Physics Reference Manual – Geant4 Version 10.1 | Complete Solution & Explanation Guide

Physics Reference Manual
Version: geant4 10.1 (5 December 2014)
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Contents

I Introduction 1
1 Introduction 2
1.1 Scope of This Manual . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Definition of Terms . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Status of this document . . . . . . . . . . . . . . . . . . . . . 3

2 Monte Carlo Methods 4
2.1 Status of this document . . . . . . . . . . . . . . . . . . . . . 5

3 Particle Transport 6
3.1 Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.1 Status of This Document . . . . . . . . . . . . . . . . . 7
3.2 True Step Length . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.1 The Interaction Length or Mean Free Path . . . . . . . 8
3.2.2 Determination of the Interaction Point . . . . . . . . . 9
3.2.3 Step Limitations . . . . . . . . . . . . . . . . . . . . . 9
3.2.4 Updating the Particle Time . . . . . . . . . . . . . . . 10
3.2.5 Status of This Document . . . . . . . . . . . . . . . . . 10


II Particle Decay 11
4 Decay 12
4.1 Mean Free Path for Decay in Flight . . . . . . . . . . . . . . . 12
4.2 Branching Ratios and Decay Channels . . . . . . . . . . . . . 12
4.2.1 G4PhaseSpaceDecayChannel . . . . . . . . . . . . . . . 13
4.2.2 G4DalitzDecayChannel . . . . . . . . . . . . . . . . . . 13
4.2.3 Muon Decay . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2.4 Leptonic Tau Decay . . . . . . . . . . . . . . . . . . . 15
4.2.5 Kaon Decay . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 Status of this document . . . . . . . . . . . . . . . . . . . . . 16


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,III Electromagnetic Interactions 17
5 Gamma Incident 18
5.1 Introduction ......................................................................................... 19
5.1.1 General Interfaces................................................................... 19
5.1.2 Status of This Document ....................................................... 19
5.2 Photoelectric Effect............................................................................. 21
5.2.1 Cross Section........................................................................... 21
5.2.2 Final State............................................................................... 21
5.2.3 Relaxation ................................................................................ 22
5.2.4 Status of this document......................................................... 23
5.3 Compton scattering............................................................................. 24
5.3.1 Cross Section........................................................................... 24
5.3.2 Sampling the Final State ....................................................... 25
5.3.3 Atomic shell effects ................................................................ 26
5.3.4 Status of This Document ....................................................... 27
5.4 Gamma Conversion into an Electron - Positron Pair ...................... 28
5.4.1 Cross Section........................................................................... 28
5.4.2 Final State............................................................................... 32
5.4.3 Ultra-Relativistic Model ....................................................... 33
5.4.4 Status of This Document ....................................................... 33
5.5 Gamma Conversion into a Muon - Anti-mu Pair............................. 35
5.5.1 Cross Section and Energy Sharing ........................................ 35
5.5.2 Parameterization of the Total Cross Section ....................... 38
5.5.3 Multi-differential Cross Section and Angular Variables 40
5.5.4 Procedure for the Generation of µ+µ− Pairs ....................... 42
5.5.5 Status of this document......................................................... 49

6 Elastic scattering 50
6.1 Multiple Scattering.............................................................................. 51
6.1.1 Introduction ............................................................................. 51
6.1.2 Definition of Terms ................................................................. 52
6.1.3 Path Length Correction ......................................................... 54
6.1.4 Angular Distribution ............................................................... 56
6.1.5 Determination of the Model Parameters .............................. 56
6.1.6 Step Limitation Algorithm ................................................... 58
6.1.7 Boundary Crossing Algorithm ............................................... 60
6.1.8 Implementation Details .......................................................... 61
6.1.9 Status of this document......................................................... 63
6.2 Discrete Processes for Charged Particles .......................................... 65
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6.2.1 Status of This Document ....................................................... 66

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6.3 Single Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3.1 Coulomb Scattering . . . . . . . . . . . . . . . . . . . . 67
6.3.2 Implementation Details . . . . . . . . . . . . . . . . . . 68
6.3.3 Status of This Document . . . . . . . . . . . . . . . . . 69
6.4 Ion Scattering ...................................................................................... 70
6.4.1 Method .................................................................................... 70
6.4.2 Implementation Details .......................................................... 74
6.4.3 Status of this document......................................................... 74
6.5 Single Scattering, Screened Coulomb Potential and NIEL .............. 76
6.5.1 Nucleus–Nucleus Interactions ................................................ 76
6.5.2 Nuclear Stopping Power ........................................................ 78
6.5.3 Non-Ionizing Energy Loss due to Coulomb Scattering . 81
6.5.4 G4IonCoulombScatteringModel .............................................. 82
6.5.5 The Method ............................................................................ 82
6.5.6 Implementation Details .......................................................... 83
6.5.7 Status of This Document ....................................................... 83
6.6 Electron Screened Single Scattering and NIEL ................................. 85
6.6.1 Scattering Cross Section of Electrons on Nuclei ................. 85
6.6.2 Nuclear Stopping Power of Electrons.................................... 94
6.6.3 Non-Ionizing Energy-Loss of Electrons................................. 95
6.7 G4eSingleScatteringModel ................................................................... 96
6.7.1 The method ............................................................................ 97
6.7.2 Implementation Details .......................................................... 99
6.8 Status of this Document..................................................................... 99

7 Energy loss of Charged Particles 101
7.1 Mean Energy Loss ............................................................................. 102
7.1.1 Method .................................................................................. 102
7.1.2 General Interfaces................................................................. 103
7.1.3 Step-size Limit ....................................................................... 103
7.1.4 Run Time Energy Loss Computation ................................. 105
7.1.5 Energy Loss by Heavy Charged Particles ........................... 106
7.1.6 Status of This Document ..................................................... 107
7.2 Energy Loss Fluctuations .................................................................. 109
7.2.1 Fluctuations in Thick Absorbers ....................................... 109
7.2.2 Fluctuations in Thin Absorbers......................................... 110
7.2.3 Width Correction Algorithm ................................................ 112
7.2.4 Sampling of Energy Loss...................................................... 112
7.2.5 Status of This Document ..................................................... 113
7.3 Correcting the Cross Section for Energy Variation........................ 114
7.3.1 Status of This Document ..................................................... 115

, 7.4 Conversion from Cut in Range to Energy Threshold .................... 116
7.4.1 Status of This Document ..................................................... 118
7.5 Photoabsorption ionization model .................................................. 119
7.5.1 Cross Section for Ionizing Collisions ................................... 119
7.5.2 Energy Loss Simulation ........................................................ 121
7.5.3 Photoabsorption Cross Section at Low Energies ............... 122
7.5.4 Status of this document....................................................... 123

8 Electron and Positron Incident 124
8.1 Ionization............................................................................................ 125
8.1.1 Method .................................................................................. 125
8.1.2 Continuous Energy Loss....................................................... 125
8.1.3 Total Cross Section per Atom and Mean Free Path ......... 127
8.1.4 Simulation of Delta-ray Production .................................... 128
8.1.5 Status of this document....................................................... 129
8.2 Bremsstrahlung .................................................................................. 130
8.2.1 Seltzer-Berger bremsstrahlung model ................................ 130
8.2.2 Bremsstrahlung of high-energy electrons ........................... 133
8.2.3 Status of this document....................................................... 136
8.3 Positron - Electron Annihilation .................................................... 138
8.3.1 Introduction ........................................................................... 138
8.3.2 Cross Section......................................................................... 138
8.3.3 Sampling the final state ....................................................... 138
8.3.4 Sampling the Gamma Energy.............................................. 139
8.3.5 Status of This Document ..................................................... 140
8.4 Positron Annihilation into µ+µ− Pair in Media ........................... 141
8.4.1 Total Cross Section .............................................................. 141
8.4.2 Sampling of Energies and Angles ........................................ 141
8.4.3 Status of this document....................................................... 144
8.5 Positron Annihilation into Hadrons ................................................ 146
8.5.1 Introduction ........................................................................... 146
8.5.2 Cross Section......................................................................... 146
8.5.3 Sampling the final state ....................................................... 146
8.5.4 Status of this document....................................................... 147

9 Low Energy Livermore 148
9.1 Introduction ....................................................................................... 149
9.1.1 Physics ................................................................................... 149
9.1.2 Data Sources ......................................................................... 149
9.1.3 Distribution of the Data Sets .............................................. 150
9.1.4 Calculation of Total Cross Sections .................................... 151
illustrate how business concepts are applied in real-world scenarios. Group discussions and practicing sample case studies can aid in refining analytical

skills.________________________________________