PENELOPE 2003 - OECD Nuclear Energy Agency

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180 Chapter 6. Structure and operation of the code system the element, the numerical labels of the active electron shells (see table 6.1), the transition probability and the energy of the emitted x-ray or electron, respectively. Table 6.1: Numerical labels used to designate atomic electron shells. In the case of nonradiative transitions, the label 99 indicates shells beyond the M5 shell. label shell label shell label shell 1 K (1s 1/2 ) 11 N2 (4p 1/2 ) 21 O5 (5d 5/2 ) 2 L1 (2s 1/2 ) 12 N3 (4p 3/2 ) 22 O6 (5f 5/2 ) 3 L2 (2p 1/2 ) 13 N4 (4d 3/2 ) 23 O7 (5f 7/2 ) 4 L3 (2p 3/2 ) 14 N5 (4d 5/2 ) 24 P1 (6s 1/2 ) 5 M1 (3s 1/2 ) 15 N6 (4f 5/2 ) 25 P2 (6p 1/2 ) 6 M2 (3p 1/2 ) 16 N7 (4f 7/2 ) 26 P3 (6p 3/2 ) 7 M3 (3p 3/2 ) 17 O1 (5s 1/2 ) 27 P4 (6d 3/2 ) 8 M4 (3d 3/2 ) 18 O2 (5p 1/2 ) 28 P5 (6d 5/2 ) 9 M5 (3d 5/2 ) 19 O3 (5p 3/2 ) 29 Q1 (7s 1/2 ) 10 N1 (4s 1/2 ) 20 O4 (5d 3/2 ) 99 outer shells 92 files named PDEELZZ.TAB with ZZ=atomic number (01–92). These files contain integrated cross sections for elastic scattering of electrons and positrons by neutral atoms, calculated by using the partial-wave methods described in section 3.1 (Salvat, 2000). The first line in each file gives the atomic number ZZ; each subsequent line has 7 columns with the following data: 1st column: kinetic energy (eV), in increasing order. 2nd column: total cross section for electrons. 3rd column: first transport cross section for electrons. 4th column: second transport cross section for electrons. 5th column: total cross section for positrons. 6th column: first transport cross section for positrons. 7th column: second transport cross section for positrons. The grid of energies is approximately logarithmic, with 15 points per decade, and is the same for all elements. All cross sections are in cm 2 . 92 files named PDEBRZZ.TAB with ZZ=atomic number (01–92). They contain the atomic bremsstrahlung scaled cross sections (energy loss spectra) and total integrated radiative cross sections of electrons, for a grid of electron kinetic energies E and reduced photon energies W/E that is dense enough to allow the use of cubic spline log-log interpolation in E and linear interpolation in W/E. The data in these files is from a database, with 32 reduced photon energies, which was provided to the authors by Steve Seltzer (a brief description of the methods used to compute the database and a reduced tabulation is given in Seltzer and Berger,
6.1. penelope 181 1986). The format of the bremsstrahlung database files is the following, 1) The first line contains the atomic number ZZ. 2) Each four-lines block contains the electron kinetic energy E, the scaled energyloss differential cross section at the 32 fixed reduced photon energies and the value of the integrated radiative cross section. Energies are in eV and the values of the scaled energy-loss cross section are in millibarn (10 −27 cm 2 ). PDBRANG.TAB . . . Gives the parameters of the analytical shape function (angular distribution) of bremsstrahlung photons, which is expressed as a statistical mixture of two Lorentz-boosted dipole distributions, eq. (3.151). The distribution parameters were obtained by fitting the benchmark partial-wave shapes tabulated by Kissel et al. (1983). 92 files named PDGPPZZ.TAB with ZZ=atomic number (01–92). Total cross sections for electron-positron pair production by photons with energies up to 100 GeV in the field of neutral atoms. The data were generated by means of the xcom program of Berger and Hubbell (1987). The first line of each file gives the atomic number ZZ; each subsequent line gives, 1st column: photon energy, in eV. The same energy grid for all elements. 2nd column: total cross section for pair+triplet production in barn (10 −24 cm 2 ). 92 files named PDGPHZZ.TAB with ZZ=atomic number (01–92), containing photoelectric total atomic cross sections and partial cross sections for photoionization of inner shells (K shell and L subshells) for the elements and photon energies in the range from 100 eV to 1 TeV. The data were extracted from the LLNL Evaluated Photon Data Library EPDL97 (Cullen et al., 1997). The format is the following, 1) the first line contains the atomic number ZZ and the number NS of shells for which the partial cross section is tabulated. 2) each of the following lines contains a value of the photon energy (in eV) and the corresponding total cross section and partial cross sections of the shells K, L1, L2 and L3, respectively (all cross sections in barn). For low-Z elements, L-subshells are empty and, therefore, they do not appear in the table. The grid of energies for each element was obtained by merging a generic grid (the same for all elements, covering the energy range from 100 eV to 100 GeV) with the grid of absorption edges of the element, and adding additional points (where needed) to ensure that linear log-log interpolation will never introduce relative errors larger than 0.02. 92 files named PDEINZZ.TAB with ZZ=atomic number (01–92), containing total (integrated) cross sections for ionization of inner shells (K shell and L subshells) by impact of electrons and positrons with kinetic energies in the range from 100 eV to 1 GeV. These cross sections were evaluated by means of the optical-data model described in section 3.2.6 using photoelectric cross sections read from the files PDGPHZZ.TAB. The format is the following, 1) the first line contains the atomic number ZZ.
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Data Bank ISBN 92-64-02145-0 PENELO
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FOREWORD The OECD/NEA Data Bank was
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TABLE OF CONTENTS Foreword ........
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4.3 Combined scattering and energy
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PREFACE Radiation transport in matt
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The present version of PENELOPE is
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Chapter 1 Monte Carlo simulation. B
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1.1. Elements of probability theory
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1.1. Elements of probability theory
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1.2. Random sampling methods 7 Tabl
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1.2. Random sampling methods 9 Nume
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1.2. Random sampling methods 11 whe
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1.2. Random sampling methods 13 can
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1.2. Random sampling methods 15 mus
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1.2. Random sampling methods 17 the
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1.3. Monte Carlo integration 19 Con
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1.4. Simulation of radiation transp
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¡ ¢ 1.4. Simulation of radiation
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1.5. Statistical averages and uncer
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1.6. Variance reduction 31 also imp
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1.6. Variance reduction 33 weight a
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Chapter 2 Photon interactions In th
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2.1. Coherent (Rayleigh) scattering
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2.1. Coherent (Rayleigh) scattering
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2.2. Photoelectric effect 41 ➤E E
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F 2.2. Photoelectric effect 43 1E+7
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2.3. Incoherent (Compton) scatterin
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C u 2.3. Incoherent (Compton) scatt
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2.4. Electron-positron pair product
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2.5. Attenuation coefficients 63 di
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2.6. Atomic relaxation 65 2.6 Atomi
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2.6. Atomic relaxation 67 two vacan
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Chapter 3 Electron and positron int
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3.1. Elastic collisions 71 nucleus
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3.1. Elastic collisions 73 1 E - 1
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ρ ρ ρ λ λ λ ρ ρ ρ λ λ λ
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3.1. Elastic collisions 77 becomes
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B ' B ' 3.1. Elastic collisions 79
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3.2. Inelastic collisions 81 where
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3.2. Inelastic collisions 83 global
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3.2. Inelastic collisions 85 plays
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3.2. Inelastic collisions 87 optica
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3.2. Inelastic collisions 89 The DC
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3.2. Inelastic collisions 91 In the
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3.2. Inelastic collisions 93 where
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c b c b 3.2. Inelastic collisions 9
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A l A u 3.2. Inelastic collisions 9
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3.2. Inelastic collisions 99 After
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3.2. Inelastic collisions 101 Table
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3.2. Inelastic collisions 103 In re
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3.2. Inelastic collisions 105 1Ε+4
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3.3. Bremsstrahlung emission 107 an
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3.3. Bremsstrahlung emission 109 1
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3.3. Bremsstrahlung emission 111 1
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3.3. Bremsstrahlung emission 113 wh
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3.3. Bremsstrahlung emission 115 Al
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3.3. Bremsstrahlung emission 117 Th
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3.4. Positron annihilation 119 (198
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3.4. Positron annihilation 121 It i
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Chapter 4 Electron/positron transpo
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4.1. Elastic scattering 125 Lewis (
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4.1. Elastic scattering 127 ⎡ ⎛
Page 141 and 142: 4.1. Elastic scattering 129 simulat
Page 143 and 144: 4.1. Elastic scattering 131 The sim
Page 145 and 146: 4.2. Soft energy losses 133 soft in
Page 147 and 148: 4.2. Soft energy losses 135 deviati
Page 149 and 150: 4.2. Soft energy losses 137 scatter
Page 151 and 152: 4.3. Combined scattering and energy
Page 159 and 160: 4.4. Generation of random tracks 14
Page 165 and 166: Chapter 5 Constructive quadric geom
Page 167 and 168: 5.1. Rotations and translations 155
Page 169 and 170: 5.2. Quadric surfaces 157 Given a f
Page 171 and 172: 5.2. Quadric surfaces 159 Table 5.1
Page 173 and 174: 5.3. Constructive quadric geometry
Page 175 and 176: 5.4. Geometry definition file 163 1
Page 177 and 178: 5.4. Geometry definition file 165
Page 179 and 180: 5.5. The subroutine package pengeom
Page 181 and 182: 5.5. The subroutine package pengeom
Page 183 and 184: 5.6. Debugging and viewing the geom
Page 185 and 186: 5.7. A short tutorial 173 MODULE (
Page 187 and 188: 5.7. A short tutorial 175 Writing a
Page 189 and 190: Chapter 6 Structure and operation o
Page 191: 6.1. penelope 179 and/or numbers in
Page 195 and 196: 6.1. penelope 183 The connection of
Page 197 and 198: 6.1. penelope 185 that has to be lo
Page 199 and 200: G y y y y y 6.1. penelope 187 CALL
Page 201 and 202: 6.1. penelope 189 It is the respons
Page 203 and 204: 6.2. Examples of MAIN programs 191
Page 213 and 214: 6.3. Selecting the simulation param
Page 215 and 216: ! 6.3. Selecting the simulation par
Page 217 and 218: 6.5. Installation 205 radiation is
Page 219 and 220: 6.5. Installation 207 To get the ex
Page 221 and 222: Appendix A Collision kinematics To
Page 223 and 224: A.1. Two-body reactions 211 Clearly
Page 225 and 226: A.2. Inelastic collisions of charge
Page 227 and 228: m A.2. Inelastic collisions of char
Page 229 and 230: Appendix B Numerical tools B.1 Cubi
Page 231 and 232: B.1. Cubic spline interpolation 219
Page 233 and 234: B.2. Numerical quadrature 221 B.2 N
Page 235 and 236: Appendix C Electron/positron transp
Page 237 and 238: C.1. Tracking particles in vacuum.
Page 239 and 240: C.1. Tracking particles in vacuum.
Page 241 and 242: C.2. Exact tracking in homogeneous
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C.2. Exact tracking in homogeneous
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Bibliography Abramowitz M. and I.A.
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Bibliography 235 Briesmeister J.F.
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Bibliography 237 James F. (1990),
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Bibliography 239 Reimer L. and E.R.
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Bibliography 241 Yates A.C. (1968),
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