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Physics Reference Manual Release 10.4 Physics Reference Manual Release 10.4 Geant4 Collaboration Dec 8, 2017 CONTENTS: 1 Introduction 1 1.1 Introduction...............................................1 1.1.1 Scope of This Manual......................................1 1.1.2 Definition of Terms.......................................1 1.2 Monte Carlo Methods..........................................1 1.3 Particle transport.............................................2 2 Transportation 5 2.1 Transportation..............................................5 3 Decay 7 3.1 Decay...................................................7 3.1.1 Mean Free Path for Decay in Flight..............................7 3.1.2 Branching Ratios and Decay Channels.............................7 4 Electromagnetic 13 4.1 Standard................................................. 13 4.1.1 Positron Annihilation into 휇+휇− Pair in Media........................ 13 4.1.2 Positron - Electron Annihilation................................ 15 4.1.3 Positron Annihilation into Hadrons in Media......................... 16 4.1.4 Discrete Processes for Charged Particles............................ 17 4.1.5 Compton scattering....................................... 18 4.1.6 Gamma Conversion into e + e - Pair.............................. 20 4.1.7 Bremsstrahlung......................................... 24 4.1.8 Ionization............................................ 28 4.1.9 Hadron and Ion Ionization................................... 31 4.1.10 Single Scattering, Screened Coulomb Potential and NIEL................... 35 4.1.11 Multiple Scattering....................................... 40 4.1.12 Ion Scattering.......................................... 48 4.1.13 Photoabsorption Ionization Model............................... 51 4.1.14 PhotoElectric effect....................................... 54 4.1.15 Introduction........................................... 55 4.1.16 Ionization............................................ 59 4.1.17 Positron - Electron Annihilation................................ 62 4.1.18 Polarized Compton scattering.................................. 65 4.1.19 Polarized Bremsstrahlung for electron and positron...................... 68 4.1.20 Polarized Gamma conversion into an electron–positron pair.................. 70 4.1.21 Polarized Photoelectric Effect................................. 71 4.1.22 Photoabsorption Cross Section at Low Energies........................ 72 4.1.23 Single Scattering........................................ 73 i 4.1.24 Synchrotron Radiation..................................... 74 4.1.25 MuPGen............................................. 75 4.2 Low Energy............................................... 81 4.2.1 Bremsstrahlung......................................... 81 4.2.2 Compton Scattering....................................... 84 4.2.3 Geant4-DNA processes and models.............................. 85 4.2.4 Gamma Conversion....................................... 85 4.2.5 Low energy extentions..................................... 86 4.2.6 Electron ionisation....................................... 90 4.2.7 Ionisation............................................ 90 4.2.8 The MicroElec [1] extension for microelectronics applications................ 91 4.2.9 Monash Low Energy Photon Processes............................. 92 4.2.10 Introduction........................................... 93 4.2.11 Penelope physics........................................ 94 4.2.12 Photoelectric effect....................................... 104 4.2.13 PIXE.............................................. 106 4.2.14 Compton Scattering by Linearly Polarized Gamma Rays................... 106 4.2.15 Pair production by Linearly Polarized Gamma Rays...................... 107 4.2.16 Rayleigh Scattering....................................... 109 4.2.17 Atomic relaxation........................................ 110 4.2.18 Triple Gamma Conversion................................... 111 4.3 Miscellaneous.............................................. 116 4.3.1 True Step Length........................................ 116 4.3.2 Conversion from Cut in Range to Energy Threshold...................... 117 4.4 Muons.................................................. 119 4.4.1 Multiple scattering....................................... 119 4.4.2 Bremsstrahlung......................................... 120 4.4.3 Muon Ionization........................................ 123 4.4.4 Muon Photonuclear Interaction................................. 124 4.4.5 Positron - Electron Pair Production by Muons......................... 126 4.5 Precision................................................. 130 4.5.1 Overview............................................ 130 4.5.2 Impact ionisation by hadrons and PIXE............................ 130 4.6 Utils................................................... 132 4.6.1 Density effect.......................................... 132 4.6.2 Introduction........................................... 133 4.6.3 Mean Energy Loss....................................... 134 4.6.4 Energy Loss Fluctuations.................................... 137 4.6.5 Correcting the Cross Section for Energy Variation....................... 140 4.7 Xrays................................................... 141 4.7.1 Cerenkovˇ Effect......................................... 141 4.7.2 Scintillation........................................... 141 4.7.3 Transition radiation....................................... 142 5 Optical 159 5.1 Interactions of optical photons...................................... 159 5.1.1 Physics processes for optical photons............................. 159 5.1.2 Photon polarization....................................... 160 5.1.3 Tracking of the photons..................................... 160 5.1.4 Mie Scattering in Henyey-Greensterin Approximation..................... 163 6 Phonon 167 6.1 Introduction............................................... 167 6.2 Phonon Propagation........................................... 167 ii 6.3 Lattice Parameters............................................ 168 6.4 Scattering and Mode Mixing....................................... 168 6.5 Anharmonic Downconversion...................................... 168 7 Hadronic 171 7.1 Elastic.................................................. 171 7.1.1 Coherent elastic scattering................................... 171 7.2 Elastic_he................................................ 171 7.2.1 Hadron-nucleus Elastic Scattering at Medium and High Energy................ 171 7.3 LowEnergyChargedParticles....................................... 173 7.3.1 Low Energy Charged Particle Interactions........................... 173 7.4 LowEnergyNeutrons........................................... 186 7.4.1 Geant4 Low Energy Nuclear Data (LEND) Package...................... 186 7.4.2 Neutrons............................................ 186 7.5 LPBias.................................................. 195 7.5.1 Leading Particle Bias...................................... 195 7.6 Radioactive Decay............................................ 197 7.6.1 Radioactive Decay....................................... 197 7.7 Stopping................................................. 199 7.7.1 Complementary parameterised and theoretical treatment................... 199 7.7.2 Pion absorption at rest..................................... 199 7.7.3 Interactions of Stopping Particles................................ 200 7.8 Theory-Driven.............................................. 200 7.8.1 Abla............................................... 200 7.8.2 AbrasionAblation........................................ 201 7.8.3 BinaryCascade......................................... 207 7.8.4 CrossSection.......................................... 213 7.8.5 Evaporation........................................... 220 7.8.6 Fermi Breakup......................................... 228 7.8.7 Fermi Breakup......................................... 230 7.8.8 Gamma Interaction....................................... 230 7.8.9 Incl............................................... 232 7.8.10 Multifragmentation....................................... 236 7.8.11 Parton string........................................... 240 7.8.12 Parton string........................................... 249 7.8.13 QMD.............................................. 249 7.8.14 Stopped Absorption....................................... 252 8 Photolepton 259 8.1 Introduction............................................... 259 8.2 Gamma-nuclear Interactions....................................... 259 8.2.1 Process and Cross Section................................... 259 8.2.2 Final State Generation..................................... 259 8.3 Electro-nuclear Interactions....................................... 260 8.3.1 Process and Cross Section................................... 260 8.3.2 Final State Generation..................................... 260 8.4 Muon-nuclear Interactions........................................ 260 8.4.1 Process and Cross Section................................... 260 8.4.2 Final State Generation..................................... 260 iii iv CHAPTER ONE INTRODUCTION 1.1 Introduction 1.1.1 Scope of This Manual The Physics Reference Manual provides detailed explanations of the physics implemented in the Geant4 toolkit. The manual’s purpose is threefold: • to present the theoretical formulation, model, or parameterization of the physics interactions included in Geant4, • to describe the probability of the occurrence of an
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