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24 | // ******************************************************************** |
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25 | // |
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26 | // $Id: G4eBremsstrahlungRelModel.cc,v 1.14 2009/04/09 18:41:18 vnivanch Exp $ |
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27 | // GEANT4 tag $Name: geant4-09-03-beta-cand-01 $ |
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28 | // |
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29 | // ------------------------------------------------------------------- |
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30 | // |
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31 | // GEANT4 Class file |
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32 | // |
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33 | // |
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34 | // File name: G4eBremsstrahlungRelModel |
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35 | // |
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36 | // Author: Andreas Schaelicke |
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37 | // |
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38 | // Creation date: 12.08.2008 |
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39 | // |
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40 | // Modifications: |
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41 | // |
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42 | // 13.11.08 add SetLPMflag and SetLPMconstant methods |
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43 | // 13.11.08 change default LPMconstant value |
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44 | // |
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45 | // Main References: |
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46 | // Y.-S.Tsai, Rev. Mod. Phys. 46 (1974) 815; Rev. Mod. Phys. 49 (1977) 421. |
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47 | // S.Klein, Rev. Mod. Phys. 71 (1999) 1501. |
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48 | // T.Stanev et.al., Phys. Rev. D25 (1982) 1291. |
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49 | // M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media, Wiley, 1972. |
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50 | // |
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51 | // ------------------------------------------------------------------- |
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52 | // |
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53 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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54 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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55 | |
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56 | #include "G4eBremsstrahlungRelModel.hh" |
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57 | #include "G4Electron.hh" |
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58 | #include "G4Positron.hh" |
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59 | #include "G4Gamma.hh" |
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60 | #include "Randomize.hh" |
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61 | #include "G4Material.hh" |
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62 | #include "G4Element.hh" |
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63 | #include "G4ElementVector.hh" |
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64 | #include "G4ProductionCutsTable.hh" |
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65 | #include "G4ParticleChangeForLoss.hh" |
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66 | #include "G4LossTableManager.hh" |
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67 | |
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68 | |
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69 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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70 | |
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71 | const G4double G4eBremsstrahlungRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083, |
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72 | 0.5917, 0.7628, 0.8983, 0.9801 }; |
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73 | const G4double G4eBremsstrahlungRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813, |
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74 | 0.1813, 0.1569, 0.1112, 0.0506 }; |
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75 | const G4double G4eBremsstrahlungRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71} ; |
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76 | const G4double G4eBremsstrahlungRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924} ; |
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77 | |
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78 | |
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79 | using namespace std; |
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80 | |
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81 | G4eBremsstrahlungRelModel::G4eBremsstrahlungRelModel(const G4ParticleDefinition* p, |
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82 | const G4String& name) |
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83 | : G4VEmModel(name), |
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84 | particle(0), |
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85 | fXiLPM(0), fPhiLPM(0), fGLPM(0), |
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86 | isElectron(true), |
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87 | fMigdalConstant(classic_electr_radius*electron_Compton_length*electron_Compton_length*4.0*pi), |
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88 | fLPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)*0.5), |
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89 | bremFactor(fine_structure_const*classic_electr_radius*classic_electr_radius*16./3.), |
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90 | use_completescreening(true),isInitialised(false) |
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91 | { |
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92 | if(p) SetParticle(p); |
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93 | theGamma = G4Gamma::Gamma(); |
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94 | |
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95 | minThreshold = 1.0*keV; |
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96 | SetLowEnergyLimit(GeV); |
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97 | |
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98 | nist = G4NistManager::Instance(); |
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99 | InitialiseConstants(); |
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100 | |
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101 | SetLPMFlag(true); |
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102 | } |
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103 | |
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104 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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105 | |
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106 | void G4eBremsstrahlungRelModel::InitialiseConstants() |
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107 | { |
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108 | facFel = log(184.15); |
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109 | facFinel = log(1194.); |
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110 | |
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111 | preS1 = 1./(184.15*184.15); |
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112 | logTwo = log(2.); |
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113 | } |
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114 | |
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115 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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116 | |
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117 | G4eBremsstrahlungRelModel::~G4eBremsstrahlungRelModel() |
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118 | { |
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119 | } |
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120 | |
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121 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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122 | |
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123 | void G4eBremsstrahlungRelModel::SetParticle(const G4ParticleDefinition* p) |
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124 | { |
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125 | particle = p; |
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126 | particleMass = p->GetPDGMass(); |
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127 | if(p == G4Electron::Electron()) isElectron = true; |
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128 | else isElectron = false; |
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129 | } |
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130 | |
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131 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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132 | |
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133 | G4double G4eBremsstrahlungRelModel::MinEnergyCut(const G4ParticleDefinition*, |
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134 | const G4MaterialCutsCouple*) |
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135 | { |
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136 | return minThreshold; |
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137 | } |
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138 | |
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139 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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140 | |
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141 | void G4eBremsstrahlungRelModel::SetupForMaterial(const G4ParticleDefinition*, |
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142 | const G4Material* mat, G4double kineticEnergy) |
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143 | { |
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144 | densityFactor = mat->GetElectronDensity()*fMigdalConstant; |
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145 | lpmEnergy = mat->GetRadlen()*fLPMconstant; |
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146 | |
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147 | // Threshold for LPM effect (i.e. below which LPM hidden by density effect) |
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148 | if (LPMFlag()) |
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149 | energyThresholdLPM=sqrt(densityFactor)*lpmEnergy; |
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150 | else |
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151 | energyThresholdLPM=1.e39; // i.e. do not use LPM effect |
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152 | |
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153 | // calculate threshold for density effect |
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154 | kinEnergy = kineticEnergy; |
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155 | totalEnergy = kineticEnergy + particleMass; |
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156 | densityCorr = densityFactor*totalEnergy*totalEnergy; |
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157 | |
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158 | // define critical gamma energies (important for integration/dicing) |
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159 | klpm=totalEnergy*totalEnergy/lpmEnergy; |
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160 | kp=sqrt(densityCorr); |
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161 | |
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162 | } |
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163 | |
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164 | |
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165 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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166 | |
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167 | void G4eBremsstrahlungRelModel::Initialise(const G4ParticleDefinition* p, |
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168 | const G4DataVector& cuts) |
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169 | { |
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170 | if(p) SetParticle(p); |
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171 | |
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172 | highKinEnergy = HighEnergyLimit(); |
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173 | lowKinEnergy = LowEnergyLimit(); |
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174 | |
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175 | currentZ = 0.; |
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176 | |
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177 | InitialiseElementSelectors(p, cuts); |
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178 | |
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179 | if(isInitialised) return; |
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180 | fParticleChange = GetParticleChangeForLoss(); |
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181 | isInitialised = true; |
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182 | } |
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183 | |
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184 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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185 | |
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186 | G4double G4eBremsstrahlungRelModel::ComputeDEDXPerVolume( |
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187 | const G4Material* material, |
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188 | const G4ParticleDefinition* p, |
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189 | G4double kineticEnergy, |
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190 | G4double cutEnergy) |
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191 | { |
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192 | if(!particle) SetParticle(p); |
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193 | if(kineticEnergy < lowKinEnergy) return 0.0; |
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194 | G4double cut = std::min(cutEnergy, kineticEnergy); |
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195 | if(cut == 0.0) return 0.0; |
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196 | |
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197 | SetupForMaterial(particle, material,kineticEnergy); |
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198 | |
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199 | const G4ElementVector* theElementVector = material->GetElementVector(); |
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200 | const G4double* theAtomicNumDensityVector = material->GetAtomicNumDensityVector(); |
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201 | |
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202 | G4double dedx = 0.0; |
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203 | |
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204 | // loop for elements in the material |
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205 | for (size_t i=0; i<material->GetNumberOfElements(); i++) { |
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206 | |
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207 | G4VEmModel::SetCurrentElement((*theElementVector)[i]); |
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208 | SetCurrentElement((*theElementVector)[i]->GetZ()); |
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209 | |
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210 | dedx += theAtomicNumDensityVector[i]*currentZ*currentZ*ComputeBremLoss(cut); |
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211 | } |
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212 | dedx *= bremFactor; |
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213 | |
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214 | |
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215 | return dedx; |
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216 | } |
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217 | |
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218 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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219 | |
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220 | G4double G4eBremsstrahlungRelModel::ComputeBremLoss(G4double cut) |
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221 | { |
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222 | G4double loss = 0.0; |
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223 | |
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224 | // number of intervals and integration step |
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225 | G4double vcut = cut/totalEnergy; |
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226 | G4int n = (G4int)(20*vcut) + 3; |
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227 | G4double delta = vcut/G4double(n); |
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228 | |
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229 | G4double e0 = 0.0; |
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230 | G4double xs; |
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231 | |
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232 | // integration |
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233 | for(G4int l=0; l<n; l++) { |
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234 | |
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235 | for(G4int i=0; i<8; i++) { |
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236 | |
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237 | G4double eg = (e0 + xgi[i]*delta)*totalEnergy; |
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238 | |
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239 | if(totalEnergy > energyThresholdLPM) { |
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240 | xs = ComputeRelDXSectionPerAtom(eg); |
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241 | } else { |
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242 | xs = ComputeDXSectionPerAtom(eg); |
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243 | } |
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244 | loss += wgi[i]*xs/(1.0 + densityCorr/(eg*eg)); |
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245 | } |
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246 | e0 += delta; |
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247 | } |
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248 | |
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249 | loss *= delta*totalEnergy; |
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250 | |
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251 | return loss; |
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252 | } |
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253 | |
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254 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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255 | |
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256 | G4double G4eBremsstrahlungRelModel::ComputeCrossSectionPerAtom( |
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257 | const G4ParticleDefinition* p, |
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258 | G4double kineticEnergy, |
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259 | G4double Z, G4double, |
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260 | G4double cutEnergy, |
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261 | G4double maxEnergy) |
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262 | { |
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263 | if(!particle) SetParticle(p); |
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264 | if(kineticEnergy < lowKinEnergy) return 0.0; |
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265 | G4double cut = std::min(cutEnergy, kineticEnergy); |
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266 | G4double tmax = std::min(maxEnergy, kineticEnergy); |
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267 | |
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268 | if(cut >= tmax) return 0.0; |
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269 | |
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270 | SetCurrentElement(Z); |
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271 | |
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272 | G4double cross = ComputeXSectionPerAtom(cut); |
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273 | |
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274 | // allow partial integration |
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275 | if(tmax < kinEnergy) cross -= ComputeXSectionPerAtom(tmax); |
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276 | |
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277 | cross *= Z*Z*bremFactor; |
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278 | |
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279 | return cross; |
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280 | } |
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281 | |
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282 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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283 | |
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284 | |
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285 | G4double G4eBremsstrahlungRelModel::ComputeXSectionPerAtom(G4double cut) |
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286 | { |
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287 | G4double cross = 0.0; |
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288 | |
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289 | // number of intervals and integration step |
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290 | G4double vcut = log(cut/totalEnergy); |
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291 | G4double vmax = log(kinEnergy/totalEnergy); |
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292 | G4int n = (G4int)(0.45*(vmax - vcut)) + 4; |
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293 | // n=1; // integration test |
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294 | G4double delta = (vmax - vcut)/G4double(n); |
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295 | |
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296 | G4double e0 = vcut; |
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297 | G4double xs; |
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298 | |
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299 | // integration |
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300 | for(G4int l=0; l<n; l++) { |
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301 | |
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302 | for(G4int i=0; i<8; i++) { |
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303 | |
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304 | G4double eg = exp(e0 + xgi[i]*delta)*totalEnergy; |
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305 | |
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306 | if(totalEnergy > energyThresholdLPM) { |
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307 | xs = ComputeRelDXSectionPerAtom(eg); |
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308 | } else { |
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309 | xs = ComputeDXSectionPerAtom(eg); |
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310 | } |
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311 | cross += wgi[i]*xs/(1.0 + densityCorr/(eg*eg)); |
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312 | } |
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313 | e0 += delta; |
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314 | } |
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315 | |
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316 | cross *= delta; |
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317 | |
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318 | return cross; |
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319 | } |
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320 | |
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321 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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322 | void G4eBremsstrahlungRelModel::CalcLPMFunctions(G4double k) |
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323 | { |
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324 | // *** calculate lpm variable s & sprime *** |
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325 | // Klein eqs. (78) & (79) |
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326 | G4double sprime = sqrt(0.125*k*lpmEnergy/(totalEnergy*(totalEnergy-k))); |
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327 | |
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328 | G4double s1 = preS1*z23; |
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329 | G4double logS1 = 2./3.*lnZ-2.*facFel; |
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330 | G4double logTS1 = logTwo+logS1; |
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331 | |
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332 | xiLPM = 2.; |
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333 | |
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334 | if (sprime>1) |
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335 | xiLPM = 1.; |
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336 | else if (sprime>sqrt(2.)*s1) { |
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337 | G4double h = log(sprime)/logTS1; |
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338 | xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1; |
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339 | } |
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340 | |
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341 | G4double s = sprime/sqrt(xiLPM); |
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342 | |
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343 | // *** merging with density effect*** should be only necessary in region "close to" kp, e.g. k<100*kp |
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344 | // using Ter-Mikaelian eq. (20.9) |
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345 | G4double k2 = k*k; |
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346 | s = s * (1 + (densityCorr/k2) ); |
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347 | |
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348 | // recalculate Xi using modified s above |
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349 | // Klein eq. (75) |
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350 | xiLPM = 1.; |
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351 | if (s<=s1) xiLPM = 2.; |
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352 | else if ( (s1<s) && (s<=1) ) xiLPM = 1. + log(s)/logS1; |
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353 | |
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354 | |
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355 | // *** calculate supression functions phi and G *** |
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356 | // Klein eqs. (77) |
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357 | G4double s2=s*s; |
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358 | G4double s3=s*s2; |
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359 | G4double s4=s2*s2; |
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360 | |
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361 | if (s<0.1) { |
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362 | // high suppression limit |
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363 | phiLPM = 6.*s - 18.84955592153876*s2 + 39.47841760435743*s3 |
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364 | - 57.69873135166053*s4; |
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365 | gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4; |
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366 | } |
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367 | else if (s<1.9516) { |
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368 | // intermediate suppression |
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369 | // using eq.77 approxim. valid s<2. |
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370 | phiLPM = 1.-exp(-6.*s*(1.+(3.-pi)*s) |
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371 | +s3/(0.623+0.795*s+0.658*s2)); |
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372 | if (s<0.415827397755) { |
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373 | // using eq.77 approxim. valid 0.07<s<2 |
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374 | G4double psiLPM = 1-exp(-4*s-8*s2/(1+3.936*s+4.97*s2-0.05*s3+7.50*s4)); |
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375 | gLPM = 3*psiLPM-2*phiLPM; |
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376 | } |
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377 | else { |
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378 | // using alternative parametrisiation |
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379 | G4double pre = -0.16072300849123999 + s*3.7550300067531581 + s2*-1.7981383069010097 |
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380 | + s3*0.67282686077812381 + s4*-0.1207722909879257; |
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381 | gLPM = tanh(pre); |
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382 | } |
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383 | } |
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384 | else { |
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385 | // low suppression limit valid s>2. |
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386 | phiLPM = 1. - 0.0119048/s4; |
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387 | gLPM = 1. - 0.0230655/s4; |
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388 | } |
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389 | |
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390 | // *** make sure suppression is smaller than 1 *** |
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391 | // *** caused by Migdal approximation in xi *** |
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392 | if (xiLPM*phiLPM>1. || s>0.57) xiLPM=1./phiLPM; |
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393 | } |
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394 | |
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395 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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396 | |
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397 | |
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398 | G4double G4eBremsstrahlungRelModel::ComputeRelDXSectionPerAtom(G4double gammaEnergy) |
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399 | // Ultra relativistic model |
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400 | // only valid for very high energies, but includes LPM suppression |
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401 | // * complete screening |
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402 | { |
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403 | if(gammaEnergy < 0.0) return 0.0; |
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404 | |
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405 | G4double y = gammaEnergy/totalEnergy; |
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406 | G4double y2 = y*y*.25; |
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407 | G4double yone2 = (1.-y+2.*y2); |
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408 | |
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409 | // ** form factors complete screening case ** |
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410 | |
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411 | // ** calc LPM functions -- include ter-mikaelian merging with density effect ** |
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412 | // G4double xiLPM, gLPM, phiLPM; // to be made member variables !!! |
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413 | CalcLPMFunctions(gammaEnergy); |
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414 | |
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415 | G4double mainLPM = xiLPM*(y2 * gLPM + yone2*phiLPM) * ( (Fel-fCoulomb) + Finel/currentZ ); |
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416 | G4double secondTerm = (1.-y)/12.*(1.+1./currentZ); |
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417 | |
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418 | G4double cross = mainLPM+secondTerm; |
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419 | return cross; |
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420 | } |
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421 | |
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422 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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423 | |
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424 | G4double G4eBremsstrahlungRelModel::ComputeDXSectionPerAtom(G4double gammaEnergy) |
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425 | // Relativistic model |
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426 | // only valid for high energies (and if LPM suppression does not play a role) |
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427 | // * screening according to thomas-fermi-Model (only valid for Z>5) |
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428 | // * no LPM effect |
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429 | { |
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430 | |
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431 | if(gammaEnergy < 0.0) return 0.0; |
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432 | |
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433 | G4double y = gammaEnergy/totalEnergy; |
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434 | |
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435 | G4double main=0.,secondTerm=0.; |
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436 | |
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437 | if (use_completescreening|| currentZ<5) { |
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438 | // ** form factors complete screening case ** |
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439 | main = (3./4.*y*y - y + 1.) * ( (Fel-fCoulomb) + Finel/currentZ ); |
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440 | secondTerm = (1.-y)/12.*(1.+1./currentZ); |
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441 | } |
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442 | else { |
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443 | // ** intermediate screening using Thomas-Fermi FF from Tsai only valid for Z>=5** |
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444 | G4double dd=100.*electron_mass_c2*y/(totalEnergy-gammaEnergy); |
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445 | G4double gg=dd*z13; |
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446 | G4double eps=dd*z23; |
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447 | G4double phi1=Phi1(gg,currentZ), phi1m2=Phi1M2(gg,currentZ); |
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448 | G4double psi1=Psi1(eps,currentZ), psi1m2=Psi1M2(eps,currentZ); |
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449 | |
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450 | main = (3./4.*y*y - y + 1.) * ( (0.25*phi1-1./3.*lnZ-fCoulomb) + (0.25*psi1-2./3.*lnZ)/currentZ ); |
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451 | secondTerm = (1.-y)/8.*(phi1m2+psi1m2/currentZ); |
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452 | } |
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453 | G4double cross = main+secondTerm; |
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454 | return cross; |
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455 | } |
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456 | |
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457 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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458 | |
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459 | void G4eBremsstrahlungRelModel::SampleSecondaries( |
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460 | std::vector<G4DynamicParticle*>* vdp, |
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461 | const G4MaterialCutsCouple* couple, |
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462 | const G4DynamicParticle* dp, |
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463 | G4double cutEnergy, |
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464 | G4double maxEnergy) |
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465 | { |
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466 | G4double kineticEnergy = dp->GetKineticEnergy(); |
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467 | if(kineticEnergy < lowKinEnergy) return; |
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468 | G4double cut = std::min(cutEnergy, kineticEnergy); |
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469 | G4double emax = std::min(maxEnergy, kineticEnergy); |
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470 | if(cut >= emax) return; |
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471 | |
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472 | SetupForMaterial(particle, couple->GetMaterial(),kineticEnergy); |
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473 | |
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474 | const G4Element* elm = |
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475 | SelectRandomAtom(couple,particle,kineticEnergy,cut,emax); |
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476 | SetCurrentElement(elm->GetZ()); |
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477 | |
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478 | kinEnergy = kineticEnergy; |
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479 | totalEnergy = kineticEnergy + particleMass; |
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480 | densityCorr = densityFactor*totalEnergy*totalEnergy; |
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481 | G4ThreeVector direction = dp->GetMomentumDirection(); |
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482 | |
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483 | // G4double fmax= fMax; |
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484 | G4bool highe = true; |
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485 | if(totalEnergy < energyThresholdLPM) highe = false; |
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486 | |
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487 | G4double xmin = log(cut*cut + densityCorr); |
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488 | G4double xmax = log(emax*emax + densityCorr); |
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489 | G4double gammaEnergy, f, x; |
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490 | |
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491 | do { |
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492 | x = exp(xmin + G4UniformRand()*(xmax - xmin)) - densityCorr; |
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493 | if(x < 0.0) x = 0.0; |
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494 | gammaEnergy = sqrt(x); |
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495 | if(highe) f = ComputeRelDXSectionPerAtom(gammaEnergy); |
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496 | else f = ComputeDXSectionPerAtom(gammaEnergy); |
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497 | |
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498 | if ( f > fMax ) { |
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499 | G4cout << "### G4eBremsstrahlungRelModel Warning: Majoranta exceeded! " |
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500 | << f << " > " << fMax |
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501 | << " Egamma(MeV)= " << gammaEnergy |
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502 | << " E(mEV)= " << kineticEnergy |
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503 | << G4endl; |
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504 | } |
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505 | |
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506 | } while (f < fMax*G4UniformRand()); |
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507 | |
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508 | // |
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509 | // angles of the emitted gamma. ( Z - axis along the parent particle) |
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510 | // |
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511 | // universal distribution suggested by L. Urban |
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512 | // (Geant3 manual (1993) Phys211), |
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513 | // derived from Tsai distribution (Rev Mod Phys 49,421(1977)) |
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514 | |
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515 | G4double u; |
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516 | const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ; |
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517 | |
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518 | if (9./(9.+d) > G4UniformRand()) u = - log(G4UniformRand()*G4UniformRand())/a1; |
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519 | else u = - log(G4UniformRand()*G4UniformRand())/a2; |
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520 | |
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521 | G4double theta = u*particleMass/totalEnergy; |
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522 | G4double sint = sin(theta); |
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523 | G4double phi = twopi * G4UniformRand(); |
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524 | G4ThreeVector gammaDirection(sint*cos(phi),sint*sin(phi), cos(theta)); |
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525 | gammaDirection.rotateUz(direction); |
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526 | |
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527 | // create G4DynamicParticle object for the Gamma |
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528 | G4DynamicParticle* g = new G4DynamicParticle(theGamma,gammaDirection, |
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529 | gammaEnergy); |
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530 | vdp->push_back(g); |
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531 | |
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532 | G4double totMomentum = sqrt(kineticEnergy*(totalEnergy + electron_mass_c2)); |
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533 | G4ThreeVector dir = totMomentum*direction - gammaEnergy*gammaDirection; |
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534 | direction = dir.unit(); |
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535 | |
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536 | // energy of primary |
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537 | G4double finalE = kineticEnergy - gammaEnergy; |
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538 | |
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539 | // stop tracking and create new secondary instead of primary |
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540 | if(gammaEnergy > SecondaryThreshold()) { |
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541 | fParticleChange->ProposeTrackStatus(fStopAndKill); |
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542 | fParticleChange->SetProposedKineticEnergy(0.0); |
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543 | G4DynamicParticle* el = |
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544 | new G4DynamicParticle(const_cast<G4ParticleDefinition*>(particle), |
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545 | direction, finalE); |
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546 | vdp->push_back(el); |
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547 | |
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548 | // continue tracking |
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549 | } else { |
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550 | fParticleChange->SetProposedMomentumDirection(direction); |
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551 | fParticleChange->SetProposedKineticEnergy(finalE); |
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552 | } |
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553 | } |
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554 | |
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555 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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556 | |
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557 | |
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