strong>of</strong> 3 to 4%. The e ciency in <strong>the</strong> case <strong>of</strong> 2 2 decay mode is largely depend
on <strong>the</strong> threshold energy <strong>of</strong> <strong>the</strong> detection system and is plotted as a function <strong>of</strong> threshold in Fig.13. A
factor, which determines <strong>the</strong> threshold energy in 2 2 decay events, is a triggering level determined
by <strong>the</strong> number <strong>of</strong> photoelectrons. As <strong>the</strong> level increases, <strong>the</strong> e ciency decreases as shown in Fig.14.
As our next step, <strong>the</strong> angular correlation should be incorporated into <strong>the</strong> simulation <strong>of</strong> <strong>the</strong> double
beta decays, because we assume two beta rays emit back-to-back in <strong>the</strong> simulation.
References
[1] M. Doi et al., Prog. Th. Phys. 66(1981)1739 M. Doi et al., Prog. Th. Phys. 66(1981)1765.
[2] M.Miyajima et al., AIPconf. Proc. 388, Resonance Ionization Spectroscopy 253(1996).
[3] T. Takahashi et al., Phys. Rev. 12A(1975)1771.
[4] L. S. Miller, S. Home and W. E. Spear, Phys. Rev. 116(1968)871.
[5] M. Miyajima et al., IEEE Trans. Nucl. Sci. NS39(1992)536.
[6] S. Kubota et al., Nucl. Instr. and Meth. 196(1982)101.
[7] M. Miyajima et al., Presented at <strong>the</strong> 55th <strong>the</strong> meeting <strong>of</strong> Physical Society <strong>of</strong> Japan, Sep. 2000.
[8] V. I. Tretyak and YU. G. Zdesenko, At. Data Nucl. Data Tabl. 61(1993)43.
4

0
42mm
PMT
scintillation
PMT
fluorescence
PMT
fluorescence
50mm
200mm
PMT
flourescence
PMT
fluorescence
Figure 1: Simulation model for EGS4. Size:200 50 42mm 3 , matter:liquid xenon enriched 136 Xe (outside:
vacuum)
Count
10 5
10 4
10 3
10 2
0 0.5 1 1.5 2 2.5 3
Energy(MeV)
Figure 2: Spectrum <strong>of</strong> <strong>the</strong> total energy deposition
in <strong>the</strong> active volume in <strong>the</strong> case <strong>of</strong> 2 0 decay
events
Count
10 3
10 2
10
1
Z
X
Y
0 0.5 1 1.5 2 2.5 3
Energy(MeV)
Figure 3: Spectrum <strong>of</strong> <strong>the</strong> total energy deposition
in <strong>the</strong> active volume in <strong>the</strong> case <strong>of</strong> 2 2 decay
events
5

Count
5000
4000
3000
2000
1000
Constant 4680.
Mean 0.1617E-03
Sigma 0.6391E-01
0-1
-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
∆Y(cm)
Figure 4: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> charge signals from strips in
2 0 decay
Count
7000
6000
5000
4000
3000
2000
1000
Constant 5697.
Mean 0.2732E-04
Sigma 0.5240E-01
0-1
-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
∆Y(cm)
Figure 6: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> charge signals from strips in
2 2 decay
Count
7000
6000
5000
4000
3000
2000
1000
Constant 5348.
Mean 0.2398E-01
Sigma 0.5317E-01
0-1
-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
∆Z(cm)
Figure 5: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> charge signals from strips in
2 0 decay
Count
10000
8000
6000
4000
2000
Constant 9109.
Mean 0.9443E-02
Sigma 0.3179E-01
0-1
-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
∆Z(cm)
Figure 7: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> charge signals from strips in
2 2 decay
6

Count
1800
1600
1400
1200
1000
800
600
400
200
Constant 1311.
Mean -0.8838E-01
Sigma 0.4220
0-4
-3 -2 -1 0 1 2 3 4
∆Y(cm)
Figure 8: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> signals from PMTs in 2 0
decay
Count
1800
1600
1400
1200
1000
800
600
400
200
Constant 1367.
Mean -0.8843E-01
Sigma 0.4078
0-4
-3 -2 -1 0 1 2 3 4
∆Y(cm)
Figure 10: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> signals from PMTs in 2 2
decay
Count
2000
1750
1500
1250
1000
750
500
250
Constant 1360.
Mean -0.1912
Sigma 0.3642
0-4
-3 -2 -1 0 1 2 3 4
∆Z(cm)
Figure 9: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> signals from PMTs in 2 0
decay
Count
2000
1750
1500
1250
1000
750
500
250
Constant 1411.
Mean -0.1893
Sigma 0.3593
0-4
-3 -2 -1 0 1 2 3 4
∆Z(cm)
Figure 11: Distribution <strong>of</strong> <strong>the</strong> displacement: <strong>the</strong>
position where <strong>the</strong> double beta decay occurs and
<strong>the</strong> centroid <strong>of</strong> <strong>the</strong> signals from PMTs in 2 2
decay
7

Detection efficiency(%)
84.8
84.6
84.4
84.2
84
83.8
1 1.5 2 2.5 3 3.5 4 4.5 5
energy resolution(%)
Figure 12: Detection e ciency <strong>of</strong> 2 0 decay
events as a function <strong>of</strong> energy resolution
Detection efficiency(%)
100
99
98
97
96
95
94
93
Detection efficiency(%)
100
95
90
85
80
75
70
65
60
55
100 200 300 400 500 600 700 800
Cut energy(keV)
Figure 13: Detection e ciency <strong>of</strong> 2 2 decay
events as a function <strong>of</strong> threshold energy
92
0 1 2 3 4 5 6 7 8 9 10
Threshold <strong>of</strong> Photo-electron
Figure 14: Detection e ciency <strong>of</strong> two decay modes as a function <strong>of</strong> triggering level where : 2 0 decay mode,
2 : 2 2 decay mode
8

<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Second</strong> <strong>International</strong> <strong>Workshop</strong> on EGS, 8.-12. August 2000, Tsukuba, Japan
KEK <strong>Proceedings</strong> 200-20, pp.324-329
Observation <strong>of</strong> Intense Radiation During Thunderstorm
and Monte Carlo Simulation <strong>of</strong> Bremsstrahlung Generation
1 Introduction
T. Torii 1 , M. Takeishi 1 , T. Hosono 1 and T. Sugita 2
1 Tsuruga Head O ce, Japan Nuclear Cycle Development Institute,
Shiraki 2-1, Tsuruga, Fukui-ken 919-1279, Japan
2 Science and System Lab. Inc.,
Sumiyoshi 1342-6, Tomobe, Ibaraki-ken 309-1716, Japan
Following Wilson's suggestion[1] <strong>of</strong> electron acceleration by <strong>the</strong> electric elds in thunderclouds, a
number <strong>of</strong> experiments were attempted to investigate whe<strong>the</strong>r or not energetic electrons and bremsstrahlung
X-rays were generated by thunderstorm electric elds or lightning discharge processes. In
recent years, enhanced radiation at high altitude has been detected in experiments using scintillation
detectors on a jet[2, 3] and an arti cial satellite[4], demonstrating that radiation is indeed associated
with lightning activities. However <strong>the</strong>re are few experimental reports <strong>of</strong> detection near <strong>the</strong> ground
since Whitmire's investigation[5] using <strong>the</strong>rmoluminescent dosimeters (TLDs) in 1979.
In winter, many thunderstorms occur on <strong>the</strong> west coast <strong>of</strong> Japan, and it has been suggested
that gamma-ray dose may increase occasionally during winter thunderstorms[6]. Recently, a gammaray
dose enhancement which might be caused by <strong>the</strong> lightning activity was measured by TLDs and
environmental radiation monitors around <strong>the</strong> site <strong>of</strong> <strong>the</strong> fast breeder reactor \Monju", a nuclear power
plant facing <strong>the</strong> Japan Sea. (see Fig. 1)
2 Observation
On <strong>the</strong> night <strong>of</strong> Jan. 28, 1997, <strong>the</strong>re was a thunderstorm lasting until dawn, during which <strong>the</strong>re
was much lightning activity in <strong>the</strong> area accompanied by snow. In particular, a large lightning ash
occurred at 4:31 JST on Jan. 29. At that time, dose-rate <strong>of</strong> <strong>the</strong> environmental radiation monitors using
an NaI(Tl) detector around <strong>the</strong> site increased transiently. Fur<strong>the</strong>rmore, radiation monitors installed
on <strong>the</strong> most upper oor in <strong>the</strong> buildings were a ected at that time. During that night, although 20
cloud-to-ground discharges were detected by <strong>the</strong> LLS (Lightning Location System) around Tsuruga
Peninsula, a dose-rate increase <strong>of</strong> <strong>the</strong> NaI(Tl) detectors was recorded only once. Some radiation
monitors installed in <strong>the</strong> buildings were rose count-rate at that time, and all <strong>of</strong> those were set on
<strong>the</strong> most upper oor. Dose increases were also measured by TLDs exposed during <strong>the</strong> periods which
included <strong>the</strong> day when <strong>the</strong> lightning occurred. Absorbed doses <strong>of</strong> <strong>the</strong> TLDs exceeded over 3 <strong>of</strong> <strong>the</strong>
mean values at almost all <strong>of</strong> <strong>the</strong> measuring points outside <strong>the</strong> buildings <strong>of</strong> Monju (see Fig. 2), and
highest dose increase was recorded about 0.1 mGy at <strong>the</strong> north-east area <strong>of</strong> <strong>the</strong> site. Whereas doses
in <strong>the</strong> buildings were within <strong>the</strong> normal range at all measuring points.
3 Energy Spectrum and Dose Estimation
The NaI(Tl) detector system <strong>of</strong> <strong>the</strong> environmental radiation monitor (MP-1) is connected to a
multi-channel analyzer (MCA) with 2,048 channels in <strong>the</strong> energy range up to about 5MeV,and <strong>the</strong>
1

MCA stores <strong>the</strong> pulse-height distribution at one hour intervals. Fig. 3 shows dose rate indicated
by <strong>the</strong> monitor and <strong>the</strong> pulse-height distributions <strong>of</strong> <strong>the</strong> MCA around <strong>the</strong> time that <strong>the</strong> lightning
occurred. From \net" pulse-height distribution, which is <strong>the</strong> pulse-height distribution subtracted
from <strong>the</strong> background distribution, we calculated <strong>the</strong> photon energy spectrum by <strong>the</strong> unfolding method.
Here, we usedaversatile code SAND II for <strong>the</strong> spectrum unfolding, and EGS4/PRESTA code[7, 8] for
<strong>the</strong> response calculation <strong>of</strong> <strong>the</strong> NaI(Tl) detector system. The unfolded energy spectrum is illustrated
in Fig. 4(a). This indicates a continuous spectrum with energy up to several MeV, and dose increase is
estimated about 36 nGy at that time. It is quite di erent from dose increase obtained by <strong>the</strong> TLD at
<strong>the</strong> same point (TL-E1). It may be caused by dead time losses <strong>of</strong> <strong>the</strong> detector and <strong>the</strong> MCA system,
and low and/or high energy component cut o by <strong>the</strong> MCA.
4 Discussion
As mentioned above on <strong>the</strong> measured result <strong>of</strong> TLDs and radiation monitors, it is seen that this
dose enhancement is caused by external radiation. Also, from <strong>the</strong> unfolded spectrum, this phenomenon
may be caused by bremsstrahlung X-rays from energetic electrons generated in <strong>the</strong> thunderstorm.
Next, we calculated X-ray spectra on <strong>the</strong> ground generated from downward electrons emitted at 500
m and 1,000 m high, which is altitude <strong>of</strong> <strong>the</strong> base <strong>of</strong> thunderclouds. As shown <strong>the</strong> results in Figs. 4(a)
and 4(b), <strong>the</strong> unfolded spectrum is consistent with <strong>the</strong> bremsstrahlung spectra.
4.1 Electron transport in electric elds
To verify <strong>the</strong> electron acceleration and <strong>the</strong> bremsstrahlung generation in thunderstorms, we have
made macros to calculate electron behavior in air with external electric elds according as Bielajew's
manner[9]. The macros
$SET-TUSTEP-EM-FIELD,
$SET-USTEP-EM-FIELD,
$SET-ANGLES-EM-FIELD,
..............................,
have been located within SUBROUTINE ELECTR.
Here, we have put <strong>the</strong> following equations described electron transport in <strong>the</strong> macros.
- Transverse force on <strong>the</strong> electron due to external elds:
~uf = ~u0 + ~umsret + uex
~uem =
es
( ~ D0 ; ~u0(~u0 ~ D0))
m0 (E0) v 2
0
where ~uf , ~u0 are nal and original unit direction vector, respectively. ~umsret is <strong>the</strong> de ection due
to multi scattering and inelastic collisions, and uex is that due to <strong>the</strong> external electric eld.
- Final position and energy <strong>of</strong> electrons:
~xf = ~x0 + ~u0 s + s
2 ( ~umsret + ~uex)
Ef = E0 ; Eret + e ~ D0 (~xf ; ~x0)
where Eret is <strong>the</strong> energy loss due to inelastic collisions.
2

4.2 Simulation in thunderstorm
After a test <strong>of</strong> electron transport in a vacuum to verify <strong>the</strong> behavior with <strong>the</strong> analytical solution,
we modeled electric elds in thunderclouds and calculated <strong>the</strong> transport using <strong>the</strong> above code. As
shown in Fig. 5, it is obtained that <strong>the</strong> avalanche <strong>of</strong> electrons caused by <strong>the</strong> acceleration and collisions
occurred at a eld strength <strong>of</strong> about 3 MV/m for electrons with energy up to 1 MeV as a original
energy. Fur<strong>the</strong>rmore, it can be seen that bremsstrahlung X-rays generated at high altitude above <strong>the</strong>
ground. Details are presented at <strong>the</strong> workshop.
References
[1] Wilson, C. T. R., Proc. Cambridge Phil. Soc., 22, 534 (1925)
[2] Parks, G. K. et al., Geophys. Res. Lett., 8, 1176 (1981)
[3] McCarthy, M. and Parks, G. K., Geophys. Res. Lett., 12, 393 (1985)
[4] Fishman, G. J. et al., Science, 264, 1313 (1994)
[5] Whitmire, D. P., Lett. al Nuovo Cimento, 26, 497 (1979)
[6] Yoshioka, M. et al., Annual Rep. <strong>of</strong> Fukui Pref. ERMC, 16, p129 (1993) (in Japanese)
[7] Nelson, W. R., Hirayama, H., and Rogers, D. W. O., SLAC-265, (1985)
[8] Bielajew, A. F. and Rogers, D. W. O., Nucl. Instr. Meth., B18, 165 (1987)
[9] Bielajew, A. F., in Monte Carlo Transport <strong>of</strong> Electrons and Photons (Jenkins, T. M., et al., eds),
421 (1988, Plenum Press, N.Y.)
3

4

5

6

Predicted Angular Distribution <strong>of</strong>
Fast Charged Particles with Ionization
T. Nakatsuka
Okayama Shoka University, Okayama 700-8601, Japan
Abstract
Moliere <strong>the</strong>ory <strong>of</strong> angular distribution for fast charged particles is improved to take into account
ionization loss, by using Kamata-Nishimura formulation <strong>of</strong> <strong>the</strong> <strong>the</strong>ory. Decrease <strong>of</strong> <strong>the</strong> particle
energy along <strong>the</strong> passage hence increase <strong>of</strong> <strong>the</strong> screening angle brings a slight di erent results from
those derived by Moliere-Be<strong>the</strong> formulation for xed energies. The present results are reduced to <strong>the</strong>
same Moliere distribution with modi ed values <strong>of</strong> <strong>the</strong> expansion parameter and <strong>the</strong> unit <strong>of</strong> Moliere
angle. Properties <strong>of</strong> <strong>the</strong> new distribution and di erences from <strong>the</strong> traditional one are discussed.
Angular distributions <strong>of</strong> particles penetrating through <strong>the</strong> mixed or compound substances are
also investigated both under <strong>the</strong> relativistic and <strong>the</strong> nonrelativistic conditions, toge<strong>the</strong>r with <strong>the</strong>
Kamata-Nishimura constants characterizing <strong>the</strong>ir formulation.
1 Introduction
Highly accurate <strong>the</strong>ories <strong>of</strong> multiple Coulomb scattering are important when we design and analyze
experiments concerning charged particle and trace charged particles in computer simulation. Among
various <strong>the</strong>oretical predictions <strong>of</strong> <strong>the</strong> multiple scattering process, Moliere <strong>the</strong>ory [1, 2, 3] is recognized
most advanced re ecting <strong>the</strong> single and <strong>the</strong> plural scatterings in <strong>the</strong> <strong>the</strong>ory, so that it has been widely
used in computer simulation codes [4, 5, 6]. In spite <strong>of</strong> its excellent formulation <strong>of</strong> <strong>the</strong> <strong>the</strong>ory, ithad
been a defect <strong>of</strong> Moliere <strong>the</strong>ory that almost no <strong>the</strong>oretical improvements and applications to o<strong>the</strong>r
problems were achieved after his original constructions [1, 2, 7].
Kamata and Nishimura proposed ano<strong>the</strong>r formulation <strong>of</strong> Moliere <strong>the</strong>ory in <strong>the</strong>ir description <strong>of</strong> cascade
shower <strong>the</strong>ory [8, 9], whichisequivalent with <strong>the</strong> Moliere-Be<strong>the</strong> formulation within <strong>the</strong> expansion
errors [10]. They described <strong>the</strong> <strong>the</strong>ory in a di erential form with traversed thickness, so that we can
regard it as a thorough extension <strong>of</strong> Fermi-Yang formulation [11, 12, 13, 14], and it made applications
<strong>of</strong> <strong>the</strong> Moliere <strong>the</strong>ory very easy to o<strong>the</strong>r problems, for example, Kamata and Nishimura could add <strong>the</strong>
next higher term re ecting <strong>the</strong> single and <strong>the</strong> plural scatterings to <strong>the</strong>ir shower <strong>the</strong>ory [8, 9] and <strong>the</strong>
author could discuss <strong>the</strong> Moliere e ect on <strong>the</strong> actual path length problem [13].
Recently we have found ano<strong>the</strong>r superior aspect <strong>of</strong> <strong>the</strong> Kamata-Nishimura formulation that we
can easily take into account ionization loss in <strong>the</strong> Moliere angular distribution by only modifying
parameter values in <strong>the</strong> Moliere <strong>the</strong>ory [15, 16, 17, 18]. It improves <strong>the</strong> accuracy and <strong>the</strong> reliability <strong>of</strong>
Moliere distribution. It has ano<strong>the</strong>r important e ect from <strong>the</strong> practical point <strong>of</strong> view that it improves
sampling e ciency in computer simulations. In case using <strong>the</strong> traditional Moliere <strong>the</strong>ory <strong>of</strong> xed
energies, <strong>the</strong> sampling path length had to be restricted short so as not <strong>the</strong> distribution deformed due
to <strong>the</strong> decrease <strong>of</strong> particle energy [4, 19]. By using our distribution this restriction will be removed.
Unfortunately for us, Kamata-Nishimura formulation <strong>of</strong> Moliere <strong>the</strong>ory is written for electron in <strong>the</strong>
relativistic condition and <strong>the</strong> characteristic constants are indicated for only restricted substances [8, 9].
So we have attempted to describe <strong>the</strong> formulation suitable for general energy range, and applicable
to variety <strong>of</strong> particles irrespective <strong>of</strong> mass and charge. The characteristic constants appearing in
<strong>the</strong> formulation are tabulated for various substances. Method to obtain <strong>the</strong> distribution for particles
traversing through mixed or compound substances is also discussed.
1

2 The Angular Distribution With Ionization Under The Relativistic
Condition
Kamata and Nishimura proposed a very simple formulation <strong>of</strong> Moliere <strong>the</strong>ory for electrons <strong>of</strong>
relativistic condition. Let f( t)2 d be <strong>the</strong> angular distribution <strong>of</strong> electrons after traversing through
athickness <strong>of</strong> t measured in radiation unit [11], receiving multiple Coulomb scattering under <strong>the</strong> axially
symmetric condition. The di usion equation is described as
@ ~ f
@t
2
= ;K2
4E2 ~ ff1 ; 1 2
K2
ln g (1)
4E2 in <strong>the</strong> Fourier space [8, 9]. The equation possesses only two constants speci c to <strong>the</strong> substance. Under
<strong>the</strong> xed energy condition, <strong>the</strong> solution <strong>of</strong> equation becomes
~f = 1
2 expf;
2
G 2
4 (1 ; 1 ln
2
G 2
4t
)g with
2
G = K2t : (2)
E2 Using <strong>the</strong> translation formula indicated in <strong>the</strong> Appendix, <strong>the</strong> Kamata-Nishimura formulation is reduced
to <strong>the</strong> Moliere-Be<strong>the</strong> one and we get <strong>the</strong> Moliere angular distribution characterized by <strong>the</strong> two
parameters, <strong>the</strong> expansion parameter B and <strong>the</strong> unit <strong>of</strong> Moliere angle # = = M, determined by [13]
q
B= : (3)
B ; ln B = ; ln +lnt and M = G
If we assume ionization loss <strong>of</strong> constant rate
<strong>the</strong> di usion equation becomes
Then we have <strong>the</strong> solution
where
@ ~ f
@t
~f = 1
2 expf;
E = E0 ; "t: (4)
2
= ;K2
4E2 ~ ff1 ; 1 2
K2
ln
4E2 g + " @ ~ f
: (5)
@E
2
G 2
4 (1 ; 1 ln
The characteristic parameters B and M are determined by
2
G 2
4 t )g with 2
G = K2t (6)
E0E
= e 2 (E=E0) (E0+E)=(E0;E) : (7)
B ; ln B = ; ln +ln t and M = G
q B= : (8)
The angular distributions with ionization are compared with those without ionization in Fig. 1.
The width <strong>of</strong> distribution increases rapidly with dissipation <strong>of</strong> energy.
3 The Angular Distribution With Ionization Under The General
Energy Condition
The di usion equation for <strong>the</strong> angular distribution in Kamata-Nishimura formulation equivalent
with that in Moliere-Be<strong>the</strong> one is described as
@ ~ f
z2 2
= ;
@t w2 ~ ff1 ; 1 ln
2
02 2
g (9)
w2

in <strong>the</strong> Fourier space. We de ne
and
02 = 1:13 + 3:76 2
1:13 + 3:76 2 0
w =2pv=K = 2E
f1 ; (mc2
K E )2g (10)
2 with = zZ
137
K and denote Kamata-Nishimura constants [8, 9].
Under <strong>the</strong> ionization process <strong>of</strong>
we get <strong>the</strong> solution as
~f = 1
2 expf;
and 0 = Z
: (11)
137
E = E0 ; "z 2 t (12)
2
G 2
4 (1 ; 1 ln
2
G 2
4 z2t= where G denotes <strong>the</strong> gaussian root-mean-square angle with Es replaced by K,
2
G =
Z t
0
4z 2
dt =
w2 K 2
fmc2
2"mc2 pv
and denotes <strong>the</strong> scale factor derived by
ln 02 =ln
2
G
4z 2 t
mc2
; +
p0v0
1
; 4z2
2
G
Z t
0
02 )g (13)
2 ln (E0 ; mc 2 )=(E ; mc 2 )
(E0 + mc2 )=(E + mc2 )
1
ln
w2 02
g (14)
dt: (15)
w2 So that <strong>the</strong> angular distribution is determined by <strong>the</strong> expansion parameter B and <strong>the</strong> unit <strong>of</strong> Moliere
angle M, derived from
q
B= : (16)
B ; ln B = ; ln +ln( z 2 t= 02 ) and M = G
In case <strong>of</strong> 0 ,which is realized for e.g. light substances <strong>of</strong> 1 or for singly-charged relativistic
particle <strong>of</strong> 0, determined from Eq. (15) becomes <strong>the</strong> function <strong>of</strong> E0=mc 2 and E=mc 2 . in this
case is plotted against fractional thickness, t=(E0="), in Fig. 2 for various E0=mc 2 . B and M in this
case are plotted against <strong>the</strong> traversed thickness in Fig. 3 and Fig. 4. Di erences <strong>of</strong> B and M due to
di erent E0=mc 2 are small.
4 Derivation <strong>of</strong> Kamata-Nishimura Formulation and De nition <strong>of</strong>
Kamata-Nishimura Constants
We take <strong>the</strong> single scattering formula as
( )2 d = 4z2 Z(Z +1)e 4
p 2 v 2
;4 2 d with > p e a (17)
where a is called <strong>the</strong> characteristic screening angle [3]. Then <strong>the</strong> probability density to receive
de ection angle after an in nitesimal passage <strong>of</strong> dx measured in g/cm 2 is
N
A
( )2 d dx = 4N
A
=
1
4 L
z 2 Z(Z +1)e 4
3
E 2 s
p 2 v 2
p 2 v 2
;4 2 d z 2 dx
;4 2 d dx
X0
(18)

where X0 denotes <strong>the</strong> radiation length [20] and L <strong>the</strong> so-called radiation logarithm with its correction
term [21].
The di usion equation for Moliere angular distribution becomes [8, 9]
df = N
A dx
ZZ ff( ~ ; ~0 ) ; f( ~ )g ( ~0 )d ~0 : (19)
Under <strong>the</strong> azimuthally symmetrical condition, Hankel transforms <strong>of</strong> Eq. (19) becomes
d ~ f = ;2 N
A
Z 1
~fdx
0
= ; E2 s z
2L
2 dt
p2v2 ~ Z 1
f p
e a
[1 ; J0( )] ( ) d
where t denotes <strong>the</strong> traversed thickness measured in radiation unit:
[1 ; J0( )] ;3 d (20)
t x=X0: (21)
Evaluating <strong>the</strong> integration using <strong>the</strong> formula (14) <strong>of</strong> Be<strong>the</strong> [3], we get <strong>the</strong> following di erential equation
; d
z 2 dt ln ~ f = E2 s
8L
= E2 s
4L
2
p 2 v 2 [1+ln2; C ; ln(p e a )]
2
4p2 [1 ; 2C +ln
v2 2 2
Es =(4Lp 2 v 2 2 0)
[ 2 a = 2 0 ]rel
2 2
a =
; ln
2 0
[ 2 a = 2 0 ]rel
; ln( E2 s
4L
where we introduced <strong>the</strong> angular constant 0 [3] called <strong>the</strong> Born screening angle [22],
and [ 2 a = 2 0 ]rel denotes <strong>the</strong> value <strong>of</strong> 2 a = 2 0
2
4p2 )] (22)
v2 0 =h=(ap) (23)
for electrons <strong>of</strong> high energy limit.
Now we de ne <strong>the</strong> Kamata-Nishimura constants as
; ln =1; 2C +ln E2 s =(4Lp2c 2 2 0)
[ 2 a = 2 0 ]rel
(24)
K 2 = E2 s
4L
(25)
<strong>the</strong>n and K are constants speci c to <strong>the</strong> substance. It can be easily con rmed that <strong>the</strong>se de nitions
agree with (A.3.26) and (A.3.28) <strong>of</strong> Nishimura de ned in <strong>the</strong> relativistic condition [9]. We also
introduce <strong>the</strong> factor
02 =
2
a = 2 0
[ 2 a = 2 0 ]rel
2 (26)
re ecting <strong>the</strong> velocity <strong>of</strong> penetrating particle and <strong>the</strong> di erence between <strong>the</strong> characteristic screening
angle and <strong>the</strong> Born screening angle.
Then <strong>the</strong> di usion equation becomes
so that we get
; d
z 2 dt ln ~ f =
K2 2
d
z2dt ln ~ 2
f = ;
w2 [1 ; 1 ln
4p2 02 2
[ ; ln ; ln(K2
v2 4p2 )] (27)
v2 02 2
] where w =2pv=K: (28)
w2 Many authors evaluated a and 0 respectively in <strong>the</strong>ir multiple scattering <strong>the</strong>ories, depending
on <strong>the</strong>ir models <strong>of</strong> screening potential. We listed in Table 1 some screening models adopted by
representative authors <strong>of</strong> multiple scattering <strong>the</strong>ory.
4

Table 1: Screening potentials adopted by representative authors. V (r), a, 0, a denote screening potential,
atomic radius, Born screening angle, and <strong>the</strong> characteristic screening angle, respectively. Bohr radius and <strong>the</strong>
Born parameter, a0 =h 2 =me 2 and = zZ=137 , are used in <strong>the</strong> table.
Author V (r) a 0 a
Goudsmit-Saunderson Ze2 Moliere
exp(;r=a) r
zZe
;1=3
a0Z h=(ap) 0
2
!(r=a)
;1=3
0:885a0Z h=(ap) p 1:13 + 3:76 2 0
Snyder-Scott
r
Ze 2
r
exp(;r=a) a0Z ;1=3
h=(ap) 0
5 Evaluation <strong>of</strong> Kamata-Nishimura Constants for Pure Substances
5.1 Moliere screening model
If we adopt <strong>the</strong> Moliere screening model [1], we get <strong>the</strong> equations for and K as
; ln =1; 2C +ln 1373 (0:885Z ;1=3 ) 2
(1:13 + 3:76Z2 =1372 (29)
)L
K 2 = E2 s
4L
Using <strong>the</strong> value <strong>of</strong> radiation length X0 [23] <strong>of</strong>
1
X0
: (30)
= 4N
137A Z(Z +1)r2 e L (31)
instead <strong>of</strong> L, we can determine and K consistent with widely-used table <strong>of</strong> material constants
indicated by Particle Data Group [24]:
; ln =ln 6680(Z +1)Z1=3X0 (1 + 3:34Z2 =1372 (32)
)A
K 2 ;4 Z(Z +1)
=3:49 10
A
In this case Kamata-Nishimura equation becomes
d
z2dt ln ~ 2
f = ;
w2 [1 ; 1 ln
02 2
] where
w2 Kamata-Nishimura constants so obtained are listed in Table 2.
X0 E 2 s : (33)
02 = 1+3:34z 2 Z 2 =(137 ) 2
1+3:34Z 2 =137 2
2 : (34)
5.2 O<strong>the</strong>r simple models which do not distinguish <strong>the</strong> characteristic screening
angle from <strong>the</strong> Born screening angle
According to Goudsmit and Saunderson [25], Snyder and Scot [26], and Rossi [20], <strong>the</strong>y do not
distinguish <strong>the</strong> characteristic screening angle from <strong>the</strong> Born screening angle
In those cases, it satis es
a = 0: (35)
0 = (36)
5

Table 2: Kamata-Nishimura constants and K for pure substances derived from <strong>the</strong> Moliere screening model,
toge<strong>the</strong>r with those (embraced) from <strong>the</strong> simple model <strong>of</strong> a = 0.
Material Z A X0 K
g/cm 2 MeV
H 1 1.008 61.28 16.40(16.54) 17.69(17.76)
He 2 4.003 94.32 16.07(16.20) 18.88(18.96)
Li 3 6.941 82.76 15.80(15.93) 18.83(18.91)
C 6 12.011 42.70 15.34(15.48) 18.96(19.04)
N 7 14.007 37.99 15.25(15.39) 19.06(19.15)
O 8 15.999 34.24 15.17(15.31) 19.15(19.24)
Al 13 26.982 24.01 14.85(15.02) 19.43(19.53)
Si 14 28.086 21.82 14.80(14.97) 19.47(19.58)
S 16 32.066 19.50 14.71(14.89) 19.54(19.66)
Ar 18 39.948 19.55 14.63(14.82) 19.60(19.73)
Fe 26 55.845 13.84 14.34(14.60) 19.79(19.96)
Cu 29 63.546 12.86 14.25(14.53) 19.84(20.03)
Br 35 79.904 11.42 14.08(14.42) 19.94(20.19)
Ag 47 107.868 8.97 13.77(14.25) 20.13(20.48)
I 53 126.904 8.48 13.62(14.19) 20.22(20.63)
W 74 183.840 6.76 13.15(14.02) 20.52(21.19)
Pb 82 207.200 6.37 12.99(13.97) 20.65(21.42)
so that we get <strong>the</strong> Kamata-Nishimura constants from
or by using X0 we get
; ln =1; 2C +ln 1373 (0:885Z ;1=3 ) 2
K 2 = E2 s
4L
L
(37)
(38)
; ln =ln 1:13 6680(Z +1)Z1=3X0 (39)
A
K 2 ;4 Z(Z +1)
=3:49 10
A
This time, Kamata-Nishimura equation becomes
d
z2dt ln ~ 2
f = ;
w2 [1 ; 1 ln
X0 E 2 s : (40)
2 2
]: (41)
w2 Kamata-Nishimura constants obtained in this case are tabulated in Table 2, embraced by brackets.
6 Angular Distribution <strong>of</strong> Charged Particles Traversing Through
Mixed or Compound Substance
The di usion equation for <strong>the</strong> angular distribution <strong>of</strong> charged particles is described as
2
d ~ f = ;
w2 ~ f(1 ; 1 ln
02 2
w 2 )z2 dt (42)
in <strong>the</strong> Fourier space. So <strong>the</strong> increase <strong>of</strong> Fourier component in <strong>the</strong> di erential passage becomes
6

;d ln ~ f = 1
X0w 2 (1 ; 1 ln
02
w 2 ) 2 z 2 dx ;
1
X0w 2 ( 2 ln 2 )z 2 dx: (43)
In case <strong>of</strong> charged particles traversing through mixed or compound substance, <strong>the</strong> coe cients appearing
in <strong>the</strong> right-hand side changes discontinuously corresponding to <strong>the</strong> atoms <strong>the</strong>y encounter. So we
take <strong>the</strong>value <strong>of</strong> coe cient as <strong>the</strong> expectation value <strong>of</strong> it. Thus we get
; ln 2 ~ f = 2
Z x
0
1
Pr[
X0w2 (1 ; 1 ln
02
w 2 )]z2 dx ; 2 ln 2
Z x
0
Pr[
1
X0 w 2 ]z2 dx (44)
where <strong>the</strong> expectation value is taken as <strong>the</strong> weighted mean value by <strong>the</strong> fractions <strong>of</strong> mass:
Pr[Q] X
piQi: (45)
thus
~f = 1
2
expf; 2
Z x
0
1
Pr[
X0w2 (1 ; 1 ln
i
02
w 2 )]z2 dx + 2 ln 2
Z x
0
Pr[
1
X0 w 2 ]z2 dxg: (46)
So using <strong>the</strong> translation formula indicated in <strong>the</strong> Appendix, we get <strong>the</strong> angular distribution characterized
by <strong>the</strong> expansion parameter B <strong>of</strong>
B ; ln B =
Z x
and <strong>the</strong> unit <strong>of</strong> Moliere angle
0
1
Pr[
X0w2 (1 ; 1 02
ln
w2 )]z2dx= M =2
s
B
Z x
0
Z x
0
Pr[
Pr[
1
1
X0 w 2 ]z2 dx +ln
Z x
0
Pr[
1
X0 w 2 ]z2 dx (47)
X0 w 2 ]z2 dx: (48)
If we assume homogeneous mixture <strong>of</strong> substances, integration <strong>of</strong> <strong>the</strong> expectation value along <strong>the</strong>
thickness should become
Z x
0
Pr[f(x)]dx =Pr[ XR
XR
Z x=(XR=XR)
where XR denotes <strong>the</strong> range <strong>of</strong> particle measured in g/cm 2 ,
XR
E0= dE
dx
0
f(x)dx] (49)
and XR E0=Pr[ dE
] (50)
dx
In case <strong>of</strong> 0 , which is realized for singly charged particles <strong>of</strong> relativistic condition or charged
particles penetrating through light substances in such a condition as zZ 137 ,wehave
Thus
; ln 2 ~ f =
;d ln ~ f = f K2
(1 ; 1 ln K 2 )
Z x
0
X0
Pr[ K2
X0
(1 ; 1 ln K 2 )]
2
4p2 K2
;
v2 X0
2
4p2 dx ;
v2 Z x
0
2
4p2 ln
v2 Pr[ K2
X0
2 2
4p2 gdx: (51)
v2 ]
2
4p2 ln
v2 2 2
4p2 dx: (52)
v2 If we introduce <strong>the</strong> reduced Kamata-Nishimura constants for mixed or compound substance, and
K, from <strong>the</strong> equations
K 2
(1 ;
X0
1 ln K 2 ) = Pr[ K2
(1 ;
X0
1 ln K 2 )] (53)
K 2
X0
= Pr[ K2
X0
] (54)
7

Table 3: The reduced Kamata-Nishimura constants, and K, for mixed or compound substances derived from
<strong>the</strong> Moliere screening model, toge<strong>the</strong>r with those (embraced) from <strong>the</strong> simple model <strong>of</strong> a = 0.
Material X0 K
g/cm 2 MeV
Air 36.61 15.21(15.35) 19.10(19.19)
SiO2 27.04 14.95(15.11) 19.34(19.44)
H2O 36.02 15.23(15.37) 19.06(19.15)
LiH 79.24 15.88(16.02) 18.65(18.73)
Emulsion 11.32 13.94(14.36) 20.01(20.31)
<strong>the</strong>n, taking X0 as <strong>the</strong> radiation length for <strong>the</strong> compound substance [20], we get
; ln =Pr[ K2
(1 ; 1 ln K 2 )]=Pr[ K2
] + ln Pr[ K2
]+lnX0 (55)
K =
s
X0
X0 Pr[ K2
X0
X0
]: (56)
In this case we can get <strong>the</strong> Moliere angular distribution for mixed or compound substances by regarding
<strong>the</strong>y are pure materials with <strong>the</strong> reduced Kamata-Nishimura constants, and K. So that <strong>the</strong>
distribution is determined by <strong>the</strong> expansion parameter B and <strong>the</strong> unit <strong>of</strong> Moliere angle M derived
from
q
B= (57)
B ; ln B = ; ln +ln( z 2 t= 2 ) and M = G
where G is derived from Eq. (14) with and K replaced by and K. The reduced Kamata-Nishimura
constants, and K, for mixed or compound substance are tabulated in Table 3. The distribution for
mixed or compound substances can also be got by <strong>the</strong> reduced constants in case we can neglect energy
loss or in case assuming simple screening model <strong>of</strong> a = 0.
By using <strong>the</strong> reduced constants, we can slightly simplify Eqs. (47) and (48) for general energy
conditions, as
B ; ln B =
and <strong>the</strong> unit <strong>of</strong> Moliere angle
Z x
0
X0
1
Pr[
X0w2 (1 ; 1 02
ln
w2 )]z2 2
G
dx=
4 +ln
M = G
2
G
4
(58)
q B= : (59)
In general energy conditions we should get exact B and M from <strong>the</strong> above equations. But in
practical use, <strong>the</strong> approximation to regard <strong>the</strong> mixed or compound substance as a pure one with <strong>the</strong>
reduced Kamata-Nishimura constants will be available. The results <strong>of</strong> exact B and M are compared
with those from <strong>the</strong> approximate method for nuclear emulsion in Figs. 5 and 6. We used Pr[Z] for
<strong>the</strong> charge number in <strong>the</strong> approximate method. We cannot observe almost any di erences.
7 Conclusions and Discussions
Kamata-Nishimura formulation <strong>of</strong> <strong>the</strong> Moliere <strong>the</strong>ory, having been described for electrons <strong>of</strong>
relativistic condition, is reconstructed to be valid in <strong>the</strong> general energy range and to wider variety <strong>of</strong>
charged particles irrespective <strong>of</strong> mass and charge. Moliere <strong>the</strong>ory is simply described in <strong>the</strong> Kamata-
Nishimura formulation by anordinary di erential equation <strong>of</strong> Fermi-Yang type in <strong>the</strong> Fourier space,
possessing <strong>the</strong> two Kamata-Nishimura constants speci c to <strong>the</strong> substance. We can obtain <strong>the</strong> Moliere
8

distribution much easily, moreover improve Moliere angular distribution to take into account ionization
loss, by <strong>the</strong> formulation. The Kamata-Nishimura constants are recalculated so that <strong>the</strong>y should be
consistent with <strong>the</strong> widely-used material constants <strong>of</strong> Particle Data Group [24] and are tabulated in
Table 2.
The method to obtain <strong>the</strong> angular distribution for charged particles traversing through mixed or
compound substance is investigated on <strong>the</strong> Kamata-Nishimura formulation. In general, Moliere distribution
in <strong>the</strong> substances can be obtained by taking <strong>the</strong> expectation values for coe cients in <strong>the</strong>
equation as <strong>the</strong> weighted mean values by <strong>the</strong> fraction <strong>of</strong> mass. In case <strong>of</strong> e.g. xed energy approximation,
traversing through light substances, or assuming o<strong>the</strong>r simple screening model than Moliere,
we can regard <strong>the</strong> mixed or compound substance as a pure one with <strong>the</strong> reduced Kamata-Nishimura
constants listed in Table 3. Approximated method to apply <strong>the</strong> reduced constants even in general
cases have shown good accuracies in so far from our restricted investigations.
The present formulation will be valuable in cross check for o<strong>the</strong>r <strong>the</strong>oretical works or simulation
results as a scarce multiple scattering <strong>the</strong>ory with ionization. Examinations by and applications to
experiments will also be followed using <strong>the</strong> Particle Telescope <strong>of</strong> Okayama University [28].
Aknowledgments
The author is very much indebted to Pr<strong>of</strong>. J. Nishimura for his hearty encouragements and valuable
advises through <strong>the</strong> work.
Appendix
We show a translation formula between <strong>the</strong> Kamata-Nishimura formulation and <strong>the</strong> Moliere-Be<strong>the</strong>
one. Let <strong>the</strong> image function by Kamata-Nishimura be <strong>of</strong> a form [27]
~f = 1
2 expf;a 2 + b 2 ln(c 2 )g: (60)
If we new de ne <strong>the</strong> expansion parameter B and <strong>the</strong> composite transform-variable u, as
B ; ln B = a c
; ln
<strong>the</strong>n we get <strong>the</strong> well known Moliere form
b
~f = 1
2
b
and u =2 p
bB (61)
u2 1
expf; (1 ;
4 B
So that <strong>the</strong> probability density can be represented in <strong>the</strong> Moliere series <strong>of</strong>
u2
ln )g: (62)
4
f(#) =f (0) (#)+B ;1 f (1) (#)+B ;2 f (2) (#)+::: (63)
where <strong>the</strong> Moliere angle is de ned by <strong>the</strong> new unit,
References
[1] G. Moliere, Z. Naturforsch. 2a(1947)133.
[2] G. Moliere, Z. Naturforsch. 3a(1948)78.
[3] H. A. Be<strong>the</strong>, Phys. Rev. 89(1953)1256.
# = = M with M =(2 p
bB): (64)
9

[4] M. Messel and D. F. Crawford, Electron-Photon Shower Distribution Function Tables for Lead
Copper and Air Absorbers (Pergamon, Oxford, 1970).
[5] W. R. Nelson, H. Hirayama, and D. W. O. Rogers, \The EGS4 Code System," SLAC-265,
Stanford Linear Accelerator Center (Dec. 1985).
[6] D. Heck, J. Knapp, J. N. Capdevielle, G. Shatz, and T. Thouw, Forschungszentrum Karlsruhe
Report FZKA6019(1998).
[7] G. Moliere, Z. Naturforsch. 10a(1955)177.
[8] K. Kamata and J. Nishimura, Prog. Theor. Phys. Suppl. 6(1958)93.
[9] J. Nishimura, in Handbuch der Physik, Band 46, edited by S. Flugge (Springer, Berlin, 1967),
Teil 2, p.1.
[10] T. Nakatsuka, "<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> 26th <strong>International</strong> Cosmic Ray Conference," HE2.5.36, Salt
Lake City, 1999.
[11] B. Rossi and K. Greisen, Rev. Mod. Phys. 27 (1941)240.
[12] C. N. Yang, Phys. Rev. 84(1951)599.
[13] T. Nakatsuka, Phys. Rev. D35(1987)210.
[14] T. Nakatsuka, Phys. Rev. D35(1987)210 D58(1998)056002.
[15] T. Nakatsuka, \<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> Seventh EGS4 User's Meeting in Japan," KEK <strong>Proceedings</strong>
98-7, 13(1998).
[16] T. Nakatsuka, \<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> Eighth EGS4 User's Meeting in Japan," KEK <strong>Proceedings</strong>
99-15, 12(1999).
[17] T. Nakatsuka, \<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> 26th <strong>International</strong> Cosmic Ray Conference," HE2.5.25, Salt
Lake City, 1999.
[18] T. Nakatsuka, Submitted to \<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> 8th Asia Paci c Physics Conference," BH4,
Taipei, 2000.
[19] A. F. Bielajew and D. W. O. Rogers, Nucl. Instrum. Methods Phys. Res. B18(1987)165.
[20] B. Rossi, High Energy Particles (Prentice-Hall, Englewood Cli s, NJ, 1952).
[21] O. I. Dovzhenko and A. A. Pomanskii, Soviet Physics (JETP) 35(1964)187.
[22] W. T. Scott, Rev. Mod. Phys. 35(1963)231.
[23] Y. S. Tsai, Rev. Mod. Phys. 46(1974)815.
[24] Particle Data Group, Eur. Phys. J. C3(1998)1.
[25] S. A. Goudsmit and J. L. Saunderson, Phys. Rev. 57(1940)24 and 58(1940)36.
[26] H. Snyder and W. T. Scott, Phys. Rev. 76(1949)220.
[27] Combination <strong>of</strong> coe cients a and c is not unique. We can put a = 0 or c = 1 without loss <strong>of</strong>
generality, <strong>the</strong>n <strong>the</strong> o<strong>the</strong>r is determined uniquely.
[28] Y. Yamashita et. al., Nucl. Instrum. Methods Phys. Res. A374(1996)245.
10

θ 2 × f(θ)
θ 2 × f(θ)
10 0
10 –1
10 –2
10 –3
10 –1
10 –2
10 –2 10 –3
(a) fixed energy
(b) with ionization
10 –1
E 0/ε = 10 5 Ωe –Ω
in WATER
10 0
DEFLECTION ANGLE (rad)
Figure 1: Angular distributions multiplied by 2 at
depth t=(E0=") <strong>of</strong>0.1, 0.3, 0.5, 0.7, and 0.9 from left
to right. Dot lines indicate accumulations <strong>of</strong> single
scatterings.
SCALE FACTOR ν
1
0.5
10 1
mc
0
0 0.5 1
2 /E0 = 1/10
mc 2 /E0 = 1/20
mc 2 /E0 = 1/50
mc 2 /E0 = 0
FRACTIONAL THICKNESS
Figure 2: Variation <strong>of</strong> <strong>the</strong> scale factor against t. Abscissa
means t=(E0="). The curves correspond to incident
energies E0=(mc 2 ) <strong>of</strong> 10, 20, 50, and 1.
EXPANSION PARAMETER B
10
5
0
10 0
mc 2 /E 0 = 1/10
mc 2 /E 0 = 1/20
mc 2 /E 0 = 1/50
mc 2 = 0
mc 2 = 0, Fixed E
10 2
10 4
TRAVERSED THICKNESS t/(Ωe –Ω )
Figure 3: Depth-variation <strong>of</strong> B for various incident energies,
E0=" <strong>of</strong> 10, 10 2 ,10 3 , and 10 4 in unit <strong>of</strong> e ; ,
from left to right. Thin line indicates traditional B for
xed energy.
11
UNIT OF MOLIERE ANGLE θ M/(Ke –Ω/2 /E 0)
10 3
10 2
10 1
10 0 10 0
mc 2 /E 0 = 1/10
mc 2 /E 0 = 1/20
mc 2 /E 0 = 1/50
mc 2 = 0
mc 2 = 0, Fixed E
10 2
10 4
TRAVERSED THICKNESS t/(Ωe –Ω )
Figure 4: Depth-variation <strong>of</strong> M for various incident
energies, E0=" <strong>of</strong> 10, 10 2 ,10 3 , and 10 4 in unit <strong>of</strong> e ; ,
from left to right. Thin line indicates traditional M for
xed energy.
EXPANSION PARAMETER B
10
5
0
10 0
Emulsion
mc 2 /E 0 = 1/20
exact results
approx. results
10 2
10 4
TRAVERSED THICKNESS t/(Ωe –Ω )
Figure 5: Comparison <strong>of</strong> B for mixed or compound
substance, between exact results and approximated
ones. Four curves correspond to E0=" <strong>of</strong> 10, 10 2 ,10 3 ,
and 10 4 in unit <strong>of</strong> e ; , from left to right.
UNIT OF MOLIERE ANGLE θ M/(Ke –Ω/2 /E 0)
10 3
10 2
10 1
10 0 10 0
Emulsion
mc 2 /E 0 = 1/20
exact results
approx. results
10 2
10 4
TRAVERSED THICKNESS t/(Ωe –Ω )
Figure 6: Comparison <strong>of</strong> M for mixed or compound
substance, between exact results and approximated
ones. Four curves correspond to E0=" <strong>of</strong> 10, 10 2 ,10 3 ,
and 10 4 in unit <strong>of</strong> e ; , from left to right.

List <strong>of</strong> Participants
(excluded Participants <strong>of</strong> Short EGS4 Course only)
Lars-Eric Adam
University <strong>of</strong>Pennsylvania
110 Donner Bldg, 3400 Spruce Street
Philadelphia, PA 19104, USA
Email:lars@rad.upenn.edu
Noha Aly
Dept. <strong>of</strong> Quantum Engineering and
Systems Science School <strong>of</strong> Engineering
The University <strong>of</strong>Tokyo
7-3-1 Hongo, Bunkyo-Ku
Tokyo, JAPAN
Email:nohapr<strong>of</strong>@hotmail.com
Hidetoshi Arai
Ishikawajima-Harima
Heavy Industries Co.,Ltd.
1, Shin-Nakahara-Cho, Isogo-Ku,
Yokohama, 235-8501 JAPAN
Email:hideyuki arai@ihi.co.jp
Eiji Ariga
Nagoya Daini Red Cross Hospital
2-9 Myouken-cho, Shouwa-ku.
Nagoya, JAPAN
Email:ariga@nagoya2.jrc.or.jp
Kazumi Asamura
Department <strong>of</strong>Physics,
Yamagata University
1-4-12 Kojirakawa, Yamagata
990-8560 Japan
Email:asamura@kspirit.kj.yamagata-u.ac.jp
Yoshihiro Asano
Synchrotron Radiation Research Center
Japan Atomic Energy Research Institute
SPring-8, Mikatuki-cho, Hyogo-ken
679-5143 Japan
Email:asano@spring8.or.jp
1
A. F. Bielajew
Department <strong>of</strong> Nuclear Engineering and
Radiological Sciences
The University <strong>of</strong>Michigan
Cooley Building (North Campus)
2355 Bonisteel Boulevard
Ann Arbor, Michigan 48109-4540, USA
Email:bielajew@engin.umich.edu
Syuichi Ban
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305 Japan
Email: s.ban@kek.jp
Kotaro Bessyo
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305 Japan
Email: kotaro.bessyo@kek.jp
Hiroyuki Date
Hokkiadou University
Kitaku N12 W5, Sapporo,
060-0812 JAPAN
date@cme.hokudai.ac.jp
Cheung Yiu Chung Joel
Gamma Knife Centre (HK)
Canossa Hospital
No.1 Old Peak Road, Hong Kong
Email:joel@gammaknife.com.hk
William L. Dunn
Quantum Research Services, Inc.
5410-W Apex Highway, Durham,
NC 27713-9434, USA
Email:wldunn@quantumres.com

Zhigao Fang
The Graduate University
for Advanced Studies
1-1, Oho, Tsukuba, Ibaraki
305-0801, Japan
Email:fang@post.kek.jp
Tatsuya Fujisaki
Ibaraki Prefectural University
<strong>of</strong> Health Sciences
4669-2 Ami-Machi ,Inashiki-Gun,
Ibaraki, Japan
Email:hujisaki@ipu.ac.jp
Jun Funabiki
Mitusbishi Research Institute Inc.
3-6 Ohtemachi 2 Chome, Chiyoda-ku,
Tokyo, 100-8141 Japan
Email:funabiki@mri.co.jp
Yoshiko Harima
CRC Reserach Institute, Inc.
2-7-5, Minamisuna, Koto-ku
Tokyo 136, Japan
Email:j90204@sinet.ad.jp
Mitsuyasu Hashimoto
<strong>International</strong> University
<strong>of</strong> Health and Welfare
2600-1 Kitakanemura, Otawara City
Tochigi, 324-8501 Japan
Email:hasimoto@iuhw.ac.jp
Kouji Hashimoto
Nagoya University
Furo-cho, Chikusa-ku, Nagoya
464-8603 Japan
Email:hashimoto@avocet.nucl.nagoya-u.ac.jp
Kensuke Hayashi
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-ku,
Nagoya, 461-8673 Japan
Sachiko Hibino
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-ku,
Nagoya, 461-8673 Japan
2
Shun-ichi Himeno
Morisaki Attorny O ce
2-1-4-502, Nagayama, Tama-city,Tokyo
206-0025 Japan
Email:himenosi@guitar.ocn.ne.jp
Hideo Hirayama
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: hideo.hirayama@kek.jp
Masahiro Hirota
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-ku,
Nagoya, 461-8673 Japan
Mituhiko Honma
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-ku,
Nagoya, 461-8673 Japan
Kenichi Hozumi
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: kenichi.hozumi@kek.jp
Tetsuo Iguchi
Nagoya University
Furo-cho, Chikusa-ku, Nagoya
464-8603 JAPAN
Email:t-iguchi@nucl.nagoya-u.ac.jp
Kazuhiko Iijima
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: kazuhiko.iijima@kek.jp

Kotaro Imagawa
School <strong>of</strong> Allied Health Sciences,
Faculty <strong>of</strong> Medicine,
Osaka University
1-7 Yamadaoka, Suita, Osaka
565-0871 Japan
Email:kimagawa@sahs.med.osaka-u.ac.jp
Kunihiro Ishii
Ohyo Koken Kogyo Co., Ltd.
Measuring Instruments Dep.
1642-26, Kumagawa, Fussa-Shi
Tokyo, 197-0003 Japan
Email:oken@inv.co.jp
Masaki Ishiduka
Institute for Cosmic Ray Reasearch
room234,5-1-5, Kashiwa-no-ha, Kashiwa
Chiba, 277-8582 Japan
Email:ishi@suketto.icrr.u-tokyo.ac.jp
Hidesuke Itadzu
Nagoya University
Furo-cho, Chikusa-ku, Nagoya
464-8603 JAPAN
Noriyuki Itakura
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-ku
Nagoya, 461-8673 Japan
Taku Itoh
Kyoto University, Nuclear Engineering
Yoshidahonmachi, Sakyouku, Kyoto
Japan
Email:itoh@ras.cc
Wang Jeng-Ning
Institute <strong>of</strong> Nuclear Energy Research
1000, Wenhua Rd., Chiaan Village, Lungtan,
Taiwan, R.O.C.
Email:jnwang@iner.gov.tw
Gyo Kajiwara
Shimizu Corporation
1-2-3 Shibaura Minatoku, Tokyo, Japan
Email:gkajiwara@mx4.ttcn.ne.jp
3
Yukio Kanda
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: yukio.kanda@kek.jp
Ikuo Kanno
Quantum Science and Engineering Center
Kyoto University
Sakyo, Kyoto 606-8501, Japan
Email:kanno@qsec.kyoto-u.ac.jp
Jyunnya Kato
College <strong>of</strong> Engineering
Department <strong>of</strong> Electronic Infomatics
Hosei University
3-7-2, Kajino-cho, Koganei-City
Tokyo, 184-8584 Japan
Email:junya@ogw.ei.hosei.ac.jp
Hideo Kimura
Department <strong>of</strong> Nuclear Engineering
Kyoto University
Yoshida, Sakyo
Kyoto, 606-8501 Japan
Email:hkimura@nucleng.kyoto-u.ac.jp
Sakae Kinase
Japan Atomic Energy Research Institute
Tokai-mura, Naka-gun, Ibaraki-ken
319-1195 Japan
Email:skinase@jrr3fep2.tokai.jaeri.go.jp
Shunji Kitamoto
Osaka University
1-1, Machikaneyama, Toyonaka
Osaka, 560-0043 Japan
Email:kitamoto@ess.sci.osaka-u.ac.jp
Kenjiro Kondo
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: kenjiro.kondo@kek.jp

Kichiro Koshida
Department <strong>of</strong> Radiological Technology,
School <strong>of</strong> Health Sciences
Faculty <strong>of</strong> Medicine, KANAZAWA University
5-11-80 Kodatsuno, Kanazawa
920-0942 Japan
Email:kosida@kenroku.kanazawa-u.ac.jp
Syuuji Koyama
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-Ku
Nagoya, 461-8673 Japan
Katuhisa Kudo
Electrotechnical Laboratory (ETL)
1-1-4 Umezono, Tsukuba-shi, Ibaraki
305-8568 Japan.
Email: kkudo@etl.go.jp
Tadahiro Kurosawa
Electrotechnical laboratory
1-1-4, Umezono, Tsukuba, Ibaraki
305-8568 Japan
Email:kurosawa@etl.go.jp
James C. Liu
Stanford Linear Accelerator Center
MS 48, P.O. BOX 4349,
Stanford, CA 94309, USA.
Email: james@slac.stanford.edu
Patrick Lui
Stanford Linear Accelerator Center
Stanford University, P.O. Box 4349,
MS/02, Stanford, CA 94309, USA
Email:plui@slac.stanford.edu
Ernesto Mainegra Hing
Center <strong>of</strong> Applied Studies
for Nuclear Development
calle 30 #502 e/ 5ta Ave. y 7ma Ave.,
Playa, Ciudad Habana, Cuba
Email:mainegra@ceaden.edu.cu
Takuya Maeda
Department <strong>of</strong>Physics,
Yamagata University
1-4-12 Kojirakawa, Yamagata
990-8560 Japan
Email:maeda@kspirit.kj.yamagata-u.ac.jp
4
Koujiro Minemoto
Visible Information Center, Inc.
440 Muramatsu Tokai-mura Naka-gun
Ibaraki, 319-1112 Japan
Email:minemoto@vic.co.jp
Taichi Miura
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: taichi.miura@kek.jp
Satoshi Miyajima
School <strong>of</strong> Allied Health Sciences,
Faculty <strong>of</strong> Medicine,
Osaka University
1-7 Yamadaoka, Suita, Osaka
565-0871 Japan
Email:satoshi@sahs.med.osaka-u.ac.jp
Aiko Nagamatsu
National Space Development Agency
<strong>of</strong> Japan
2-1-1, Sengen, Tsukuba, Ibaragi
305-8505 Japan
Email:Nagamatsu.Aiko@nasda.go.jp
Tsutomu Nagayoshi
Tokyo Institute <strong>of</strong> Technology
2-12-1 O-okayama Meguro Tokyo Japan
nagayosi@hp.phys.titech.ac.jp
Tomoshige Nagase
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-ku
Nagoya, 461-8673 Japan
Hajime Nakamura
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: hajime.nakamura@kek.jp

Takashi Nakamura
Cyclotron and Radioisotope Center,
Tohoku University,
Aoba, Aramaki, Aoba-ku
Sendai, 980-8578 Japan
Email:nakamura@risun1.cyric.tohoku.ac.jp
Yuzuru Nakamura
Dept. <strong>of</strong> Therapeutic Radiology
Saitama Cancer Center
818, Komuro, Ina-machi, Kita-Adachi-gun
Saitama, 362-0806 Japan
Email:ynakamura@cancer-c.pref.saitama.jp
Noriaki Nakao
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: noriaki.nakao@kek.jp
Takao Nakatsuka
Okayama Shoka University
Tsushima-Kyomachi, Okayama
700-8601 JAPAN
Email:nakatuka@osu.ac.jp
Yoshihito Namito
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801, Japan
Email:yoshihito.namito@kek.jp
Nobuteru Nariyama
Ship Research Institute
6-38-1 Shinkawa, Mitaka
Tokyo, 181-0004 Japan
Email:nari@srimot.go.jp
Water Ralph Nelson
Stanford Linear Accelerator Center (SLAC)
MS 48, P.O. BOX 4349,
Stanford, CA 94309, USA.
Email: wrnrp@SLAC.Stanford.EDU
5
Sakiko Nishio
Department <strong>of</strong> Radiological Technology,
School <strong>of</strong> Health Sciences
Faculty <strong>of</strong> Medicine, Kanazawa University
5-11-80 Kodatsuno, Kanazawa
920-0942 Japan
Email:
Shengli Niu
Northwest Institution <strong>of</strong> Nuclear Technology
P.O. BOX 69-15, XI'AN,
SHAANXI 710024 CHINA
Email:ezhou@nint.ac.cn
Ryo Nouchi
Quantum Science and Engineering Center
Kyoto University
Yoshida, Sakyo, Kyoto, 606-8501 Japan
Email:nouchi@nucleng.kyoto-u.ac.jp
Masaharu Numajiri
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: masaharu.numajiri@kek.jp
Hiroyuki Ogi
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-Ku
Nagoya, 461-8673 Japan
Jin Ohta
Hosei University
College <strong>of</strong> Engineering
Department <strong>of</strong> Electronic Infomatics
Hosei University
3-7-2, Kajino-cho, Koganei-City
Tokyo, 184-8584 Japan
Email:ohta@ogw.ei.hosei.ac.jp
Souta OKi
Department <strong>of</strong> Material
Processing Engineering
Graduate School <strong>of</strong> Engineering
Nagoya University
Furo-cho, Chikusa-ku, Nagoya
464-8603 Japan
Email:oki@nsr.numse.nagoya-u.ac.jp

Yuichi Oki
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: yuichi.oki@kek.jp
Masahiro Onoguchi
School <strong>of</strong> Health Sciences,
Faculty <strong>of</strong> Medicine,
Kanazawa University
5-11-80 Kodatsuno, Kanazawa
920-0942 Japan
Email:onoguchi@kenroku.kanazawa-u.ac.jp
Motoari Oota
Osaka University
1-1, Machikaneyama, Toyonaka,
Osaka 560-0043 Japan
A. H. D. Rasolonjatovo
Tohoku University
Cyclotron and Radioisotope Center
Aoba, Aramaki, Aoba-ku, Sendai 980-8578 Japan
Email:danielle@cyric.tohoku.ac.jp
Sheu Ren-Dih
National Tsing-Hua University
Taiwan, R.O.C
101, Section 2, Kuang Fu Road ,Hsinchu,
Taiwan 300, R.O.C
Email:d867107@oz.nthu.edu.tw
Hidetoshi Saitoh
Tokyo Metropolitan University
<strong>of</strong> Health Sciences
7-2-10 Higashi-Ogu, Arakawa-Ku,
Tokyo, 116-8551 Japan
Email:saitoh@metro-hs.ac.jp
Ryoko Sakai
Medical Front
Asahigaoka 2646-1-2-807 Hanamigawa-ku
Chiba-city Chiba, Japan
Email:ryoko-s@cba.att.ne.jp
6
Toshiya Sanami
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: toshiya.sanami@kek.jp
Shin'ichi Sasaki
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: shinichi.sasaki@kek.jp
Kaoru Sato
Department <strong>of</strong> Health Physics
Tokai Research Establishment
Japan Atomic Energy Research Institute
2-4 Shirakata-Shirane, Tokai-mura
Naka-gun, Ibaraki-ken 319-1195 Japan
Email:ksato@popsvr.tokai.jaeri.go.jp
Kazuo Sato
Atomic Energy Research Institute
Nihon University
7-24-1 Narashinodai, Funabashi-shi
Chiba-ken, 274-8501 Japan
Email:sato@acc.phys.cst.nihon-u.ac.jp
Osamu Sato
Mitusbishi Research Institute Inc.
3-6 Ohtemachi 2 Chome, Chiyoda-ku
Tokyo, 100-8141 Japan
Email:sato@mri.co.jp
Tetsuya Shimoyama
Fukui University
Bunkyo 3-9-1, Fukui, 910-8507, Japan
Email:simoyama@midori.apphy.fukui-u.ac.jp
Tokushi Shibata
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: tokushi.shibata@kek.jp

Kozo Shimizu
Department <strong>of</strong> Radiological Technology,
School <strong>of</strong> Health Sciences
Faculty <strong>of</strong> Medicine, Kanazawa University
5-11-80 Kodatsuno, Kanazawa
920-0942 Japan
Email:shimizu@mhs.mp.kanazawa-u.ac.jp
Chandra Roy Sprakash
Cyclotron and Radioisotope Center,
Tohoku University,
Aoba, Aramaki, Aoba-ku,
Sendai, 980-8578 Japan
Hiroyuki Suzuki
Cyclotron and Radioisotope Center,
Tohoku University,
Aoba, Aramaki, Aoba-ku,
Sendai, 980-8578 Japan
Email:daishin@cyric.tohoku.ac.jp
Takenori Suzuki
High Energy Accelerator
Research Organization(KEK)
1-1 Oho, Tsukuba Ibaraki
305-0801 Japan
Email:takenori.suzuki@kek.jp
Toshiji Suzuki
Department <strong>of</strong>Physics,
Yamagata University
1-4-12 Kojirakawa, Yamagata
990-8560 Japan
Email:suzuki@kspirit.kj.yamagata-u.ac.jp
Katsuyoshi Tabushi
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-Ku,
Nagoya, 461-8673 Japan
Email:tabushi@met.nagoya-u.ac.jp
JunIchiro Tada
SPring-8, JASRI
Koto 1-1-1, Mikazuki-cho, Sayo-gun,
Hyogo, 679-5198, Japan
Email:tada@spring8.or.jp
7
Shunji Takagi
Mitusbishi Research Institute Inc.
3-6 Ohtemachi 2 Chome, Chiyoda-ku,
Tokyo, 100-8141 Japan
Email:takagi@mri.co.jp
Shin-ichi Takahara
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: shin-ichi.takahara@kek.jp
Fumiaki Takahashi
Department <strong>of</strong> Health Physics,
Tokai Establishment,
Japan Atomic Energy Research Institute
(JAERI)
Tokai-Mura, Naka-gun, Ibaraki,
319-1195 Japan
Email:taka@frs.tokai.jaeri.go.jp
Yoshifumi Takashima
Institute for Molecular Science
Okazaki, 444-8585 Japan
Email:takasima@ims.ac.jp
Shigeharu Takebayashi
Department <strong>of</strong> Radiological Technology,
School <strong>of</strong> Health Sciences
Faculty <strong>of</strong> Medicine, Kanazawa University
5-11-80 Kodatsuno, Kanazawa
920-0942 Japan
Hayanori Takei
Japan Nuclear Cycle Development Institute
(JNC)
4002, Narita-cho, O-Arai-Machi,
Ibaraki-Ken, 311-1393 Japan
Email:takei@oec.jnc.go.jp
Shingo Taniguchi
Japan Synchrotron Radiation
Research Institute (SPring-8)
Koto 1-1-1, Mikazuki-cho, Sayo-gun,
Hyogo, 679-5198 Japan
Email:shingo@spring8.or.jp

Hiroko Tawara
KEK, High Energy Accelerator
Reserach Organization
1-1 Oho, Tsukuba-shi
Ibaraki, 305-0801 Japan
Email: hiroko.tawara@kek.jp
Takako Tezuka
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-Ku,
Nagoya, 461-8673 Japan
Tatsuo Torii
Monju Construction O ce, JNC
2-1 Shiraki, Tsuruga, Fukui-ken
919-1279 Japan
Email:torii@t-hq.jnc.go.jp
Shuichi Tsuda
Japan Atomic Energy Research Institute
(JAERI)
2-4, Sirakata Sirane, Tokai-mura,
Naka-gun, Ibaraki, 319-1195 Japan
Email:tsuda@frs.tokai.jaeri.go.jp
Masahiro Tsutsumi
Department <strong>of</strong> Health Physics
Japan Atomic Energy Research Institute
2-4, Sirakata Sirane, Tokai-mura,
Naka-gun, Ibaraki, 319-1195 Japan
Email:tsutsumi@sakura.tokai.jaeri.go.jp
Takeshi Uchibori
ALOKA Co., Ltd.
22-1, Mure, 6-chome, Mitaka-city, Tokyo
181-8622 Japan
Email:uchi3401@am.aloka.co.jp
Kohtaro Ueki
Ship Research Institute
6-38-1 Shinkawa, Mitaka,
Tokyo, 181-0004 Japan
Email:ueki@srimot.go.jp
8
Yasuhiro Yamaguchi
Japan Atomic Energy Research Institute
2-4 Shirakata, Tokai, Ibaraki,
319-1195 Japan
Email:yasu@frs.tokai.jaeri.go.jp
Tomohiro Yamashita
Nagoya University
School <strong>of</strong> Health Sciences
1-20 Daikominami-1-chome, Higashi-Ku,
Nagoya, 461-8673 Japan
Kenichi Yano
ALOKA Co., Ltd.
22-1, Mure, 6-chome, Mitaka-city, Tokyo
181-8622 Japan
Email:yano3149@am.aloka.co.jp
Takashi Yokoi
Department <strong>of</strong> Medical System,
Shimadzu Corporation
1 Nishinokyo-Kuwabara-Cho, Nakagyo-ku
Kyoto, Japan
Email:yokoi@shimadzu.co.jp
Koichi Yokoyama
Ibaraki Prefectural University
<strong>of</strong> Health Sciences
Ami, Ami-machi, Ibaraki-ken
300-03 JAPAN
Email:yokoyamak@ipu.ac.jp
Gwang-Ho Yoo
Dae-Bul University
Sam-Ho Myun, Young-Arm kun,
Chonnam, S.Korea
Email:ghyoo@mail.daebul.ac.kr
Runsheng Yu
Institute <strong>of</strong> High Energy Physics,
Chinese Academy <strong>of</strong> Sciences
P. O.Box 2732, Beijing 100080, China
Email:yursh@ihepa.ac.cn