1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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14 | // * regarding this software system or assume any liability for its * |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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18 | // * This code implementation is the result of the scientific and * |
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19 | // * technical work of the GEANT4 collaboration. * |
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23 | // * acceptance of all terms of the Geant4 Software license. * |
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24 | // ******************************************************************** |
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25 | // |
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26 | // |
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27 | // $Id: G4NuclNuclDiffuseElastic.hh,v 1.13 2010/09/28 16:28:58 gcosmo Exp $ |
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28 | // GEANT4 tag $Name: geant4-09-03-ref-09 $ |
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29 | // |
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30 | // |
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31 | // G4 Model: optical elastic scattering with 4-momentum balance |
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32 | // |
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33 | // Class Description |
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34 | // Final state production model for nucleus-nucleus elastic scattering; |
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35 | // Coulomb amplitude is not considered as correction |
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36 | // (as in G4DiffuseElastic) |
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37 | // Class Description - End |
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38 | // |
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39 | // |
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40 | // 17.03.09 V. Grichine implementation for Coulomb elastic scattering |
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41 | |
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42 | |
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43 | #ifndef G4NuclNuclDiffuseElastic_h |
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44 | #define G4NuclNuclDiffuseElastic_h 1 |
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45 | |
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46 | #include "globals.hh" |
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47 | #include <complex> |
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48 | #include "G4Integrator.hh" |
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49 | |
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50 | #include "G4HadronicInteraction.hh" |
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51 | #include "G4HadProjectile.hh" |
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52 | #include "G4Nucleus.hh" |
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53 | |
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54 | using namespace std; |
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55 | |
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56 | class G4ParticleDefinition; |
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57 | class G4PhysicsTable; |
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58 | class G4PhysicsLogVector; |
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59 | |
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60 | class G4NuclNuclDiffuseElastic : public G4HadronicInteraction |
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61 | { |
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62 | public: |
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63 | |
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64 | G4NuclNuclDiffuseElastic(); |
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65 | |
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66 | G4NuclNuclDiffuseElastic(const G4ParticleDefinition* aParticle); |
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67 | |
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68 | |
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69 | |
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70 | |
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71 | |
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72 | virtual ~G4NuclNuclDiffuseElastic(); |
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73 | |
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74 | void Initialise(); |
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75 | |
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76 | void InitialiseOnFly(G4double Z, G4double A); |
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77 | |
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78 | void BuildAngleTable(); |
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79 | |
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80 | |
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81 | G4HadFinalState * ApplyYourself(const G4HadProjectile & aTrack, |
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82 | G4Nucleus & targetNucleus); |
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83 | |
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84 | |
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85 | void SetPlabLowLimit(G4double value); |
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86 | |
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87 | void SetHEModelLowLimit(G4double value); |
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88 | |
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89 | void SetQModelLowLimit(G4double value); |
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90 | |
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91 | void SetLowestEnergyLimit(G4double value); |
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92 | |
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93 | void SetRecoilKinEnergyLimit(G4double value); |
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94 | |
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95 | G4double SampleT(const G4ParticleDefinition* aParticle, |
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96 | G4double p, G4double A); |
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97 | |
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98 | G4double SampleTableT(const G4ParticleDefinition* aParticle, |
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99 | G4double p, G4double Z, G4double A); |
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100 | |
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101 | G4double SampleThetaCMS(const G4ParticleDefinition* aParticle, G4double p, G4double A); |
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102 | |
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103 | G4double SampleTableThetaCMS(const G4ParticleDefinition* aParticle, G4double p, |
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104 | G4double Z, G4double A); |
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105 | |
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106 | G4double GetScatteringAngle(G4int iMomentum, G4int iAngle, G4double position); |
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107 | |
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108 | G4double SampleThetaLab(const G4HadProjectile* aParticle, |
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109 | G4double tmass, G4double A); |
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110 | |
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111 | G4double GetDiffuseElasticXsc( const G4ParticleDefinition* particle, |
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112 | G4double theta, |
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113 | G4double momentum, |
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114 | G4double A ); |
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115 | |
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116 | G4double GetInvElasticXsc( const G4ParticleDefinition* particle, |
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117 | G4double theta, |
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118 | G4double momentum, |
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119 | G4double A, G4double Z ); |
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120 | |
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121 | G4double GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle, |
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122 | G4double theta, |
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123 | G4double momentum, |
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124 | G4double A, G4double Z ); |
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125 | |
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126 | G4double GetInvElasticSumXsc( const G4ParticleDefinition* particle, |
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127 | G4double tMand, |
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128 | G4double momentum, |
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129 | G4double A, G4double Z ); |
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130 | |
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131 | G4double IntegralElasticProb( const G4ParticleDefinition* particle, |
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132 | G4double theta, |
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133 | G4double momentum, |
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134 | G4double A ); |
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135 | |
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136 | |
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137 | G4double GetCoulombElasticXsc( const G4ParticleDefinition* particle, |
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138 | G4double theta, |
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139 | G4double momentum, |
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140 | G4double Z ); |
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141 | |
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142 | G4double GetInvCoulombElasticXsc( const G4ParticleDefinition* particle, |
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143 | G4double tMand, |
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144 | G4double momentum, |
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145 | G4double A, G4double Z ); |
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146 | |
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147 | G4double GetCoulombTotalXsc( const G4ParticleDefinition* particle, |
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148 | G4double momentum, G4double Z ); |
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149 | |
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150 | G4double GetCoulombIntegralXsc( const G4ParticleDefinition* particle, |
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151 | G4double momentum, G4double Z, |
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152 | G4double theta1, G4double theta2 ); |
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153 | |
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154 | |
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155 | G4double CalculateParticleBeta( const G4ParticleDefinition* particle, |
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156 | G4double momentum ); |
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157 | |
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158 | G4double CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 ); |
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159 | |
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160 | G4double CalculateAm( G4double momentum, G4double n, G4double Z); |
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161 | |
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162 | G4double CalculateNuclearRad( G4double A); |
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163 | |
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164 | G4double ThetaCMStoThetaLab(const G4DynamicParticle* aParticle, |
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165 | G4double tmass, G4double thetaCMS); |
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166 | |
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167 | G4double ThetaLabToThetaCMS(const G4DynamicParticle* aParticle, |
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168 | G4double tmass, G4double thetaLab); |
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169 | |
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170 | void TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom, |
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171 | G4double Z, G4double A); |
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172 | |
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173 | |
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174 | |
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175 | G4double BesselJzero(G4double z); |
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176 | G4double BesselJone(G4double z); |
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177 | G4double DampFactor(G4double z); |
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178 | G4double BesselOneByArg(G4double z); |
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179 | |
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180 | G4double GetDiffElasticProb(G4double theta); |
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181 | G4double GetDiffElasticSumProb(G4double theta); |
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182 | G4double GetDiffElasticSumProbA(G4double alpha); |
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183 | G4double GetIntegrandFunction(G4double theta); |
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184 | |
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185 | G4double GetNuclearRadius(){return fNuclearRadius;}; |
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186 | |
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187 | |
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188 | // Technical math functions for strong Coulomb contribution |
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189 | |
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190 | G4complex GammaLogarithm(G4complex xx); |
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191 | G4complex GammaLogB2n(G4complex xx); |
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192 | |
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193 | G4double GetErf(G4double x); |
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194 | |
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195 | G4complex GetErfcComp(G4complex z, G4int nMax); |
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196 | G4complex GetErfcSer(G4complex z, G4int nMax); |
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197 | G4complex GetErfcInt(G4complex z); // , G4int nMax); |
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198 | |
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199 | G4complex GetErfComp(G4complex z, G4int nMax); // AandS algorithm != Ser, Int |
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200 | G4complex GetErfSer(G4complex z, G4int nMax); |
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201 | |
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202 | G4double GetExpCos(G4double x); |
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203 | G4double GetExpSin(G4double x); |
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204 | G4complex GetErfInt(G4complex z); // , G4int nMax); |
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205 | |
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206 | G4double GetLegendrePol(G4int n, G4double x); |
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207 | |
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208 | G4complex TestErfcComp(G4complex z, G4int nMax); |
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209 | G4complex TestErfcSer(G4complex z, G4int nMax); |
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210 | G4complex TestErfcInt(G4complex z); // , G4int nMax); |
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211 | |
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212 | G4complex CoulombAmplitude(G4double theta); |
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213 | void CalculateCoulombPhaseZero(); |
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214 | G4double CalculateCoulombPhase(G4int n); |
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215 | void CalculateRutherfordAnglePar(); |
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216 | |
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217 | G4double ProfileNear(G4double theta); |
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218 | G4double ProfileFar(G4double theta); |
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219 | |
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220 | G4complex PhaseNear(G4double theta); |
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221 | G4complex PhaseFar(G4double theta); |
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222 | |
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223 | G4complex GammaLess(G4double theta); |
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224 | G4complex GammaMore(G4double theta); |
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225 | |
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226 | G4complex AmplitudeNear(G4double theta); |
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227 | G4complex AmplitudeFar(G4double theta); |
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228 | G4complex Amplitude(G4double theta); |
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229 | G4double AmplitudeMod2(G4double theta); |
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230 | |
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231 | G4complex AmplitudeGla(G4double theta); |
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232 | G4double AmplitudeGlaMod2(G4double theta); |
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233 | |
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234 | G4complex AmplitudeGG(G4double theta); |
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235 | G4double AmplitudeGGMod2(G4double theta); |
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236 | |
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237 | void InitParameters(const G4ParticleDefinition* theParticle, |
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238 | G4double partMom, G4double Z, G4double A); |
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239 | |
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240 | void InitParametersGla(const G4DynamicParticle* aParticle, |
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241 | G4double partMom, G4double Z, G4double A); |
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242 | |
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243 | G4double GetHadronNucleonXscNS( G4ParticleDefinition* pParticle, |
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244 | G4double pTkin, |
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245 | G4ParticleDefinition* tParticle); |
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246 | |
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247 | G4double CalcMandelstamS( const G4double mp , |
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248 | const G4double mt , |
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249 | const G4double Plab ); |
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250 | |
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251 | G4double GetProfileLambda(){return fProfileLambda;}; |
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252 | |
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253 | void SetProfileLambda(G4double pl) {fProfileLambda = pl;}; |
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254 | void SetProfileDelta(G4double pd) {fProfileDelta = pd;}; |
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255 | void SetProfileAlpha(G4double pa){fProfileAlpha = pa;}; |
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256 | void SetCofLambda(G4double pa){fCofLambda = pa;}; |
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257 | void SetCofAlpha(G4double pa){fCofAlpha = pa;}; |
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258 | void SetCofDelta(G4double pa){fCofDelta = pa;}; |
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259 | void SetCofPhase(G4double pa){fCofPhase = pa;}; |
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260 | void SetCofFar(G4double pa){fCofFar = pa;}; |
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261 | void SetEtaRatio(G4double pa){fEtaRatio = pa;}; |
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262 | void SetMaxL(G4int l){fMaxL = l;}; |
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263 | |
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264 | private: |
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265 | |
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266 | |
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267 | G4ParticleDefinition* theProton; |
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268 | G4ParticleDefinition* theNeutron; |
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269 | G4ParticleDefinition* theDeuteron; |
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270 | G4ParticleDefinition* theAlpha; |
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271 | |
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272 | const G4ParticleDefinition* thePionPlus; |
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273 | const G4ParticleDefinition* thePionMinus; |
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274 | |
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275 | G4double lowEnergyRecoilLimit; |
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276 | G4double lowEnergyLimitHE; |
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277 | G4double lowEnergyLimitQ; |
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278 | G4double lowestEnergyLimit; |
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279 | G4double plabLowLimit; |
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280 | |
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281 | G4int fEnergyBin; |
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282 | G4int fAngleBin; |
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283 | |
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284 | G4PhysicsLogVector* fEnergyVector; |
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285 | G4PhysicsTable* fAngleTable; |
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286 | std::vector<G4PhysicsTable*> fAngleBank; |
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287 | |
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288 | std::vector<G4double> fElementNumberVector; |
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289 | std::vector<G4String> fElementNameVector; |
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290 | |
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291 | const G4ParticleDefinition* fParticle; |
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292 | G4double fWaveVector; |
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293 | G4double fAtomicWeight; |
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294 | G4double fAtomicNumber; |
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295 | |
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296 | G4double fNuclearRadius1; |
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297 | G4double fNuclearRadius2; |
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298 | G4double fNuclearRadius; |
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299 | G4double fNuclearRadiusSquare; |
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300 | |
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301 | G4double fBeta; |
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302 | G4double fZommerfeld; |
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303 | G4double fAm; |
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304 | G4bool fAddCoulomb; |
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305 | |
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306 | G4double fCoulombPhase0; |
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307 | G4double fHalfRutThetaTg; |
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308 | G4double fHalfRutThetaTg2; |
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309 | G4double fRutherfordTheta; |
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310 | |
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311 | G4double fProfileLambda; |
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312 | G4double fProfileDelta; |
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313 | G4double fProfileAlpha; |
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314 | |
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315 | G4double fCofLambda; |
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316 | G4double fCofAlpha; |
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317 | G4double fCofDelta; |
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318 | G4double fCofPhase; |
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319 | G4double fCofFar; |
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320 | |
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321 | G4int fMaxL; |
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322 | G4double fSumSigma; |
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323 | G4double fEtaRatio; |
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324 | |
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325 | G4double fReZ; |
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326 | |
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327 | }; |
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328 | |
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329 | |
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330 | inline void G4NuclNuclDiffuseElastic::SetRecoilKinEnergyLimit(G4double value) |
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331 | { |
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332 | lowEnergyRecoilLimit = value; |
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333 | } |
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334 | |
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335 | inline void G4NuclNuclDiffuseElastic::SetPlabLowLimit(G4double value) |
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336 | { |
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337 | plabLowLimit = value; |
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338 | } |
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339 | |
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340 | inline void G4NuclNuclDiffuseElastic::SetHEModelLowLimit(G4double value) |
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341 | { |
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342 | lowEnergyLimitHE = value; |
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343 | } |
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344 | |
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345 | inline void G4NuclNuclDiffuseElastic::SetQModelLowLimit(G4double value) |
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346 | { |
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347 | lowEnergyLimitQ = value; |
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348 | } |
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349 | |
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350 | inline void G4NuclNuclDiffuseElastic::SetLowestEnergyLimit(G4double value) |
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351 | { |
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352 | lowestEnergyLimit = value; |
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353 | } |
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354 | |
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355 | |
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356 | ///////////////////////////////////////////////////////////// |
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357 | // |
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358 | // Bessel J0 function based on rational approximation from |
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359 | // J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141 |
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360 | |
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361 | inline G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value) |
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362 | { |
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363 | G4double modvalue, value2, fact1, fact2, arg, shift, bessel; |
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364 | |
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365 | modvalue = fabs(value); |
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366 | |
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367 | if ( value < 8.0 && value > -8.0 ) |
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368 | { |
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369 | value2 = value*value; |
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370 | |
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371 | fact1 = 57568490574.0 + value2*(-13362590354.0 |
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372 | + value2*( 651619640.7 |
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373 | + value2*(-11214424.18 |
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374 | + value2*( 77392.33017 |
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375 | + value2*(-184.9052456 ) ) ) ) ); |
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376 | |
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377 | fact2 = 57568490411.0 + value2*( 1029532985.0 |
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378 | + value2*( 9494680.718 |
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379 | + value2*(59272.64853 |
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380 | + value2*(267.8532712 |
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381 | + value2*1.0 ) ) ) ); |
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382 | |
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383 | bessel = fact1/fact2; |
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384 | } |
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385 | else |
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386 | { |
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387 | arg = 8.0/modvalue; |
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388 | |
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389 | value2 = arg*arg; |
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390 | |
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391 | shift = modvalue-0.785398164; |
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392 | |
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393 | fact1 = 1.0 + value2*(-0.1098628627e-2 |
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394 | + value2*(0.2734510407e-4 |
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395 | + value2*(-0.2073370639e-5 |
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396 | + value2*0.2093887211e-6 ) ) ); |
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397 | |
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398 | fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3 |
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399 | + value2*(-0.6911147651e-5 |
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400 | + value2*(0.7621095161e-6 |
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401 | - value2*0.934945152e-7 ) ) ); |
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402 | |
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403 | bessel = sqrt(0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2 ); |
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404 | } |
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405 | return bessel; |
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406 | } |
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407 | |
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408 | ///////////////////////////////////////////////////////////// |
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409 | // |
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410 | // Bessel J1 function based on rational approximation from |
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411 | // J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141 |
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412 | |
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413 | inline G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value) |
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414 | { |
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415 | G4double modvalue, value2, fact1, fact2, arg, shift, bessel; |
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416 | |
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417 | modvalue = fabs(value); |
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418 | |
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419 | if ( modvalue < 8.0 ) |
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420 | { |
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421 | value2 = value*value; |
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422 | |
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423 | fact1 = value*(72362614232.0 + value2*(-7895059235.0 |
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424 | + value2*( 242396853.1 |
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425 | + value2*(-2972611.439 |
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426 | + value2*( 15704.48260 |
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427 | + value2*(-30.16036606 ) ) ) ) ) ); |
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428 | |
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429 | fact2 = 144725228442.0 + value2*(2300535178.0 |
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430 | + value2*(18583304.74 |
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431 | + value2*(99447.43394 |
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432 | + value2*(376.9991397 |
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433 | + value2*1.0 ) ) ) ); |
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434 | bessel = fact1/fact2; |
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435 | } |
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436 | else |
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437 | { |
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438 | arg = 8.0/modvalue; |
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439 | |
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440 | value2 = arg*arg; |
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441 | |
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442 | shift = modvalue - 2.356194491; |
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443 | |
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444 | fact1 = 1.0 + value2*( 0.183105e-2 |
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445 | + value2*(-0.3516396496e-4 |
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446 | + value2*(0.2457520174e-5 |
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447 | + value2*(-0.240337019e-6 ) ) ) ); |
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448 | |
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449 | fact2 = 0.04687499995 + value2*(-0.2002690873e-3 |
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450 | + value2*( 0.8449199096e-5 |
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451 | + value2*(-0.88228987e-6 |
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452 | + value2*0.105787412e-6 ) ) ); |
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453 | |
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454 | bessel = sqrt( 0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2); |
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455 | |
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456 | if (value < 0.0) bessel = -bessel; |
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457 | } |
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458 | return bessel; |
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459 | } |
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460 | |
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461 | //////////////////////////////////////////////////////////////////// |
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462 | // |
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463 | // damp factor in diffraction x/sh(x), x was already *pi |
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464 | |
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465 | inline G4double G4NuclNuclDiffuseElastic::DampFactor(G4double x) |
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466 | { |
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467 | G4double df; |
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468 | G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials |
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469 | |
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470 | // x *= pi; |
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471 | |
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472 | if( std::fabs(x) < 0.01 ) |
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473 | { |
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474 | df = 1./(1. + x/f2 + x*x/f3 + x*x*x/f4); |
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475 | } |
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476 | else |
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477 | { |
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478 | df = x/std::sinh(x); |
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479 | } |
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480 | return df; |
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481 | } |
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482 | |
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483 | |
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484 | //////////////////////////////////////////////////////////////////// |
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485 | // |
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486 | // return J1(x)/x with special case for small x |
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487 | |
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488 | inline G4double G4NuclNuclDiffuseElastic::BesselOneByArg(G4double x) |
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489 | { |
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490 | G4double x2, result; |
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491 | |
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492 | if( std::fabs(x) < 0.01 ) |
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493 | { |
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494 | x *= 0.5; |
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495 | x2 = x*x; |
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496 | result = 2. - x2 + x2*x2/6.; |
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497 | } |
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498 | else |
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499 | { |
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500 | result = BesselJone(x)/x; |
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501 | } |
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502 | return result; |
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503 | } |
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504 | |
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505 | //////////////////////////////////////////////////////////////////// |
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506 | // |
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507 | // return particle beta |
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508 | |
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509 | inline G4double G4NuclNuclDiffuseElastic::CalculateParticleBeta( const G4ParticleDefinition* particle, |
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510 | G4double momentum ) |
---|
511 | { |
---|
512 | G4double mass = particle->GetPDGMass(); |
---|
513 | G4double a = momentum/mass; |
---|
514 | fBeta = a/std::sqrt(1+a*a); |
---|
515 | |
---|
516 | return fBeta; |
---|
517 | } |
---|
518 | |
---|
519 | //////////////////////////////////////////////////////////////////// |
---|
520 | // |
---|
521 | // return Zommerfeld parameter for Coulomb scattering |
---|
522 | |
---|
523 | inline G4double G4NuclNuclDiffuseElastic::CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 ) |
---|
524 | { |
---|
525 | fZommerfeld = fine_structure_const*Z1*Z2/beta; |
---|
526 | |
---|
527 | return fZommerfeld; |
---|
528 | } |
---|
529 | |
---|
530 | //////////////////////////////////////////////////////////////////// |
---|
531 | // |
---|
532 | // return Wentzel correction for Coulomb scattering |
---|
533 | |
---|
534 | inline G4double G4NuclNuclDiffuseElastic::CalculateAm( G4double momentum, G4double n, G4double Z) |
---|
535 | { |
---|
536 | G4double k = momentum/hbarc; |
---|
537 | G4double ch = 1.13 + 3.76*n*n; |
---|
538 | G4double zn = 1.77*k*std::pow(Z,-1./3.)*Bohr_radius; |
---|
539 | G4double zn2 = zn*zn; |
---|
540 | fAm = ch/zn2; |
---|
541 | |
---|
542 | return fAm; |
---|
543 | } |
---|
544 | |
---|
545 | //////////////////////////////////////////////////////////////////// |
---|
546 | // |
---|
547 | // calculate nuclear radius for different atomic weights using different approximations |
---|
548 | |
---|
549 | inline G4double G4NuclNuclDiffuseElastic::CalculateNuclearRad( G4double A) |
---|
550 | { |
---|
551 | G4double r0, radius; |
---|
552 | |
---|
553 | if( A < 50. ) |
---|
554 | { |
---|
555 | if( A > 10. ) r0 = 1.16*( 1 - std::pow(A, -2./3.) )*fermi; // 1.08*fermi; |
---|
556 | else r0 = 1.1*fermi; |
---|
557 | |
---|
558 | radius = r0*std::pow(A, 1./3.); |
---|
559 | } |
---|
560 | else |
---|
561 | { |
---|
562 | r0 = 1.7*fermi; // 1.7*fermi; |
---|
563 | |
---|
564 | radius = r0*std::pow(A, 0.27); // 0.27); |
---|
565 | } |
---|
566 | return radius; |
---|
567 | } |
---|
568 | |
---|
569 | //////////////////////////////////////////////////////////////////// |
---|
570 | // |
---|
571 | // return Coulomb scattering differential xsc with Wentzel correction |
---|
572 | |
---|
573 | inline G4double G4NuclNuclDiffuseElastic::GetCoulombElasticXsc( const G4ParticleDefinition* particle, |
---|
574 | G4double theta, |
---|
575 | G4double momentum, |
---|
576 | G4double Z ) |
---|
577 | { |
---|
578 | G4double sinHalfTheta = std::sin(0.5*theta); |
---|
579 | G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta; |
---|
580 | G4double beta = CalculateParticleBeta( particle, momentum); |
---|
581 | G4double z = particle->GetPDGCharge(); |
---|
582 | G4double n = CalculateZommerfeld( beta, z, Z ); |
---|
583 | G4double am = CalculateAm( momentum, n, Z); |
---|
584 | G4double k = momentum/hbarc; |
---|
585 | G4double ch = 0.5*n/k; |
---|
586 | G4double ch2 = ch*ch; |
---|
587 | G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am); |
---|
588 | |
---|
589 | return xsc; |
---|
590 | } |
---|
591 | |
---|
592 | |
---|
593 | //////////////////////////////////////////////////////////////////// |
---|
594 | // |
---|
595 | // return Coulomb scattering total xsc with Wentzel correction |
---|
596 | |
---|
597 | inline G4double G4NuclNuclDiffuseElastic::GetCoulombTotalXsc( const G4ParticleDefinition* particle, |
---|
598 | G4double momentum, G4double Z ) |
---|
599 | { |
---|
600 | G4double beta = CalculateParticleBeta( particle, momentum); |
---|
601 | G4cout<<"beta = "<<beta<<G4endl; |
---|
602 | G4double z = particle->GetPDGCharge(); |
---|
603 | G4double n = CalculateZommerfeld( beta, z, Z ); |
---|
604 | G4cout<<"fZomerfeld = "<<n<<G4endl; |
---|
605 | G4double am = CalculateAm( momentum, n, Z); |
---|
606 | G4cout<<"cof Am = "<<am<<G4endl; |
---|
607 | G4double k = momentum/hbarc; |
---|
608 | G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl; |
---|
609 | G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl; |
---|
610 | G4double ch = n/k; |
---|
611 | G4double ch2 = ch*ch; |
---|
612 | G4double xsc = ch2*pi/(am +am*am); |
---|
613 | |
---|
614 | return xsc; |
---|
615 | } |
---|
616 | |
---|
617 | //////////////////////////////////////////////////////////////////// |
---|
618 | // |
---|
619 | // return Coulomb scattering xsc with Wentzel correction integrated between |
---|
620 | // theta1 and < theta2 |
---|
621 | |
---|
622 | inline G4double G4NuclNuclDiffuseElastic::GetCoulombIntegralXsc( const G4ParticleDefinition* particle, |
---|
623 | G4double momentum, G4double Z, |
---|
624 | G4double theta1, G4double theta2 ) |
---|
625 | { |
---|
626 | G4double c1 = std::cos(theta1); |
---|
627 | G4cout<<"c1 = "<<c1<<G4endl; |
---|
628 | G4double c2 = std::cos(theta2); |
---|
629 | G4cout<<"c2 = "<<c2<<G4endl; |
---|
630 | G4double beta = CalculateParticleBeta( particle, momentum); |
---|
631 | // G4cout<<"beta = "<<beta<<G4endl; |
---|
632 | G4double z = particle->GetPDGCharge(); |
---|
633 | G4double n = CalculateZommerfeld( beta, z, Z ); |
---|
634 | // G4cout<<"fZomerfeld = "<<n<<G4endl; |
---|
635 | G4double am = CalculateAm( momentum, n, Z); |
---|
636 | // G4cout<<"cof Am = "<<am<<G4endl; |
---|
637 | G4double k = momentum/hbarc; |
---|
638 | // G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl; |
---|
639 | // G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl; |
---|
640 | G4double ch = n/k; |
---|
641 | G4double ch2 = ch*ch; |
---|
642 | am *= 2.; |
---|
643 | G4double xsc = ch2*twopi*(c1-c2); |
---|
644 | xsc /= (1 - c1 + am)*(1 - c2 + am); |
---|
645 | |
---|
646 | return xsc; |
---|
647 | } |
---|
648 | |
---|
649 | /////////////////////////////////////////////////////////////////// |
---|
650 | // |
---|
651 | // For the calculation of arg Gamma(z) one needs complex extension |
---|
652 | // of ln(Gamma(z)) |
---|
653 | |
---|
654 | inline G4complex G4NuclNuclDiffuseElastic::GammaLogarithm(G4complex zz) |
---|
655 | { |
---|
656 | static G4double cof[6] = { 76.18009172947146, -86.50532032941677, |
---|
657 | 24.01409824083091, -1.231739572450155, |
---|
658 | 0.1208650973866179e-2, -0.5395239384953e-5 } ; |
---|
659 | register G4int j; |
---|
660 | G4complex z = zz - 1.0; |
---|
661 | G4complex tmp = z + 5.5; |
---|
662 | tmp -= (z + 0.5) * std::log(tmp); |
---|
663 | G4complex ser = G4complex(1.000000000190015,0.); |
---|
664 | |
---|
665 | for ( j = 0; j <= 5; j++ ) |
---|
666 | { |
---|
667 | z += 1.0; |
---|
668 | ser += cof[j]/z; |
---|
669 | } |
---|
670 | return -tmp + std::log(2.5066282746310005*ser); |
---|
671 | } |
---|
672 | |
---|
673 | /////////////////////////////////////////////////////////////////// |
---|
674 | // |
---|
675 | // For the calculation of arg Gamma(z) one needs complex extension |
---|
676 | // of ln(Gamma(z)) here is approximate algorithm |
---|
677 | |
---|
678 | inline G4complex G4NuclNuclDiffuseElastic::GammaLogB2n(G4complex z) |
---|
679 | { |
---|
680 | G4complex z1 = 12.*z; |
---|
681 | G4complex z2 = z*z; |
---|
682 | G4complex z3 = z2*z; |
---|
683 | G4complex z5 = z2*z3; |
---|
684 | G4complex z7 = z2*z5; |
---|
685 | |
---|
686 | z3 *= 360.; |
---|
687 | z5 *= 1260.; |
---|
688 | z7 *= 1680.; |
---|
689 | |
---|
690 | G4complex result = (z-0.5)*std::log(z)-z+0.5*std::log(twopi); |
---|
691 | result += 1./z1 - 1./z3 +1./z5 -1./z7; |
---|
692 | return result; |
---|
693 | } |
---|
694 | |
---|
695 | ///////////////////////////////////////////////////////////////// |
---|
696 | // |
---|
697 | // |
---|
698 | |
---|
699 | inline G4double G4NuclNuclDiffuseElastic::GetErf(G4double x) |
---|
700 | { |
---|
701 | G4double t, z, tmp, result; |
---|
702 | |
---|
703 | z = std::fabs(x); |
---|
704 | t = 1.0/(1.0+0.5*z); |
---|
705 | |
---|
706 | tmp = t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+ |
---|
707 | t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+ |
---|
708 | t*(-0.82215223+t*0.17087277))))))))); |
---|
709 | |
---|
710 | if( x >= 0.) result = 1. - tmp; |
---|
711 | else result = 1. + tmp; |
---|
712 | |
---|
713 | return result; |
---|
714 | } |
---|
715 | |
---|
716 | ///////////////////////////////////////////////////////////////// |
---|
717 | // |
---|
718 | // |
---|
719 | |
---|
720 | inline G4complex G4NuclNuclDiffuseElastic::GetErfcComp(G4complex z, G4int nMax) |
---|
721 | { |
---|
722 | G4complex erfcz = 1. - GetErfComp( z, nMax); |
---|
723 | return erfcz; |
---|
724 | } |
---|
725 | |
---|
726 | ///////////////////////////////////////////////////////////////// |
---|
727 | // |
---|
728 | // |
---|
729 | |
---|
730 | inline G4complex G4NuclNuclDiffuseElastic::GetErfcSer(G4complex z, G4int nMax) |
---|
731 | { |
---|
732 | G4complex erfcz = 1. - GetErfSer( z, nMax); |
---|
733 | return erfcz; |
---|
734 | } |
---|
735 | |
---|
736 | ///////////////////////////////////////////////////////////////// |
---|
737 | // |
---|
738 | // |
---|
739 | |
---|
740 | inline G4complex G4NuclNuclDiffuseElastic::GetErfcInt(G4complex z) // , G4int nMax) |
---|
741 | { |
---|
742 | G4complex erfcz = 1. - GetErfInt( z); // , nMax); |
---|
743 | return erfcz; |
---|
744 | } |
---|
745 | |
---|
746 | inline G4double G4NuclNuclDiffuseElastic::GetLegendrePol(G4int n, G4double theta) |
---|
747 | { |
---|
748 | G4double legPol, epsilon = 1.e-6; |
---|
749 | G4double x = std::cos(theta); |
---|
750 | |
---|
751 | if ( n < 0 ) legPol = 0.; |
---|
752 | else if( n == 0 ) legPol = 1.; |
---|
753 | else if( n == 1 ) legPol = x; |
---|
754 | else if( n == 2 ) legPol = (3.*x*x-1.)/2.; |
---|
755 | else if( n == 3 ) legPol = (5.*x*x*x-3.*x)/2.; |
---|
756 | else if( n == 4 ) legPol = (35.*x*x*x*x-30.*x*x+3.)/8.; |
---|
757 | else if( n == 5 ) legPol = (63.*x*x*x*x*x-70.*x*x*x+15.*x)/8.; |
---|
758 | else if( n == 6 ) legPol = (231.*x*x*x*x*x*x-315.*x*x*x*x+105.*x*x-5.)/16.; |
---|
759 | else |
---|
760 | { |
---|
761 | // legPol = ( (2*n-1)*x*GetLegendrePol(n-1,x) - (n-1)*GetLegendrePol(n-2,x) )/n; |
---|
762 | |
---|
763 | legPol = std::sqrt( 2./(n*pi*std::sin(theta+epsilon)) )*std::sin( (n+0.5)*theta+0.25*pi ); |
---|
764 | } |
---|
765 | return legPol; |
---|
766 | } |
---|
767 | |
---|
768 | |
---|
769 | |
---|
770 | ///////////////////////////////////////////////////////////////// |
---|
771 | // |
---|
772 | // |
---|
773 | |
---|
774 | inline G4complex G4NuclNuclDiffuseElastic::TestErfcComp(G4complex z, G4int nMax) |
---|
775 | { |
---|
776 | G4complex miz = G4complex( z.imag(), -z.real() ); |
---|
777 | G4complex erfcz = 1. - GetErfComp( miz, nMax); |
---|
778 | G4complex w = std::exp(-z*z)*erfcz; |
---|
779 | return w; |
---|
780 | } |
---|
781 | |
---|
782 | ///////////////////////////////////////////////////////////////// |
---|
783 | // |
---|
784 | // |
---|
785 | |
---|
786 | inline G4complex G4NuclNuclDiffuseElastic::TestErfcSer(G4complex z, G4int nMax) |
---|
787 | { |
---|
788 | G4complex miz = G4complex( z.imag(), -z.real() ); |
---|
789 | G4complex erfcz = 1. - GetErfSer( miz, nMax); |
---|
790 | G4complex w = std::exp(-z*z)*erfcz; |
---|
791 | return w; |
---|
792 | } |
---|
793 | |
---|
794 | ///////////////////////////////////////////////////////////////// |
---|
795 | // |
---|
796 | // |
---|
797 | |
---|
798 | inline G4complex G4NuclNuclDiffuseElastic::TestErfcInt(G4complex z) // , G4int nMax) |
---|
799 | { |
---|
800 | G4complex miz = G4complex( z.imag(), -z.real() ); |
---|
801 | G4complex erfcz = 1. - GetErfInt( miz); // , nMax); |
---|
802 | G4complex w = std::exp(-z*z)*erfcz; |
---|
803 | return w; |
---|
804 | } |
---|
805 | |
---|
806 | ///////////////////////////////////////////////////////////////// |
---|
807 | // |
---|
808 | // |
---|
809 | |
---|
810 | inline G4complex G4NuclNuclDiffuseElastic::GetErfComp(G4complex z, G4int nMax) |
---|
811 | { |
---|
812 | G4int n; |
---|
813 | G4double n2, cofn, shny, chny, fn, gn; |
---|
814 | |
---|
815 | G4double x = z.real(); |
---|
816 | G4double y = z.imag(); |
---|
817 | |
---|
818 | G4double outRe = 0., outIm = 0.; |
---|
819 | |
---|
820 | G4double twox = 2.*x; |
---|
821 | G4double twoxy = twox*y; |
---|
822 | G4double twox2 = twox*twox; |
---|
823 | |
---|
824 | G4double cof1 = std::exp(-x*x)/pi; |
---|
825 | |
---|
826 | G4double cos2xy = std::cos(twoxy); |
---|
827 | G4double sin2xy = std::sin(twoxy); |
---|
828 | |
---|
829 | G4double twoxcos2xy = twox*cos2xy; |
---|
830 | G4double twoxsin2xy = twox*sin2xy; |
---|
831 | |
---|
832 | for( n = 1; n <= nMax; n++) |
---|
833 | { |
---|
834 | n2 = n*n; |
---|
835 | |
---|
836 | cofn = std::exp(-0.5*n2)/(n2+twox2); // /(n2+0.5*twox2); |
---|
837 | |
---|
838 | chny = std::cosh(n*y); |
---|
839 | shny = std::sinh(n*y); |
---|
840 | |
---|
841 | fn = twox - twoxcos2xy*chny + n*sin2xy*shny; |
---|
842 | gn = twoxsin2xy*chny + n*cos2xy*shny; |
---|
843 | |
---|
844 | fn *= cofn; |
---|
845 | gn *= cofn; |
---|
846 | |
---|
847 | outRe += fn; |
---|
848 | outIm += gn; |
---|
849 | } |
---|
850 | outRe *= 2*cof1; |
---|
851 | outIm *= 2*cof1; |
---|
852 | |
---|
853 | if(std::abs(x) < 0.0001) |
---|
854 | { |
---|
855 | outRe += GetErf(x); |
---|
856 | outIm += cof1*y; |
---|
857 | } |
---|
858 | else |
---|
859 | { |
---|
860 | outRe += GetErf(x) + cof1*(1-cos2xy)/twox; |
---|
861 | outIm += cof1*sin2xy/twox; |
---|
862 | } |
---|
863 | return G4complex(outRe, outIm); |
---|
864 | } |
---|
865 | |
---|
866 | ///////////////////////////////////////////////////////////////// |
---|
867 | // |
---|
868 | // |
---|
869 | |
---|
870 | inline G4complex G4NuclNuclDiffuseElastic::GetErfSer(G4complex z, G4int nMax) |
---|
871 | { |
---|
872 | G4int n; |
---|
873 | G4double a =1., b = 1., tmp; |
---|
874 | G4complex sum = z, d = z; |
---|
875 | |
---|
876 | for( n = 1; n <= nMax; n++) |
---|
877 | { |
---|
878 | a *= 2.; |
---|
879 | b *= 2.*n +1.; |
---|
880 | d *= z*z; |
---|
881 | |
---|
882 | tmp = a/b; |
---|
883 | |
---|
884 | sum += tmp*d; |
---|
885 | } |
---|
886 | sum *= 2.*std::exp(-z*z)/std::sqrt(pi); |
---|
887 | |
---|
888 | return sum; |
---|
889 | } |
---|
890 | |
---|
891 | ///////////////////////////////////////////////////////////////////// |
---|
892 | |
---|
893 | inline G4double G4NuclNuclDiffuseElastic::GetExpCos(G4double x) |
---|
894 | { |
---|
895 | G4double result; |
---|
896 | |
---|
897 | result = std::exp(x*x-fReZ*fReZ); |
---|
898 | result *= std::cos(2.*x*fReZ); |
---|
899 | return result; |
---|
900 | } |
---|
901 | |
---|
902 | ///////////////////////////////////////////////////////////////////// |
---|
903 | |
---|
904 | inline G4double G4NuclNuclDiffuseElastic::GetExpSin(G4double x) |
---|
905 | { |
---|
906 | G4double result; |
---|
907 | |
---|
908 | result = std::exp(x*x-fReZ*fReZ); |
---|
909 | result *= std::sin(2.*x*fReZ); |
---|
910 | return result; |
---|
911 | } |
---|
912 | |
---|
913 | |
---|
914 | |
---|
915 | ///////////////////////////////////////////////////////////////// |
---|
916 | // |
---|
917 | // |
---|
918 | |
---|
919 | inline G4complex G4NuclNuclDiffuseElastic::GetErfInt(G4complex z) // , G4int nMax) |
---|
920 | { |
---|
921 | G4double outRe, outIm; |
---|
922 | |
---|
923 | G4double x = z.real(); |
---|
924 | G4double y = z.imag(); |
---|
925 | fReZ = x; |
---|
926 | |
---|
927 | G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral; |
---|
928 | |
---|
929 | outRe = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpSin, 0., y ); |
---|
930 | outIm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpCos, 0., y ); |
---|
931 | |
---|
932 | outRe *= 2./sqrt(pi); |
---|
933 | outIm *= 2./sqrt(pi); |
---|
934 | |
---|
935 | outRe += GetErf(x); |
---|
936 | |
---|
937 | return G4complex(outRe, outIm); |
---|
938 | } |
---|
939 | |
---|
940 | |
---|
941 | ///////////////////////////////////////////////////////////////// |
---|
942 | // |
---|
943 | // |
---|
944 | |
---|
945 | inline G4complex G4NuclNuclDiffuseElastic::CoulombAmplitude(G4double theta) |
---|
946 | { |
---|
947 | G4complex ca; |
---|
948 | |
---|
949 | G4double sinHalfTheta = std::sin(0.5*theta); |
---|
950 | G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta; |
---|
951 | sinHalfTheta2 += fAm; |
---|
952 | |
---|
953 | G4double order = 2.*fCoulombPhase0 - fZommerfeld*std::log(sinHalfTheta2); |
---|
954 | G4complex z = G4complex(0., order); |
---|
955 | ca = std::exp(z); |
---|
956 | |
---|
957 | ca *= -fZommerfeld/(2.*fWaveVector*sinHalfTheta2); |
---|
958 | |
---|
959 | return ca; |
---|
960 | } |
---|
961 | |
---|
962 | ///////////////////////////////////////////////////////////////// |
---|
963 | // |
---|
964 | // |
---|
965 | |
---|
966 | |
---|
967 | inline void G4NuclNuclDiffuseElastic::CalculateCoulombPhaseZero() |
---|
968 | { |
---|
969 | G4complex z = G4complex(1,fZommerfeld); |
---|
970 | // G4complex gammalog = GammaLogarithm(z); |
---|
971 | G4complex gammalog = GammaLogB2n(z); |
---|
972 | fCoulombPhase0 = gammalog.imag(); |
---|
973 | } |
---|
974 | |
---|
975 | ///////////////////////////////////////////////////////////////// |
---|
976 | // |
---|
977 | // |
---|
978 | |
---|
979 | |
---|
980 | inline G4double G4NuclNuclDiffuseElastic::CalculateCoulombPhase(G4int n) |
---|
981 | { |
---|
982 | G4complex z = G4complex(1. + n, fZommerfeld); |
---|
983 | // G4complex gammalog = GammaLogarithm(z); |
---|
984 | G4complex gammalog = GammaLogB2n(z); |
---|
985 | return gammalog.imag(); |
---|
986 | } |
---|
987 | |
---|
988 | |
---|
989 | ///////////////////////////////////////////////////////////////// |
---|
990 | // |
---|
991 | // |
---|
992 | |
---|
993 | |
---|
994 | inline void G4NuclNuclDiffuseElastic::CalculateRutherfordAnglePar() |
---|
995 | { |
---|
996 | fHalfRutThetaTg = fZommerfeld/fProfileLambda; // (fWaveVector*fNuclearRadius); |
---|
997 | fRutherfordTheta = 2.*std::atan(fHalfRutThetaTg); |
---|
998 | fHalfRutThetaTg2 = fHalfRutThetaTg*fHalfRutThetaTg; |
---|
999 | G4cout<<"fRutherfordTheta = "<<fRutherfordTheta/degree<<" degree"<<G4endl; |
---|
1000 | |
---|
1001 | } |
---|
1002 | |
---|
1003 | ///////////////////////////////////////////////////////////////// |
---|
1004 | // |
---|
1005 | // |
---|
1006 | |
---|
1007 | inline G4double G4NuclNuclDiffuseElastic::ProfileNear(G4double theta) |
---|
1008 | { |
---|
1009 | G4double dTheta = fRutherfordTheta - theta; |
---|
1010 | G4double result = 0., argument = 0.; |
---|
1011 | |
---|
1012 | if(std::abs(dTheta) < 0.001) result = fProfileAlpha*fProfileDelta; |
---|
1013 | else |
---|
1014 | { |
---|
1015 | argument = fProfileDelta*dTheta; |
---|
1016 | result = pi*argument*std::exp(fProfileAlpha*argument); |
---|
1017 | result /= std::sinh(pi*argument); |
---|
1018 | result -= 1.; |
---|
1019 | result /= dTheta; |
---|
1020 | } |
---|
1021 | return result; |
---|
1022 | } |
---|
1023 | |
---|
1024 | ///////////////////////////////////////////////////////////////// |
---|
1025 | // |
---|
1026 | // |
---|
1027 | |
---|
1028 | inline G4double G4NuclNuclDiffuseElastic::ProfileFar(G4double theta) |
---|
1029 | { |
---|
1030 | G4double dTheta = fRutherfordTheta + theta; |
---|
1031 | G4double argument = fProfileDelta*dTheta; |
---|
1032 | |
---|
1033 | G4double result = pi*argument*std::exp(fProfileAlpha*argument); |
---|
1034 | result /= std::sinh(pi*argument); |
---|
1035 | result /= dTheta; |
---|
1036 | |
---|
1037 | return result; |
---|
1038 | } |
---|
1039 | |
---|
1040 | ///////////////////////////////////////////////////////////////// |
---|
1041 | // |
---|
1042 | // |
---|
1043 | |
---|
1044 | inline G4complex G4NuclNuclDiffuseElastic::PhaseNear(G4double theta) |
---|
1045 | { |
---|
1046 | G4double twosigma = 2.*fCoulombPhase0; |
---|
1047 | twosigma -= fZommerfeld*std::log(fHalfRutThetaTg2/(1.+fHalfRutThetaTg2)); |
---|
1048 | twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi; |
---|
1049 | twosigma -= fProfileLambda*theta - 0.25*pi; |
---|
1050 | |
---|
1051 | twosigma *= fCofPhase; |
---|
1052 | |
---|
1053 | G4complex z = G4complex(0., twosigma); |
---|
1054 | |
---|
1055 | return std::exp(z); |
---|
1056 | } |
---|
1057 | |
---|
1058 | ///////////////////////////////////////////////////////////////// |
---|
1059 | // |
---|
1060 | // |
---|
1061 | |
---|
1062 | inline G4complex G4NuclNuclDiffuseElastic::PhaseFar(G4double theta) |
---|
1063 | { |
---|
1064 | G4double twosigma = 2.*fCoulombPhase0; |
---|
1065 | twosigma -= fZommerfeld*std::log(fHalfRutThetaTg2/(1.+fHalfRutThetaTg2)); |
---|
1066 | twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi; |
---|
1067 | twosigma += fProfileLambda*theta - 0.25*pi; |
---|
1068 | |
---|
1069 | twosigma *= fCofPhase; |
---|
1070 | |
---|
1071 | G4complex z = G4complex(0., twosigma); |
---|
1072 | |
---|
1073 | return std::exp(z); |
---|
1074 | } |
---|
1075 | |
---|
1076 | ///////////////////////////////////////////////////////////////// |
---|
1077 | // |
---|
1078 | // |
---|
1079 | |
---|
1080 | |
---|
1081 | inline G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta) |
---|
1082 | { |
---|
1083 | G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2); |
---|
1084 | G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2); |
---|
1085 | |
---|
1086 | G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR); |
---|
1087 | G4double kappa = u/std::sqrt(pi); |
---|
1088 | G4double dTheta = theta - fRutherfordTheta; |
---|
1089 | u *= dTheta; |
---|
1090 | G4double u2 = u*u; |
---|
1091 | G4double u2m2p3 = u2*2./3.; |
---|
1092 | |
---|
1093 | G4complex im = G4complex(0.,1.); |
---|
1094 | G4complex order = G4complex(u,u); |
---|
1095 | order /= std::sqrt(2.); |
---|
1096 | |
---|
1097 | G4complex gamma = pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*pi)); |
---|
1098 | G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR; |
---|
1099 | G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR; |
---|
1100 | G4complex out = gamma*(1. - a1*dTheta) - a0; |
---|
1101 | |
---|
1102 | return out; |
---|
1103 | } |
---|
1104 | |
---|
1105 | ///////////////////////////////////////////////////////////////// |
---|
1106 | // |
---|
1107 | // |
---|
1108 | |
---|
1109 | inline G4complex G4NuclNuclDiffuseElastic::GammaMore(G4double theta) |
---|
1110 | { |
---|
1111 | G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2); |
---|
1112 | G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2); |
---|
1113 | |
---|
1114 | G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR); |
---|
1115 | G4double kappa = u/std::sqrt(pi); |
---|
1116 | G4double dTheta = theta - fRutherfordTheta; |
---|
1117 | u *= dTheta; |
---|
1118 | G4double u2 = u*u; |
---|
1119 | G4double u2m2p3 = u2*2./3.; |
---|
1120 | |
---|
1121 | G4complex im = G4complex(0.,1.); |
---|
1122 | G4complex order = G4complex(u,u); |
---|
1123 | order /= std::sqrt(2.); |
---|
1124 | G4complex gamma = pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*pi)); |
---|
1125 | G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR; |
---|
1126 | G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR; |
---|
1127 | G4complex out = -gamma*(1. - a1*dTheta) - a0; |
---|
1128 | |
---|
1129 | return out; |
---|
1130 | } |
---|
1131 | |
---|
1132 | ///////////////////////////////////////////////////////////////// |
---|
1133 | // |
---|
1134 | // |
---|
1135 | |
---|
1136 | inline G4complex G4NuclNuclDiffuseElastic::AmplitudeNear(G4double theta) |
---|
1137 | { |
---|
1138 | G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi); |
---|
1139 | G4complex out = G4complex(kappa/fWaveVector,0.); |
---|
1140 | |
---|
1141 | out *= PhaseNear(theta); |
---|
1142 | |
---|
1143 | if( theta <= fRutherfordTheta ) |
---|
1144 | { |
---|
1145 | out *= GammaLess(theta) + ProfileNear(theta); |
---|
1146 | // out *= GammaMore(theta) + ProfileNear(theta); |
---|
1147 | out += CoulombAmplitude(theta); |
---|
1148 | } |
---|
1149 | else |
---|
1150 | { |
---|
1151 | out *= GammaMore(theta) + ProfileNear(theta); |
---|
1152 | // out *= GammaLess(theta) + ProfileNear(theta); |
---|
1153 | } |
---|
1154 | return out; |
---|
1155 | } |
---|
1156 | |
---|
1157 | ///////////////////////////////////////////////////////////////// |
---|
1158 | // |
---|
1159 | // |
---|
1160 | |
---|
1161 | inline G4complex G4NuclNuclDiffuseElastic::AmplitudeFar(G4double theta) |
---|
1162 | { |
---|
1163 | G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi); |
---|
1164 | G4complex out = G4complex(kappa/fWaveVector,0.); |
---|
1165 | out *= ProfileFar(theta); |
---|
1166 | out *= PhaseFar(theta); |
---|
1167 | return out; |
---|
1168 | } |
---|
1169 | |
---|
1170 | |
---|
1171 | ///////////////////////////////////////////////////////////////// |
---|
1172 | // |
---|
1173 | // |
---|
1174 | |
---|
1175 | inline G4complex G4NuclNuclDiffuseElastic::Amplitude(G4double theta) |
---|
1176 | { |
---|
1177 | |
---|
1178 | G4complex out = AmplitudeNear(theta) + fCofFar*AmplitudeFar(theta); |
---|
1179 | // G4complex out = AmplitudeNear(theta); |
---|
1180 | // G4complex out = AmplitudeFar(theta); |
---|
1181 | return out; |
---|
1182 | } |
---|
1183 | |
---|
1184 | ///////////////////////////////////////////////////////////////// |
---|
1185 | // |
---|
1186 | // |
---|
1187 | |
---|
1188 | inline G4double G4NuclNuclDiffuseElastic::AmplitudeMod2(G4double theta) |
---|
1189 | { |
---|
1190 | G4complex out = Amplitude(theta); |
---|
1191 | G4double mod2 = out.real()*out.real() + out.imag()*out.imag(); |
---|
1192 | return mod2; |
---|
1193 | } |
---|
1194 | |
---|
1195 | ///////////////////////////////////////////////////////////////// |
---|
1196 | // |
---|
1197 | // |
---|
1198 | |
---|
1199 | inline G4complex G4NuclNuclDiffuseElastic::AmplitudeGla(G4double theta) |
---|
1200 | { |
---|
1201 | G4int n; |
---|
1202 | G4double T12b, b, b2; // cosTheta = std::cos(theta); |
---|
1203 | G4complex out = G4complex(0.,0.), shiftC, shiftN; |
---|
1204 | G4complex im = G4complex(0.,1.); |
---|
1205 | |
---|
1206 | for( n = 0; n < fMaxL; n++) |
---|
1207 | { |
---|
1208 | shiftC = std::exp( im*2.*CalculateCoulombPhase(n) ); |
---|
1209 | // b = ( fZommerfeld + std::sqrt( fZommerfeld*fZommerfeld + n*(n+1) ) )/fWaveVector; |
---|
1210 | b = ( std::sqrt( G4double(n*(n+1)) ) )/fWaveVector; |
---|
1211 | b2 = b*b; |
---|
1212 | T12b = fSumSigma*std::exp(-b2/fNuclearRadiusSquare)/pi/fNuclearRadiusSquare; |
---|
1213 | shiftN = std::exp( -0.5*(1.-im*fEtaRatio)*T12b ) - 1.; |
---|
1214 | out += (2.*n+1.)*shiftC*shiftN*GetLegendrePol(n, theta); |
---|
1215 | } |
---|
1216 | out /= 2.*im*fWaveVector; |
---|
1217 | out += CoulombAmplitude(theta); |
---|
1218 | return out; |
---|
1219 | } |
---|
1220 | |
---|
1221 | ///////////////////////////////////////////////////////////////// |
---|
1222 | // |
---|
1223 | // |
---|
1224 | |
---|
1225 | inline G4double G4NuclNuclDiffuseElastic::AmplitudeGlaMod2(G4double theta) |
---|
1226 | { |
---|
1227 | G4complex out = AmplitudeGla(theta); |
---|
1228 | G4double mod2 = out.real()*out.real() + out.imag()*out.imag(); |
---|
1229 | return mod2; |
---|
1230 | } |
---|
1231 | |
---|
1232 | |
---|
1233 | ///////////////////////////////////////////////////////////////// |
---|
1234 | // |
---|
1235 | // |
---|
1236 | |
---|
1237 | inline G4complex G4NuclNuclDiffuseElastic::AmplitudeGG(G4double theta) |
---|
1238 | { |
---|
1239 | G4int n; |
---|
1240 | G4double T12b, a, aTemp, b2, sinThetaH = std::sin(0.5*theta); |
---|
1241 | G4double sinThetaH2 = sinThetaH*sinThetaH; |
---|
1242 | G4complex out = G4complex(0.,0.); |
---|
1243 | G4complex im = G4complex(0.,1.); |
---|
1244 | |
---|
1245 | a = -fSumSigma/twopi/fNuclearRadiusSquare; |
---|
1246 | b2 = fWaveVector*fWaveVector*fNuclearRadiusSquare*sinThetaH2; |
---|
1247 | |
---|
1248 | aTemp = a; |
---|
1249 | |
---|
1250 | for( n = 1; n < fMaxL; n++) |
---|
1251 | { |
---|
1252 | T12b = aTemp*std::exp(-b2/n)/n; |
---|
1253 | aTemp *= a; |
---|
1254 | out += T12b; |
---|
1255 | G4cout<<"out = "<<out<<G4endl; |
---|
1256 | } |
---|
1257 | out *= -4.*im*fWaveVector/pi; |
---|
1258 | out += CoulombAmplitude(theta); |
---|
1259 | return out; |
---|
1260 | } |
---|
1261 | |
---|
1262 | ///////////////////////////////////////////////////////////////// |
---|
1263 | // |
---|
1264 | // |
---|
1265 | |
---|
1266 | inline G4double G4NuclNuclDiffuseElastic::AmplitudeGGMod2(G4double theta) |
---|
1267 | { |
---|
1268 | G4complex out = AmplitudeGG(theta); |
---|
1269 | G4double mod2 = out.real()*out.real() + out.imag()*out.imag(); |
---|
1270 | return mod2; |
---|
1271 | } |
---|
1272 | |
---|
1273 | |
---|
1274 | /////////////////////////////////////////////////////////////////////////////// |
---|
1275 | // |
---|
1276 | // Test for given particle and element table of momentum, angle probability. |
---|
1277 | // For the partMom in CMS. |
---|
1278 | |
---|
1279 | inline void G4NuclNuclDiffuseElastic::InitParameters(const G4ParticleDefinition* theParticle, |
---|
1280 | G4double partMom, G4double Z, G4double A) |
---|
1281 | { |
---|
1282 | fAtomicNumber = Z; // atomic number |
---|
1283 | fAtomicWeight = A; // number of nucleons |
---|
1284 | |
---|
1285 | fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight); |
---|
1286 | G4double A1 = G4double( theParticle->GetBaryonNumber() ); |
---|
1287 | fNuclearRadius1 = CalculateNuclearRad(A1); |
---|
1288 | // fNuclearRadius = std::sqrt(fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2); |
---|
1289 | fNuclearRadius = fNuclearRadius1 + fNuclearRadius2; |
---|
1290 | |
---|
1291 | G4double a = 0.; |
---|
1292 | G4double z = theParticle->GetPDGCharge(); |
---|
1293 | G4double m1 = theParticle->GetPDGMass(); |
---|
1294 | |
---|
1295 | fWaveVector = partMom/hbarc; |
---|
1296 | |
---|
1297 | G4double lambda = fCofLambda*fWaveVector*fNuclearRadius; |
---|
1298 | G4cout<<"kR = "<<lambda<<G4endl; |
---|
1299 | |
---|
1300 | if( z ) |
---|
1301 | { |
---|
1302 | a = partMom/m1; // beta*gamma for m1 |
---|
1303 | fBeta = a/std::sqrt(1+a*a); |
---|
1304 | fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber); |
---|
1305 | fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber); |
---|
1306 | } |
---|
1307 | fProfileLambda = lambda*std::sqrt(1.-2*fZommerfeld/lambda); |
---|
1308 | G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl; |
---|
1309 | fProfileDelta = fCofDelta*fProfileLambda; |
---|
1310 | fProfileAlpha = fCofAlpha*fProfileLambda; |
---|
1311 | |
---|
1312 | CalculateCoulombPhaseZero(); |
---|
1313 | CalculateRutherfordAnglePar(); |
---|
1314 | |
---|
1315 | return; |
---|
1316 | } |
---|
1317 | |
---|
1318 | |
---|
1319 | /////////////////////////////////////////////////////////////////////////////// |
---|
1320 | // |
---|
1321 | // Test for given particle and element table of momentum, angle probability. |
---|
1322 | // For the partMom in CMS. |
---|
1323 | |
---|
1324 | inline void G4NuclNuclDiffuseElastic::InitParametersGla(const G4DynamicParticle* aParticle, |
---|
1325 | G4double partMom, G4double Z, G4double A) |
---|
1326 | { |
---|
1327 | fAtomicNumber = Z; // target atomic number |
---|
1328 | fAtomicWeight = A; // target number of nucleons |
---|
1329 | |
---|
1330 | fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight); // target nucleus radius |
---|
1331 | G4double A1 = G4double( aParticle->GetDefinition()->GetBaryonNumber() ); |
---|
1332 | fNuclearRadius1 = CalculateNuclearRad(A1); // projectile nucleus radius |
---|
1333 | fNuclearRadiusSquare = fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2; |
---|
1334 | |
---|
1335 | |
---|
1336 | G4double a = 0., kR12; |
---|
1337 | G4double z = aParticle->GetDefinition()->GetPDGCharge(); |
---|
1338 | G4double m1 = aParticle->GetDefinition()->GetPDGMass(); |
---|
1339 | |
---|
1340 | fWaveVector = partMom/hbarc; |
---|
1341 | |
---|
1342 | G4double pN = A1 - z; |
---|
1343 | if( pN < 0. ) pN = 0.; |
---|
1344 | |
---|
1345 | G4double tN = A - Z; |
---|
1346 | if( tN < 0. ) tN = 0.; |
---|
1347 | |
---|
1348 | G4double pTkin = aParticle->GetKineticEnergy(); |
---|
1349 | pTkin /= A1; |
---|
1350 | |
---|
1351 | |
---|
1352 | fSumSigma = (Z*z+pN*tN)*GetHadronNucleonXscNS(theProton, pTkin, theProton) + |
---|
1353 | (z*tN+pN*Z)*GetHadronNucleonXscNS(theProton, pTkin, theNeutron); |
---|
1354 | |
---|
1355 | G4cout<<"fSumSigma = "<<fSumSigma/millibarn<<" mb"<<G4endl; |
---|
1356 | G4cout<<"pi*R2 = "<<pi*fNuclearRadiusSquare/millibarn<<" mb"<<G4endl; |
---|
1357 | kR12 = fWaveVector*std::sqrt(fNuclearRadiusSquare); |
---|
1358 | G4cout<<"k*sqrt(R2) = "<<kR12<<" "<<G4endl; |
---|
1359 | fMaxL = (G4int(kR12)+1)*4; |
---|
1360 | G4cout<<"fMaxL = "<<fMaxL<<" "<<G4endl; |
---|
1361 | |
---|
1362 | if( z ) |
---|
1363 | { |
---|
1364 | a = partMom/m1; // beta*gamma for m1 |
---|
1365 | fBeta = a/std::sqrt(1+a*a); |
---|
1366 | fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber); |
---|
1367 | fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber); |
---|
1368 | } |
---|
1369 | |
---|
1370 | CalculateCoulombPhaseZero(); |
---|
1371 | |
---|
1372 | |
---|
1373 | return; |
---|
1374 | } |
---|
1375 | |
---|
1376 | |
---|
1377 | ///////////////////////////////////////////////////////////////////////////////////// |
---|
1378 | // |
---|
1379 | // Returns nucleon-nucleon cross-section based on N. Starkov parametrisation of |
---|
1380 | // data from mainly http://wwwppds.ihep.su:8001/c5-6A.html database |
---|
1381 | // projectile nucleon is pParticle with pTkin shooting target nucleon tParticle |
---|
1382 | |
---|
1383 | inline G4double |
---|
1384 | G4NuclNuclDiffuseElastic::GetHadronNucleonXscNS( G4ParticleDefinition* pParticle, |
---|
1385 | G4double pTkin, |
---|
1386 | G4ParticleDefinition* tParticle) |
---|
1387 | { |
---|
1388 | G4double xsection(0), Delta, A0, B0; |
---|
1389 | G4double hpXsc(0); |
---|
1390 | G4double hnXsc(0); |
---|
1391 | |
---|
1392 | |
---|
1393 | G4double targ_mass = tParticle->GetPDGMass(); |
---|
1394 | G4double proj_mass = pParticle->GetPDGMass(); |
---|
1395 | |
---|
1396 | G4double proj_energy = proj_mass + pTkin; |
---|
1397 | G4double proj_momentum = std::sqrt(pTkin*(pTkin+2*proj_mass)); |
---|
1398 | |
---|
1399 | G4double sMand = CalcMandelstamS ( proj_mass , targ_mass , proj_momentum ); |
---|
1400 | |
---|
1401 | sMand /= GeV*GeV; // in GeV for parametrisation |
---|
1402 | proj_momentum /= GeV; |
---|
1403 | proj_energy /= GeV; |
---|
1404 | proj_mass /= GeV; |
---|
1405 | G4double logS = std::log(sMand); |
---|
1406 | |
---|
1407 | // General PDG fit constants |
---|
1408 | |
---|
1409 | |
---|
1410 | // fEtaRatio=Re[f(0)]/Im[f(0)] |
---|
1411 | |
---|
1412 | if( proj_momentum >= 1.2 ) |
---|
1413 | { |
---|
1414 | fEtaRatio = 0.13*(logS - 5.8579332)*std::pow(sMand,-0.18); |
---|
1415 | } |
---|
1416 | else if( proj_momentum >= 0.6 ) |
---|
1417 | { |
---|
1418 | fEtaRatio = -75.5*(std::pow(proj_momentum,0.25)-0.95)/ |
---|
1419 | (std::pow(3*proj_momentum,2.2)+1); |
---|
1420 | } |
---|
1421 | else |
---|
1422 | { |
---|
1423 | fEtaRatio = 15.5*proj_momentum/(27*proj_momentum*proj_momentum*proj_momentum+2); |
---|
1424 | } |
---|
1425 | G4cout<<"fEtaRatio = "<<fEtaRatio<<G4endl; |
---|
1426 | |
---|
1427 | // xsc |
---|
1428 | |
---|
1429 | if( proj_momentum >= 10. ) // high energy: pp = nn = np |
---|
1430 | // if( proj_momentum >= 2.) |
---|
1431 | { |
---|
1432 | Delta = 1.; |
---|
1433 | |
---|
1434 | if( proj_energy < 40. ) Delta = 0.916+0.0021*proj_energy; |
---|
1435 | |
---|
1436 | if( proj_momentum >= 10.) |
---|
1437 | { |
---|
1438 | B0 = 7.5; |
---|
1439 | A0 = 100. - B0*std::log(3.0e7); |
---|
1440 | |
---|
1441 | xsection = A0 + B0*std::log(proj_energy) - 11 |
---|
1442 | + 103*std::pow(2*0.93827*proj_energy + proj_mass*proj_mass+ |
---|
1443 | 0.93827*0.93827,-0.165); // mb |
---|
1444 | } |
---|
1445 | } |
---|
1446 | else // low energy pp = nn != np |
---|
1447 | { |
---|
1448 | if(pParticle == tParticle) // pp or nn // nn to be pp |
---|
1449 | { |
---|
1450 | if( proj_momentum < 0.73 ) |
---|
1451 | { |
---|
1452 | hnXsc = 23 + 50*( std::pow( std::log(0.73/proj_momentum), 3.5 ) ); |
---|
1453 | } |
---|
1454 | else if( proj_momentum < 1.05 ) |
---|
1455 | { |
---|
1456 | hnXsc = 23 + 40*(std::log(proj_momentum/0.73))* |
---|
1457 | (std::log(proj_momentum/0.73)); |
---|
1458 | } |
---|
1459 | else // if( proj_momentum < 10. ) |
---|
1460 | { |
---|
1461 | hnXsc = 39.0 + |
---|
1462 | 75*(proj_momentum - 1.2)/(std::pow(proj_momentum,3.0) + 0.15); |
---|
1463 | } |
---|
1464 | xsection = hnXsc; |
---|
1465 | } |
---|
1466 | else // pn to be np |
---|
1467 | { |
---|
1468 | if( proj_momentum < 0.8 ) |
---|
1469 | { |
---|
1470 | hpXsc = 33+30*std::pow(std::log(proj_momentum/1.3),4.0); |
---|
1471 | } |
---|
1472 | else if( proj_momentum < 1.4 ) |
---|
1473 | { |
---|
1474 | hpXsc = 33+30*std::pow(std::log(proj_momentum/0.95),2.0); |
---|
1475 | } |
---|
1476 | else // if( proj_momentum < 10. ) |
---|
1477 | { |
---|
1478 | hpXsc = 33.3+ |
---|
1479 | 20.8*(std::pow(proj_momentum,2.0)-1.35)/ |
---|
1480 | (std::pow(proj_momentum,2.50)+0.95); |
---|
1481 | } |
---|
1482 | xsection = hpXsc; |
---|
1483 | } |
---|
1484 | } |
---|
1485 | xsection *= millibarn; // parametrised in mb |
---|
1486 | G4cout<<"xsection = "<<xsection/millibarn<<" mb"<<G4endl; |
---|
1487 | return xsection; |
---|
1488 | } |
---|
1489 | |
---|
1490 | //////////////////////////////////////////////////////////////////////////////////// |
---|
1491 | // |
---|
1492 | // |
---|
1493 | |
---|
1494 | inline G4double G4NuclNuclDiffuseElastic::CalcMandelstamS( const G4double mp , |
---|
1495 | const G4double mt , |
---|
1496 | const G4double Plab ) |
---|
1497 | { |
---|
1498 | G4double Elab = std::sqrt ( mp * mp + Plab * Plab ); |
---|
1499 | G4double sMand = mp*mp + mt*mt + 2*Elab*mt ; |
---|
1500 | |
---|
1501 | return sMand; |
---|
1502 | } |
---|
1503 | |
---|
1504 | |
---|
1505 | |
---|
1506 | #endif |
---|