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 | // G4 Tools program: NuMu DIS(Q2) fixed step integration |
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28 | // ..................................................... |
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29 | // Created: M.V. Kossov, CERN/ITEP(Moscow), 20-Dec-2005 |
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30 | // |
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31 | //===================================================================== |
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32 | #include "globals.hh" |
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33 | #include <iostream> |
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34 | #include <fstream> |
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35 | #include <vector> |
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36 | #include "G4ios.hh" |
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37 | //#include <CLHEP/GenericFunctions/LogGamma.hh> |
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38 | |
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39 | // All calculations have been done for C12 nucleus |
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40 | |
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41 | double nuE(double E) { return .9673/(1.+.323/E/E)/std::pow(E,.78);} // (E is in GeV) |
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42 | |
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43 | double nuX(double E, double r, double p) // (E is in GeV, r=Q2/Q2max, p=1.+nuE(E)) |
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44 | { |
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45 | double y=p-r; |
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46 | double p3=(.3088+.0012352*E)/(1.+1.836/E/E); |
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47 | return std::pow(y,6)*(r+p3)/(p3*r+1.); |
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48 | } |
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49 | |
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50 | double anuE(double E) { return .875/(1.+.2977/E/E)/std::pow(E,.78);} // (E is in GeV) |
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51 | |
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52 | double anuX(double E, double r, double p) // (E is in GeV, r=Q2/Q2max, p=1+anuE(E)) |
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53 | { |
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54 | double E2=E*E; |
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55 | double y=p-r; |
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56 | double p3=(13.88+.9373*(1.+.000033*E2)*std::sqrt(E))/(1.+(10.12+1.532/E2)/E); |
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57 | return std::pow(y,6)*(r+p3)/(p3*r+1.); |
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58 | } |
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59 | |
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60 | int main() |
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61 | { |
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62 | const double eps=.00000001; // relative accuracy of the integral calculation |
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63 | const double mmu=.105658369; // mu meson mass in GeV |
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64 | const double mmu2=mmu*mmu; // m_mu^2 in GeV^2 |
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65 | const double MN=.931494043; // Nucleon mass (inside nucleus, atomic mass unit, GeV) |
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66 | const double Emin=mmu+mmu2/(MN+MN); // the threshold energy in GeV |
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67 | const double Emax=390.; // the maximum energy in GeV |
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68 | const double lEmi=std::log(Emin); // logarithm of the threshold energy in GeV |
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69 | const double lEma=std::log(Emax); // logarithm of the maximum energy in GeV |
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70 | const int power=7; // power for the magic variable (E-dependent) |
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71 | const double pconv=1./power; // conversion power for the magic variable |
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72 | // ========= |
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73 | const int niX=20; // number of points for X table |
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74 | const int liX=niX-1; // the last index for X table |
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75 | const int niE=20; // number of points for E table |
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76 | double Xl[niE][niX]; // reversed table |
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77 | double inl[niE][niX]; // direct table |
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78 | // ----------------- nu/anu switch ------------------------------ |
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79 | //bool nu=true; |
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80 | bool nu=false; |
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81 | // -------------------------------------------------------------- |
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82 | double dE=(lEma-lEmi)/niE; |
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83 | double hE=dE/2; |
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84 | int ne=0; |
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85 | for(double len=lEmi+hE; len<lEma; len+=dE) |
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86 | { |
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87 | //G4cout<<"log(E)="<<len<<G4endl; |
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88 | double en=std::exp(len); |
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89 | double shift=0.; |
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90 | if(nu) shift=1.+nuE(en); |
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91 | else shift=1.+anuE(en); |
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92 | double Xma=std::pow(shift,power); |
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93 | double Xmi=std::pow((shift-1.),power); |
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94 | int nX=8; |
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95 | double DISmsig=0.; |
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96 | double DIStsig=1.; |
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97 | while(std::fabs(DIStsig-DISmsig)/DIStsig>eps) |
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98 | { |
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99 | DISmsig=DIStsig; |
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100 | DIStsig=0.; |
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101 | nX*=2; |
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102 | double dX=(Xma-Xmi)/nX; |
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103 | double hX=dX/2; |
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104 | for(double X=Xmi+hX; X<Xma; X+=dX) |
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105 | { |
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106 | double r=shift-std::pow(X,pconv); // the same for nu and anu |
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107 | if(nu) DIStsig+=nuX(en,r,shift); // neutrino |
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108 | else DIStsig+=anuX(en,r,shift); // anti-neutrino |
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109 | } |
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110 | DIStsig*=dX; |
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111 | //G4cout<<"E="<<en<<",nX="<<nX<<",i="<<DIStsig<<",m="<<DISmsig<<",r=" |
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112 | // <<(DIStsig-DISmsig)/DIStsig<<G4endl; |
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113 | } |
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114 | //G4cout<<"E="<<en<<", Total: nX="<<nX<<", Int="<<DIStsig<<G4endl; |
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115 | // ***************** Calculate the reversed table ***************** |
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116 | double dInt=DIStsig/niX; // Step for the integral |
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117 | DIStsig=0.; |
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118 | DISmsig=0.; |
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119 | nX*=2; |
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120 | double dX=(Xma-Xmi)/nX; // New step for the multiplied number of nodes |
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121 | dInt/=dX; // To avoid multiplication (nX is fixed) |
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122 | double sum=dInt; |
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123 | int nn=0; |
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124 | double hX=dX/2; |
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125 | G4cout<<"E="<<en<<", Xl_min="<<Xmi<<G4endl; |
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126 | for(double X=Xmi+hX; X<Xma; X+=dX) |
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127 | { |
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128 | double r=shift-std::pow(X,pconv); // the same for nu and anu |
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129 | if(nu) DIStsig+=nuX(en,r,shift); // neutrino |
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130 | else DIStsig+=anuX(en,r,shift); // anti-neutrino |
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131 | if(DIStsig>sum+eps) |
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132 | { |
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133 | inl[ne][nn]=sum*dX; |
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134 | Xl[ne][nn]=X-(DIStsig-sum)*dX/(DIStsig-DISmsig); |
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135 | G4cout<<"E="<<en<<", sum="<<inl[ne][nn]<<", Xl["<<nn<<"]="<<Xl[ne][nn]<<G4endl; |
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136 | nn++; |
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137 | sum+=dInt; |
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138 | } |
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139 | DISmsig=DIStsig; |
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140 | } |
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141 | inl[ne][nn]=sum*dX; |
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142 | Xl[ne][nn]=Xma; |
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143 | G4cout<<"E="<<en<<", sum="<<inl[ne][nn]<<", Xl["<<nn<<"]="<<Xma<<G4endl; |
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144 | // ************* The following is just a test (better than .5%) ************ |
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145 | //for(int i=1; i<niX; i++) |
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146 | //{ |
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147 | // DIStsig=0.; |
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148 | // double Xm=Xl[ne][i]; |
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149 | // double dX=(Xm-Xmi)/nX; |
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150 | // double hX=dX/2; |
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151 | // for(double X=Xmi+hX; X<Xm; X+=dX) |
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152 | // { |
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153 | // double r=shift-pow(X,pconv); // the same for nu and anu |
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154 | // if(nu) DIStsig+=nuX(en,r,shift); // neutrino |
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155 | // else DIStsig+=anuX(en,r,shift); // anti-neutrino |
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156 | // } |
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157 | // DIStsig*=dX; |
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158 | // G4cout<<"i="<<i<<", v="<<DIStsig<<", d="<<fabs(DIStsig-inl[ne][i])/DIStsig<<G4endl; |
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159 | //} |
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160 | // ***************** Calculate the direct table ***************** |
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161 | dX=(Xma-Xmi)/niX; |
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162 | double nor=inl[ne][liX]/niX; |
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163 | //G4cout<<"E="<<en<<", i=0, Xm="<<Xmi<<", I=0."<<G4endl; |
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164 | for(int i=1; i<=niX; i++) |
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165 | { |
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166 | DIStsig=0.; |
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167 | double Xm=Xmi+dX*i; |
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168 | double rX=(Xm-Xmi)/nX; |
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169 | double hX=rX/2; |
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170 | for(double X=Xmi+hX; X<Xm; X+=rX) |
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171 | { |
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172 | double r=shift-std::pow(X,pconv); // the same for nu and anu |
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173 | if(nu) DIStsig+=nuX(en,r,shift); // neutrino |
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174 | else DIStsig+=anuX(en,r,shift); // anti-neutrino |
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175 | } |
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176 | DIStsig*=rX/nor; |
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177 | //////////G4cout<<"E="<<en<<", i="<<i<<", Xm="<<Xm<<", I="<<DIStsig<<G4endl; |
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178 | } |
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179 | ne++; |
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180 | } // End of the big loop over log(E) |
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181 | G4cout<<"End"<<G4endl; |
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182 | return 0; |
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183 | } |
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