1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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4 | // * * |
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5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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7 | // * conditions of the Geant4 Software License, included in the file * |
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8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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9 | // * include a list of copyright holders. * |
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10 | // * * |
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11 | // * Neither the authors of this software system, nor their employing * |
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12 | // * institutes,nor the agencies providing financial support for this * |
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13 | // * work make any representation or warranty, express or implied, * |
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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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16 | // * for the full disclaimer and the limitation of liability. * |
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17 | // * * |
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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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20 | // * By using, copying, modifying or distributing the software (or * |
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21 | // * any work based on the software) you agree to acknowledge its * |
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22 | // * use in resulting scientific publications, and indicate your * |
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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 | // GEANT 4 class header file |
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28 | // |
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29 | // History: |
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30 | // 17 August 2004 P.Gumplinger and T.MacPhail |
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31 | // samples Michel spectrum including 1st order |
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32 | // radiative corrections |
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33 | // Reference: Florian Scheck "Muon Physics", in Physics Reports |
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34 | // (Review Section of Physics Letters) 44, No. 4 (1978) |
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35 | // 187-248. North-Holland Publishing Company, Amsterdam |
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36 | // at page 210 cc. |
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37 | // |
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38 | // W.E. Fisher and F. Scheck, Nucl. Phys. B83 (1974) 25. |
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39 | // |
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40 | // ------------------------------------------------------------ |
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41 | // |
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42 | #include "G4MuonDecayChannelWithSpin.hh" |
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43 | |
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44 | #include "Randomize.hh" |
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45 | #include "G4DecayProducts.hh" |
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46 | #include "G4LorentzVector.hh" |
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47 | |
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48 | G4MuonDecayChannelWithSpin::G4MuonDecayChannelWithSpin(const G4String& theParentName, |
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49 | G4double theBR) |
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50 | : G4MuonDecayChannel(theParentName,theBR) |
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51 | { |
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52 | } |
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53 | |
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54 | G4MuonDecayChannelWithSpin::~G4MuonDecayChannelWithSpin() |
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55 | { |
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56 | } |
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57 | |
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58 | G4DecayProducts *G4MuonDecayChannelWithSpin::DecayIt(G4double) |
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59 | { |
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60 | // This version assumes V-A coupling with 1st order radiative correctons, |
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61 | // the standard model Michel parameter values, but |
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62 | // gives incorrect energy spectrum for neutrinos |
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63 | |
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64 | #ifdef G4VERBOSE |
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65 | if (GetVerboseLevel()>1) G4cout << "G4MuonDecayChannelWithSpin::DecayIt "; |
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66 | #endif |
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67 | |
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68 | if (parent == 0) FillParent(); |
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69 | if (daughters == 0) FillDaughters(); |
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70 | |
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71 | // parent mass |
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72 | G4double parentmass = parent->GetPDGMass(); |
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73 | |
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74 | EMMU = parentmass; |
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75 | |
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76 | //daughters'mass |
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77 | G4double daughtermass[3]; |
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78 | G4double sumofdaughtermass = 0.0; |
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79 | for (G4int index=0; index<3; index++){ |
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80 | daughtermass[index] = daughters[index]->GetPDGMass(); |
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81 | sumofdaughtermass += daughtermass[index]; |
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82 | } |
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83 | |
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84 | EMASS = daughtermass[0]; |
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85 | |
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86 | //create parent G4DynamicParticle at rest |
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87 | G4ThreeVector dummy; |
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88 | G4DynamicParticle * parentparticle = new G4DynamicParticle( parent, dummy, 0.0); |
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89 | //create G4Decayproducts |
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90 | G4DecayProducts *products = new G4DecayProducts(*parentparticle); |
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91 | delete parentparticle; |
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92 | |
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93 | // calcurate electron energy |
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94 | |
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95 | G4double michel_rho = 0.75; //Standard Model Michel rho |
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96 | G4double michel_delta = 0.75; //Standard Model Michel delta |
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97 | G4double michel_xsi = 1.00; //Standard Model Michel xsi |
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98 | G4double michel_eta = 0.00; //Standard Model eta |
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99 | |
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100 | G4double rndm, x, ctheta; |
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101 | |
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102 | G4double FG; |
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103 | G4double FG_max = 2.00; |
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104 | |
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105 | G4double W_mue = (EMMU*EMMU+EMASS*EMASS)/(2.*EMMU); |
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106 | G4double x0 = EMASS/W_mue; |
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107 | |
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108 | G4double x0_squared = x0*x0; |
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109 | |
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110 | // *************************************************** |
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111 | // x0 <= x <= 1. and -1 <= y <= 1 |
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112 | // |
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113 | // F(x,y) = f(x)*g(x,y); g(x,y) = 1.+g(x)*y |
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114 | // *************************************************** |
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115 | |
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116 | // ***** sampling F(x,y) directly (brute force) ***** |
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117 | |
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118 | do{ |
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119 | |
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120 | // Sample the positron energy by sampling from F |
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121 | |
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122 | rndm = G4UniformRand(); |
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123 | |
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124 | x = x0 + rndm*(1.-x0); |
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125 | |
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126 | G4double x_squared = x*x; |
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127 | |
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128 | G4double F_IS, F_AS, G_IS, G_AS; |
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129 | |
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130 | F_IS = 1./6.*(-2.*x_squared+3.*x-x0_squared); |
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131 | F_AS = 1./6.*std::sqrt(x_squared-x0_squared)*(2.*x-2.+std::sqrt(1.-x0_squared)); |
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132 | |
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133 | G_IS = 2./9.*(michel_rho-0.75)*(4.*x_squared-3.*x-x0_squared); |
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134 | G_IS = G_IS + michel_eta*(1.-x)*x0; |
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135 | |
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136 | G_AS = 3.*(michel_xsi-1.)*(1.-x); |
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137 | G_AS = G_AS+2.*(michel_xsi*michel_delta-0.75)*(4.*x-4.+std::sqrt(1.-x0_squared)); |
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138 | G_AS = 1./9.*std::sqrt(x_squared-x0_squared)*G_AS; |
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139 | |
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140 | F_IS = F_IS + G_IS; |
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141 | F_AS = F_AS + G_AS; |
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142 | |
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143 | // *** Radiative Corrections *** |
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144 | |
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145 | G4double R_IS = F_c(x,x0); |
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146 | |
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147 | G4double F = 6.*F_IS + R_IS/std::sqrt(x_squared-x0_squared); |
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148 | |
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149 | // *** Radiative Corrections *** |
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150 | |
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151 | G4double R_AS = F_theta(x,x0); |
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152 | |
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153 | rndm = G4UniformRand(); |
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154 | |
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155 | ctheta = 2.*rndm-1.; |
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156 | |
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157 | G4double G = 6.*F_AS - R_AS/std::sqrt(x_squared-x0_squared); |
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158 | |
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159 | FG = std::sqrt(x_squared-x0_squared)*F*(1.+(G/F)*ctheta); |
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160 | |
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161 | if(FG>FG_max){ |
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162 | G4cout<<"***Problem in Muon Decay *** : FG > FG_max"<<G4endl; |
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163 | FG_max = FG; |
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164 | } |
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165 | |
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166 | rndm = G4UniformRand(); |
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167 | |
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168 | }while(FG<rndm*FG_max); |
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169 | |
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170 | G4double energy = x * W_mue; |
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171 | |
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172 | rndm = G4UniformRand(); |
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173 | |
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174 | G4double phi = twopi * rndm; |
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175 | |
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176 | if(energy < EMASS) energy = EMASS; |
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177 | |
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178 | // calculate daughter momentum |
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179 | G4double daughtermomentum[3]; |
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180 | |
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181 | daughtermomentum[0] = std::sqrt(energy*energy - EMASS*EMASS); |
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182 | |
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183 | G4double stheta = std::sqrt(1.-ctheta*ctheta); |
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184 | G4double cphi = std::cos(phi); |
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185 | G4double sphi = std::sin(phi); |
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186 | |
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187 | //Coordinates of the decay positron with respect to the muon spin |
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188 | |
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189 | G4double px = stheta*cphi; |
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190 | G4double py = stheta*sphi; |
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191 | G4double pz = ctheta; |
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192 | |
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193 | G4ThreeVector direction0(px,py,pz); |
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194 | |
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195 | direction0.rotateUz(parent_polarization); |
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196 | |
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197 | G4DynamicParticle * daughterparticle0 |
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198 | = new G4DynamicParticle( daughters[0], daughtermomentum[0]*direction0); |
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199 | |
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200 | products->PushProducts(daughterparticle0); |
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201 | |
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202 | |
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203 | // daughter 1 ,2 (neutrinos) |
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204 | // create neutrinos in the C.M frame of two neutrinos |
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205 | G4double energy2 = parentmass*(1.0 - x/2.0); |
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206 | G4double vmass = std::sqrt((energy2-daughtermomentum[0])*(energy2+daughtermomentum[0])); |
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207 | G4double beta = -1.0*daughtermomentum[0]/energy2; |
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208 | G4double costhetan = 2.*G4UniformRand()-1.0; |
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209 | G4double sinthetan = std::sqrt((1.0-costhetan)*(1.0+costhetan)); |
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210 | G4double phin = twopi*G4UniformRand()*rad; |
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211 | G4double sinphin = std::sin(phin); |
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212 | G4double cosphin = std::cos(phin); |
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213 | |
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214 | G4ThreeVector direction1(sinthetan*cosphin,sinthetan*sinphin,costhetan); |
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215 | G4DynamicParticle * daughterparticle1 |
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216 | = new G4DynamicParticle( daughters[1], direction1*(vmass/2.)); |
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217 | G4DynamicParticle * daughterparticle2 |
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218 | = new G4DynamicParticle( daughters[2], direction1*(-1.0*vmass/2.)); |
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219 | |
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220 | // boost to the muon rest frame |
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221 | G4LorentzVector p4; |
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222 | p4 = daughterparticle1->Get4Momentum(); |
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223 | p4.boost( direction0.x()*beta, direction0.y()*beta, direction0.z()*beta); |
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224 | daughterparticle1->Set4Momentum(p4); |
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225 | p4 = daughterparticle2->Get4Momentum(); |
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226 | p4.boost( direction0.x()*beta, direction0.y()*beta, direction0.z()*beta); |
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227 | daughterparticle2->Set4Momentum(p4); |
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228 | products->PushProducts(daughterparticle1); |
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229 | products->PushProducts(daughterparticle2); |
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230 | daughtermomentum[1] = daughterparticle1->GetTotalMomentum(); |
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231 | daughtermomentum[2] = daughterparticle2->GetTotalMomentum(); |
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232 | |
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233 | // output message |
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234 | #ifdef G4VERBOSE |
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235 | if (GetVerboseLevel()>1) { |
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236 | G4cout << "G4MuonDecayChannelWithSpin::DecayIt "; |
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237 | G4cout << " create decay products in rest frame " <<G4endl; |
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238 | products->DumpInfo(); |
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239 | } |
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240 | #endif |
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241 | return products; |
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242 | } |
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243 | |
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244 | G4double G4MuonDecayChannelWithSpin::R_c(G4double x){ |
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245 | |
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246 | G4int n_max = (int)(100.*x); |
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247 | |
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248 | if(n_max<10)n_max=10; |
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249 | |
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250 | G4double L2 = 0.0; |
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251 | |
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252 | for(G4int n=1; n<=n_max; n++){ |
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253 | L2 += std::pow(x,n)/(n*n); |
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254 | } |
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255 | |
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256 | G4double omega = std::log(EMMU/EMASS); |
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257 | |
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258 | G4double r_c; |
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259 | |
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260 | r_c = 2.*L2-(pi*pi/3.)-2.; |
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261 | r_c = r_c + omega * (1.5+2.*std::log((1.-x)/x)); |
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262 | r_c = r_c - std::log(x)*(2.*std::log(x)-1.); |
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263 | r_c = r_c + (3.*std::log(x)-1.-1./x)*std::log(1.-x); |
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264 | |
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265 | return r_c; |
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266 | } |
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