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Physics Reference Manual

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Physics Reference Manual Physics Reference Manual Version: geant4 9.2 (19 December, 2008) Contents I Introduction 1 1 Introduction 2 1.1 Scope of This Manual ....................... 2 1.2 De¯nition of Terms ........................ 2 1.3 Status of this document ..................... 3 2 Monte Carlo Methods 4 2.1 Status of this document ..................... 5 3 Transportation 6 II Particle Decay 7 4 Decay 8 4.1 Mean Free Path for Decay in Flight ............... 8 4.2 Branching Ratios and Decay Channels ............. 8 4.2.1 G4PhaseSpaceDecayChannel ............... 9 4.2.2 G4DalitzDecayChannel .................. 9 4.2.3 Muon Decay ........................ 10 4.2.4 Leptonic Tau Decay ................... 11 4.2.5 Kaon Decay ........................ 11 4.3 Status of this document ..................... 12 III Electromagnetic Interactions 13 5 Particle Transport 14 5.1 The Interaction Length or Mean Free Path ........... 15 5.2 Determination of the Interaction Point ............. 16 5.3 Updating the Particle Lifetime .................. 17 5.4 Status of this document ..................... 17 -10 6 Gamma Incident 18 6.1 Introduction ............................ 19 6.1.1 General Interfaces ..................... 19 6.1.2 Status of this document ................. 22 6.2 Photoelectric E®ect ........................ 23 6.2.1 Cross Section and Mean Free Path ........... 23 6.2.2 Final State ........................ 23 6.2.3 Status of this document ................. 25 6.3 Compton scattering ........................ 26 6.3.1 Cross Section and Mean Free Path ........... 26 6.3.2 Sampling the Final State ................. 27 6.3.3 Validity .......................... 28 6.3.4 Status of this document ................. 28 6.4 Gamma Conversion into an Electron - Positron Pair ...... 30 6.4.1 Cross Section and Mean Free Path ........... 30 6.4.2 Final State ........................ 31 6.4.3 Status of this document ................. 35 6.5 Gamma Conversion into a Muon - Anti-mu Pair ........ 36 6.5.1 Cross Section and Energy Sharing ............ 36 6.5.2 Parameterization of the Total Cross Section ...... 39 6.5.3 Multi-di®erential Cross Section and Angular Variables 42 6.5.4 Procedure for the Generation of Muon - Anti-muon Pairs 44 6.5.5 Status of this document ................. 54 7 Common to All Charged Particles 55 7.1 Computing the Mean Energy Loss ................ 56 7.1.1 Method .......................... 56 7.1.2 Implementation Details .................. 57 7.1.3 Energy Loss by Heavy Charged Particles ........ 62 7.1.4 Status of this document ................. 62 7.2 Energy loss fluctuations ..................... 64 7.2.1 Fluctuations in thick absorbers ............. 64 7.2.2 Fluctuations in thin absorbers .............. 65 7.2.3 Status of this document ................. 68 7.3 Correcting the cross section for energy variation ........ 69 7.3.1 Status of this document ................. 70 7.4 Conversion from range cut to kinetic energy cut ........ 71 7.4.1 Status of this document ................. 72 7.5 Multiple Scattering ........................ 74 7.5.1 Introduction ........................ 74 7.5.2 De¯nition of Terms .................... 75 7.5.3 Path Length Correction ................. 77 7.5.4 Angular Distribution ................... 79 7.5.5 Determination of the Model Parameters ........ 80 7.5.6 The MSC Process in Geant4 ............... 83 7.5.7 Step Limitation Algorithm ................ 83 7.5.8 Boundary Crossing Algorithm .............. 85 7.5.9 Implementation Details .................. 86 7.5.10 Status of this document ................. 88 7.6 Single Scattering ......................... 90 7.6.1 Coulomb Scattering .................... 90 7.6.2 Implementation Details .................. 91 7.6.3 Status of this document ................. 92 7.7 Ion Scattering ........................... 93 7.7.1 Method .......................... 93 7.7.2 Implementation Details .................. 97 7.7.3 Status of this document ................. 97 7.8 Transition radiation ........................ 99 7.8.1 Relationship of Transition Rad to Cherenkov Rad ... 99 7.8.2 Calculating the X-ray Transition Radiation Yield ... 100 7.8.3 Simulating X-ray Transition Radiation Production ... 102 7.8.4 Status of this document ................. 105 7.9 Scintillation ............................ 106 7.9.1 Status of this document ................. 106 7.10 Cerenkov· E®ect .......................... 107 7.10.1 Status of this document ................. 108 7.11 Photoabsorption ionization model ................ 109 7.11.1 Cross Section for Ionizing Collisions ........... 109 7.11.2 Energy Loss Simulation ................. 111 7.11.3 Status of this document ................. 112 7.12 Photoabsorption cross section at low energies .......... 113 7.12.1 Method .......................... 113 7.12.2 Status of this document ................. 113 8 Electron and Positron Incident 115 8.1 Ionization ............................. 116 8.1.1 Method .......................... 116 8.1.2 Continuous Energy Loss ................. 116 8.1.3 Total Cross Section per Atom and Mean Free Path .. 118 8.1.4 Simulation of Delta-ray Production ........... 119 8.1.5 Status of this document ................. 120 8.2 Bremsstrahlung .......................... 121 8.2.1 Cross Section and Energy Loss ............. 121 8.2.2 Simulation of Discrete Bremsstrahlung ......... 126 8.2.3 Bremsstrahlung of high-energy electrons ........ 130 8.2.4 Status of this document ................. 133 8.3 Positron - Electron Annihilation ................. 135 8.3.1 Introduction ........................ 135 8.3.2 Cross Section and Mean Free Path ........... 135 8.3.3 Sampling the ¯nal state ................. 135 8.3.4 Status of this document ................. 137 8.4 Positron - Electron Annihilation into Muon - Anti-muon ... 139 8.4.1 Total Cross Section .................... 139 8.4.2 Sampling of Energies and Angles ............ 139 8.4.3 Status of this document ................. 142 8.5 Positron - Electron Annihilation into Hadrons ......... 144 8.5.1 Introduction ........................ 144 8.5.2 Cross Section and Mean Free Path ........... 144 8.5.3 Sampling the ¯nal state ................. 144 8.5.4 Status of this document ................. 144 8.6 Synchrotron Radiation ...................... 146 8.6.1 Photon spectrum ..................... 146 8.6.2 Validity .......................... 147 8.6.3 Direct inversion/generation of photon energy spectrum 148 8.6.4 Properties of the photon energy and power spectra .. 153 8.6.5 Status of this document ................. 154 9 Charged Hadron Incident 156 9.1 Ionization ............................. 157 9.1.1 Method .......................... 157 9.1.2 Continuous Energy Loss ................. 157 9.1.3 Total Cross Section per Atom and Mean Free Path .. 163 9.1.4 Simulating Delta-ray Production ............ 163 9.1.5 Status of this document ................. 165 10 Muon Incident 167 10.1 Ionization ............................. 168 10.1.1 Status of this document ................. 169 10.2 Bremsstrahlung .......................... 170 10.2.1 Di®erential Cross Section ................. 170 10.2.2 Continuous Energy Loss ................. 171 10.2.3 Total Cross Section .................... 171 10.2.4 Sampling ......................... 172 10.2.5 Status of this document ................. 173 10.3 Positron - Electron Pair Production by Muons ......... 175 10.3.1 Di®erential Cross Section ................. 175 10.3.2 Total Cross Section and Restricted Energy Loss .... 178 10.3.3 Sampling of Positron - Electron Pair Production .... 179 10.3.4 Status of this document ................. 180 10.4 Muon Photonuclear Interaction ................. 182 10.4.1 Di®erential Cross Section ................. 182 10.4.2 Sampling ......................... 183 10.4.3 Status of this document ................. 185 11 Polarized Electron/Positron/Gamma Incident 187 11.1 Introduction ............................ 188 11.1.1 Stokes vector ....................... 188 11.1.2 Transfer matrix ...................... 190 11.1.3 Coordinate transformations ............... 191 11.1.4 Polarized beam and material ............... 192 11.1.5 Status of this document ................. 194 11.2 Ionization ............................. 195 11.2.1 Method .......................... 195 11.2.2 Total cross section and mean free path ......... 195 11.2.3 Sampling the ¯nal state ................. 197 11.2.4 Status of this document ................. 200 11.3 Positron - Electron Annihilation ................. 202 11.3.1 Method .......................... 202 11.3.2 Total cross section and mean free path ......... 202 11.3.3 Sampling the ¯nal state ................. 204 11.3.4 Annihilation at Rest ................... 206 11.3.5 Status of this document ................. 207 11.4 Polarized Compton scattering .................. 208 11.4.1 Method .......................... 208 11.4.2 Total cross section and mean free path ......... 208 11.4.3 Sampling the ¯nal state ................. 209 11.4.4 Status of this document ................. 212 11.5 Polarized Bremsstrahlung for electron and positron ...... 213 11.5.1 Method .......................... 213 11.5.2 Polarization in gamma conversion and bremsstrahlung 213 11.5.3 Polarization transfer to the photon ........... 214 11.5.4 Polarization transfer to the lepton ............ 215 11.5.5 Status of this document ................. 217 11.6 Polarized Gamma conversion into an electron{positron pair .. 219 11.6.1 Method .......................... 219 11.6.2 Polarization transfer ................... 219 11.6.3 Status
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