THE EGS5 CODE SYSTEM

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Photoelectron angular distribution In standard EGS4, a photoelectron, the electron produced when a photon is absorbed by an atom by the photoelectric effect, is set in motion in the same direction as the incident photon. In order to try to refine the comparison with low-energy experiments using thermoluminescent dosimeters, Bielajew and Rogers[30] employed the theory of Sauter[145] and made it an option for EGS4. Although Sauter’s theory is relativistic (v ≈ c), it was adopted universally, even though Fischer’s non-relativistic theory[58] was derived for use in the (v
high Z materials. Del Guerra et al.[51] developed a K- and L-edge sampling method for compounds in EGS4, and Conti et al.[47] used this scheme in investigating the response of HgI 2 and CdTe photon detectors in the diagnostic range. In 2000, Hirayama and Namito published a general treatment of photoelectric-related phenomena for compounds or mixtures in EGS4[72]. The energy dependent branching ratio of each sub-shell (L1-, L2- and L3-) was introduced in this improvement by fitting to a quadratic function in log-log from data provided for limited materials (Ag, Pb and U). For compounds and mixtures, the ratio of photoelectric effect cross section of each element to total photoelectric cross section was calculated in PEGS4 and output as piece-wise linear fits. In addition to K- and L- x-rays, K- and L- Auger electrons could be treated. Very recently, Hirayama and Namito published an improvement of their previous generalized treatment [73]. In this work, K-, L1-, L2-, L3- and other sub-shell photoelectric cross sections taken from the PHOTX data base (see below) are fitted to cubic functions in log-log form and the fitted coefficients and other associated data are initialized in a BLOCK DATA subprogram of EGS. It thus becomes possible to calculate the branching ratios for each element of compounds and mixtures inside EGS, negating the need to use approximate piece-wise linear-fitted data from PEGS. This new method is included in the default version of <strong>EGS5</strong>. Improved photon cross sections The standard EGS4 photon cross section data was based on the library compiled by Storm and Israel[167]. Sakamoto[143] updated EGS4 to use the more recent photon cross sections of the PHOTX library[131]. As discussed by Sakamoto, the principal differences between the Storm and Israel data and that of PHOTX lie in the low energy photoelectric cross sections. It should be noted that although the attenuation coefficients in the two photon libraries are different, the practical effect in many applications, such as the calculation of exposure buildup factors, is small. PHOTX is the default library for <strong>EGS5</strong>. Binding effects in Compton interactions In its treatment of Compton scattering, standard EGS4 assumed the electrons in the atomic clouds of the target atoms to be “free,” ignoring the binding of the atomic electrons to the nucleus. This is a good approximation for photon energies down to 10’s of keV for most materials. The lower bound where this approximation works reasonably well is defined by the K-shell energy, although the effects can have significant influence above it, particularly for the low-Z elements. Namito and Hirayama included binding effects in the Compton interaction model in EGS4 taking into account the change in the total Compton cross section as well as the angular distribution of the emergent particles[119]. The bound Compton modeling was shown to have noticeable effect in lowenergy gamma-ray buildup factors in various materials at low energy (40–200 keV) with the effect being stronger at the lower energies studied[76]. Explicit treatment of binding effects in Compton 17
Page 1 and 2: THE EGS5 CODE SYSTEM 1 Hideo Hiraya
Page 3 and 4: Contents 1 INTRODUCTION 1 1.1 Inten
Page 5 and 6: 2.15.6 Electron Step-Size Selection
Page 7 and 8: B.4.9 Output of Results (Step 9) .
Page 9 and 10: List of Figures 2.1 Program flow an
Page 11 and 12: C.4 Subprogram relationships in PEG
Page 13 and 14: B.5 Variable descriptions for COMMO
Page 15 and 16: PREFACE In the nineteen years since
Page 17 and 18: Chapter 1 INTRODUCTION 1.1 Intent o
Page 19 and 20: “shower book”. For various reas
Page 21 and 22: 1.2.2 EGS1 About this time Nelson b
Page 23 and 24: MSCAT. These versions of EGS, PEGS,
Page 25 and 26: ten for energies less than 100 MeV
Page 27 and 28: - Molière multiple scattering (i.e
Page 29 and 30: EGS5. The primary advantages of thi
Page 31: ICRU37-compliant using the NIST dat
Page 35 and 36: One of these six cross sections is
Page 37 and 38: at low energies. The latter, couple
Page 39 and 40: If E 1 and E 2 are expressions invo
Page 41 and 42: The result of this algorithm is tha
Page 43 and 44: 2.4 Particle Transport Simulation T
Page 45 and 46: from appropriate distribution funct
Page 47 and 48: parameters which may be needed. The
Page 49 and 50: arrived at their values in a very m
Page 51 and 52: Math FORTRAN Program Table 2.1 (con
Page 53 and 54: Figure 2.2: Feynman diagrams for br
Page 55 and 56: defined by δ ij = 1 if i = j, 0 ot
Page 57 and 58: Davies, Bethe and Maximon[49] (e.g.
Page 59 and 60: cross section given in Equation 2.4
Page 61 and 62: and use this as the variable to be
Page 63 and 64: we have Now define δ ′ = ∆ C
Page 65 and 66: This agrees with formula (10) of Bu
Page 67 and 68: That is, using Equations 2.122 and
Page 69 and 70: d˘Σ P air, Run−time dE = [ 2 3
Page 71 and 72: Angular distribution formulas The f
Page 73 and 74: at either x = 0, x = (πE 0 ) 2 (i.
Page 75 and 76: The following table, derived from t
Page 77 and 78: Figure 2.3: Feynman diagrams for tw
Page 79 and 80: where X 0 = radiation length (cm),
Page 81 and 82: where α ′ 1 = α ′ 2 = k 0 ′
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+ 1 E 2 ′ − 1 E 1 ′ − C 2 l
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PEGS functions BHABDM, BHABRM, and
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To find the limits of E, we first c
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Figure 2.5: Feynman diagram for sin
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Ī adj = average adjusted mean ioni
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Table 2.2 (cont.) Z Symbol Atomic D
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Table 2.3 (cont.) LABEL a m s x 0 x
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(c) If 10.5 ≤ −C < 11.0 then x
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obtain the real scattering angle. E
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ρ = material mass density (g/cm 3
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Hence, so that ln [1.13 + 3.76(αZ
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g 3 (θ) = θ4 ( ) λf (0) (θ) + f
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Actually, b = 0 does not correspond
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Assume that an electron starts off
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At small path lengths t, a very lar
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x Final Direction φ Θ ∆x t Init
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shown that this version of the rand
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and as we noted earlier, they are d
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Final Direction x Energy Hinges φ
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Transport Steps, ∆ E = E x ESTEPE
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tranport step 1 DEINITIAL1 DERESID1
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= ∆E ( ∣ ∣∣∣ dE −1 ∣
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Since the CSDA range is uniquely de
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short steps accurate, but slow step
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Table 2.4: Materials used in refere
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Average Lateral Displacement (cm) 0
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100 MeV Electrons 0.01 0.001 Li C L
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actions involving photons with ener
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Cu 40 keV Counts (/keV/sr/source) 1
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Table 2.6: Data sources for general
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2.16.2 Photoelectron Angular Distri
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where r 0 is the classical electron
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second term on the right-hand side
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Z θ k Y O φ e 0 X k 0 Figure 2.23
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Note the similarities and differenc
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X Z ω k 0 O e 0 Y Figure 2.25: Dir
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W = Atomic, molecular and mixture w
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In order to use EGS5 to answer the
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write(6,100) 100 FORMAT(’ PEGS5-c
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! plate is 1 mm thick !------------
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implicit none include ’include/eg
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0.989 MeV kinetic energy Brem photo
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! locally (in fact EDEP = particles
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inmax=max(binmax,ebin(j)) end do wr
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0.40 0.0058 * 0.60 0.0054 * 0.80 0.
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!----------------------------------
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endif if(loop.lt.3) then write(6,12
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180 FORMAT(/’ Knock-on electrons
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common/score/escore(3), iscore(3) r
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Brem photons can be created and any
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in any combination of 31 well speci
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end do end do ! nmed and dunit defa
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! ------------------------------ cl
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if (iarg.eq.17) then ! A Compton sc
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! the general purpose geometry subr
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eturn end !------------------------
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open(UNIT= 6,FILE=’egs5job.out’
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write(6,130) 130 format(/’ Start
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icol= * int(dlog10(ebin(j)*10000.0/
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0.0300 0.0000* 0.0320 0.0001* 0.034
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0.0780 0.0014 * 0.0800 0.0012 * 0.0
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The main purpose of this section, h
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4.1.3 Leading Particle Biasing The
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• Sum the weighted energy deposit
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4 z 6 Vac 11 5 Pb 6 5 Air 7 4 9 10
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Figure 4.3: UCBEND simulation at 3.
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necessary geometry input. The follo
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Appendix A EGS5 FLOW DIAGRAMS Hideo
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subroutine annih Version 051219-143
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¡ eq 1 anormr = 1./sqrt(anorm2) si
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1 br = max(br,0.D0) ekse2 = br*ekin
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1 2 3 br = br*p esg = eie*br yes es
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¤ ne ¤ ne subroutine collis (lele
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¦ ne ¦ ne call ausgab(iarg) 6 iq(
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subroutine compt Version 051219-143
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3 4 5 6 icprof(medium) .eq. 3 no ye
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subroutine counters_out Version 051
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1 2 3 4 5 6 7 no ii .ne. jj yes no
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© ne 1 2 3 neispl = (2*neispl + 1)
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subroutine electr(ircode) ielectr =
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7 8 9 10 11 12 13 detot = e(np)-ecu
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2324 25 26 27 28 29 30 ustep .gt. d
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4142 43 44 45 46 47 48 49 ecut(irne
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5859 60 61 62 63 64 tmscat .eq. 0.0
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73 74 75 76 no edep .lt. e(np) yes
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subroutine hardx (charge,kEnergy,ke
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1 2 3 4 5 iz = izz iz .eq. 0 no xsi
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13 14 15 16 17 sint .ne. 0. yes rde
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19 im=1 im=im+1 im >nmed no yes no
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22 23 write(kmpo,1610) read(kmpi,12
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26 27 28 iprofm(im) .ne. 1 no yes w
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30 31 32 33 34 esig0(i,im) = esig0(
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36 37 38 no iedgfl(ii).ne.0 .or. ia
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no kaug .eq. 6 call lshell(3) kaug.
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subroutine kxray Version 051219-143
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1 2 3 dfl3aug(5,iz) .eq. 0. no naug
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1 2 3 4 rnnow .le. omegal2(iz) + f2
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1 2 dflx3(6,iz) .eq. 0. no nxray=nx
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1 impacr(ir(np)).eq.1 .and. iedgfl(
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1 2 fject = (ktot - k1grd(iprt,ik1)
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5 6 7 8 9 thr = 1./eta "Central cor
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1 2 3 delta = delcm(medium)*del "Re
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8 9 10 11 12 galpha .ge. 0.0 yes no
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subroutine photo Version 051219-143
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4 5 6 7 8 rnnow .le. pbran(i) no ye
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12 13 14 beta = sqrt((eelec - RM)*(
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subroutine photon Version 051219-14
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6 7 8 9 10 idisc .gt. 0 yes no edep
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17 18 19 20 21 iausfl(iarg+1) ne 0
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27 28 iausfl(iarg+1) ne 0 no ircod
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subroutine rk1 Version 060313-0945
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4 5 6 j=1 j=j+1 j>neke-1 no yes j .
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18 19 20 21 22 23 elkeold = elke k1
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1 2 "end of file; go to 13" read(17
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4 5 "go to 30" no abs(k1mine-k1grd(
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7 8 read(17,'(72a1)') buffer read(1
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subroutine shower (iqi,ei,xi,yi,zi,
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subroutine uphi(ientry,lvl) Version
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subroutine randomset(rndum) Version
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subroutine rluxinit Version 051219-
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1 i=1 i=i+1 i>24 no yes seeds(i) =
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subroutine rluxin Version 051219-14
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Appendix B EGS5 USER MANUAL Hideo H
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Table B.1: Variable descriptions fo
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Page 333 and 334:
Page 335 and 336:
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Table B.12: Variable descriptions f
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Optional parameter modifications Th
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the call to PEGS5 may be skipped if
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egions. Execution of EGS5 is termin
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of the transport in the walls of el
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call rluxinit after specifying LUXL
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END OF FILE ON UNIT 12 PROGRAM STOP
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do i=1,ncases uf(1)=ufi vf(1)=vfi w
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crossed, then USTEP should be set t
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subroutine howfar implicit none inc
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Table B.18: IARG values program sta
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As an example of how to write an AU
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!**********************************
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nreg=3 do i=2,nreg ecut(i)=100.0 pc
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nlines=0 nwrite=15 !---------------
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if (nlines.lt.nwrite) then write(6,
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Appendix C PEGS USER MANUAL Hideo H
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is entered. On each pass through th
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(from previous figure) (to previous
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(from previous figure) | | + ------
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+------+ |BREMTR| +------+ | V +---
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+------+ |PAIRTR| +------+ | V +---
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Name DCSLOAD DCSSTOR DCSTAB ELASTIN
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Name AFFACT AINTP ALKE ALKEI ALIN A
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Table C.5: Functions in PEGS, part
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+------+ +------+ +------+ +------+
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Table C.8: ELEM option input data l
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Table C.10: MIXT option input data
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Table C.12: PWLF option input data
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Table C.17: PLTN option input data
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ICPROF is set to 3, the user must c
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Column Line 12345678911234567892123
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interiors of the intervals. If FEXA
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C.3.6 The TEST Option The TEST opti
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C.3.9 The HPLT Option The Histogram
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Appendix D EGS5 INSTALLATION GUIDE
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egs5 directory (preferably using th
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6. The user is then asked to key-in
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* User code tutor1.f has been compi
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Appendix E CONTENTS OF THE EGS5 DIS
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All of the actual FORTRAN source co
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aprime.data Data for empirical brem
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eryllium iron silicon bismuth krypt
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The tutorial problems and advanced
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Bibliography [1] R. G. Alsmiller Jr
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[28] A. F. Bielajew. HOWFAR and HOW
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[59] K. Flöttmann. Investigations
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[92] H. Kolbenstvedt. Simple theory
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[123] Y. Namito, H. Hirayama, A. Ta
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[156] Y. A. Shreider, editor. The M
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Index “shower book”, 37 AE, 28,
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Klein-Nishina formula, 62 Landau di
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