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 | |
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28 | #include "globals.hh" |
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29 | #include "G4ios.hh" |
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30 | #include "G4HadronicException.hh" |
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31 | #include "G4Clebsch.hh" |
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32 | #include "Randomize.hh" |
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33 | #include "G4Proton.hh" |
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34 | #include "G4HadTmpUtil.hh" |
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35 | |
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36 | G4Clebsch::G4Clebsch() |
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37 | { |
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38 | G4int nLogs = 101; |
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39 | logs.push_back(0.); |
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40 | G4int i; |
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41 | for (i=1; i<nLogs; i++) |
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42 | { |
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43 | G4double previousLog = logs.back(); |
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44 | G4double value = previousLog + std::log((G4double)i); |
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45 | logs.push_back(value); |
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46 | } |
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47 | } |
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48 | |
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49 | |
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50 | G4Clebsch::~G4Clebsch() |
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51 | { } |
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52 | |
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53 | |
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54 | G4bool G4Clebsch::operator==(const G4Clebsch &right) const |
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55 | { |
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56 | return (this == (G4Clebsch *) &right); |
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57 | } |
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58 | |
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59 | |
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60 | G4bool G4Clebsch::operator!=(const G4Clebsch &right) const |
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61 | { |
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62 | return (this != (G4Clebsch *) &right); |
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63 | } |
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64 | |
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65 | |
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66 | const std::vector<G4double>& G4Clebsch::GetLogs() const |
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67 | { |
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68 | return logs; |
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69 | } |
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70 | |
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71 | |
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72 | |
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73 | G4double G4Clebsch::Weight(G4int isoIn1, G4int iso3In1, |
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74 | G4int isoIn2, G4int iso3In2, |
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75 | G4int isoOut1, G4int isoOut2) const |
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76 | { |
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77 | G4double value = 0.; |
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78 | |
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79 | G4int m = iso3In1 + iso3In2; |
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80 | |
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81 | G4int jMinIn = std::max(std::abs(isoIn1 - isoIn2), std::abs(m)); |
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82 | G4int jMaxIn = isoIn1 + isoIn2; |
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83 | |
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84 | G4int jMinOut = std::max(std::abs(isoOut1 - isoOut2), std::abs(m)); |
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85 | G4int jMaxOut = isoOut1 + isoOut2; |
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86 | |
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87 | G4int jMin = std::max(jMinIn,jMinOut); |
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88 | G4int jMax = std::min(jMaxIn,jMaxOut); |
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89 | |
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90 | G4int j; |
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91 | for (j=jMin; j<=jMax; j+=2) |
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92 | { |
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93 | value += ClebschGordan(isoIn1,iso3In1, isoIn2,iso3In2, j); |
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94 | } |
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95 | |
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96 | return value; |
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97 | } |
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98 | |
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99 | |
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100 | G4double G4Clebsch::ClebschGordan(G4int isoIn1, G4int iso3In1, |
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101 | G4int isoIn2, G4int iso3In2, |
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102 | G4int jOut) const |
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103 | { |
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104 | // Calculates Clebsch-Gordan coefficient |
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105 | |
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106 | G4double j1 = isoIn1 / 2.0; |
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107 | G4double j2 = isoIn2 / 2.0; |
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108 | G4double j3 = jOut / 2.0; |
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109 | |
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110 | G4double m1 = iso3In1 / 2.0; |
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111 | G4double m2 = iso3In2 / 2.0; |
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112 | G4double m3 = - (m1 + m2); |
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113 | |
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114 | G4int n = G4lrint(m3+j1+j2+.1); |
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115 | G4double argument = 2. * j3 + 1.; |
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116 | if (argument < 0.) |
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117 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::ClebschGordan - sqrt of negative argument"); |
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118 | G4double coeff = std::sqrt(argument) / (std::pow(-1.,n)); |
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119 | G4double clebsch = coeff * Wigner3J(j1,j2,j3, m1,m2,m3); |
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120 | G4double value = clebsch * clebsch; |
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121 | |
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122 | // G4cout << "ClebschGordan(" |
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123 | // << isoIn1 << "," << iso3In1 << "," |
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124 | // << isoIn2 << "," << iso3In2 << "," << jOut |
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125 | // << ") = " << value << G4endl; |
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126 | |
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127 | return value; |
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128 | } |
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129 | |
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130 | |
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131 | G4double G4Clebsch::Wigner3J(G4double j1, G4double j2, G4double j3, |
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132 | G4double m1, G4double m2, G4double m3) const |
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133 | { |
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134 | // Calculates Wigner 3-j symbols |
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135 | |
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136 | G4double value = 0.; |
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137 | |
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138 | G4double sigma = j1 + j2 + j3; |
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139 | std::vector<G4double> n; |
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140 | n.push_back(-j1 + j2 + j3); // n0 |
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141 | n.push_back(j1 - m1); // n1 |
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142 | n.push_back(j1 + m1); // n2 |
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143 | n.push_back(j1 - j2 + j3); // n3 |
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144 | n.push_back(j2 - m2); // n4 |
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145 | n.push_back(j2 + m2); // n5 |
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146 | n.push_back(j1 + j2 - j3); // n6 |
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147 | n.push_back(j3 - m3); // n7 |
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148 | n.push_back(j3 + m3); // n8 |
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149 | |
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150 | // Some preliminary checks |
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151 | |
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152 | G4bool ok = true; |
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153 | size_t i; |
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154 | for(i=1; i<=3; i++) |
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155 | { |
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156 | G4double sum1 = n[i-1] + n[i+2] + n[i+5]; |
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157 | G4double sum2 = n[3*i-1] + n[3*i-2] + n[3*i-3]; |
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158 | if (sum1 != sigma || sum2 != sigma) ok = false; |
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159 | G4int j; |
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160 | for(j=1; j<=3; j++) |
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161 | { |
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162 | if (n[i+3*j-4] < 0.) ok = false; |
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163 | } |
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164 | } |
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165 | |
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166 | if (ok) |
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167 | { |
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168 | G4int iMin = 1; |
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169 | G4int jMin = 1; |
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170 | G4double smallest = n[0]; |
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171 | |
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172 | // Find the smallest n |
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173 | for (i=1; i<=3; i++) |
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174 | { |
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175 | G4int j; |
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176 | for (j=1; j<=3; j++) |
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177 | { |
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178 | if (n[i+3*j-4] < smallest) |
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179 | { |
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180 | smallest = n[i+3*j-4]; |
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181 | iMin = i; |
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182 | jMin = j; |
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183 | } |
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184 | } |
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185 | } |
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186 | |
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187 | G4int sign = 1; |
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188 | |
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189 | if(iMin > 1) |
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190 | { |
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191 | for(G4int j=1; j<=3; ++j) |
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192 | { |
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193 | G4double tmp = n[j*3-3]; |
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194 | n[j*3-3] = n[iMin+j*3-4]; |
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195 | n[iMin+j*3-4] = tmp; |
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196 | } |
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197 | sign = (G4int) std::pow(-1.,sigma); |
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198 | } |
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199 | |
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200 | if (jMin > 1) |
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201 | { |
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202 | for(i=1; i<=3; i++) |
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203 | { |
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204 | G4double tmp = n[i-1]; |
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205 | n[i-1] = n[i+jMin*3-4]; |
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206 | n[i+jMin*3-4] = tmp; |
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207 | } |
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208 | sign *= (G4int) std::pow(-1.,sigma); |
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209 | } |
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210 | |
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211 | const std::vector<G4double> logVector = GetLogs(); |
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212 | size_t n1 = G4lrint(n[0]); |
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213 | |
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214 | // Some boundary checks |
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215 | G4int logEntries = logVector.size() - 1; |
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216 | for (i=0; i<n.size(); i++) |
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217 | { |
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218 | if (n[i] < 0. || n[i] > logEntries) |
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219 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::Wigner3J - Outside logVector boundaries, n"); |
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220 | } |
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221 | |
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222 | G4double r1 = n[0]; |
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223 | G4double r2 = n[3]; |
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224 | G4double r3 = n[6]; |
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225 | G4double r4 = n[1]; |
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226 | G4double r5 = n[4]; |
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227 | G4double r6 = n[7]; |
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228 | G4double r7 = n[2]; |
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229 | G4double r8 = n[5]; |
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230 | G4double r9 = n[8]; |
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231 | |
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232 | G4double l1 = logVector[(G4int)r1]; |
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233 | G4double l2 = logVector[(G4int)r2]; |
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234 | G4double l3 = logVector[(G4int)r3]; |
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235 | G4double l4 = logVector[(G4int)r4]; |
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236 | G4double l5 = logVector[(G4int)r5]; |
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237 | G4double l6 = logVector[(G4int)r6]; |
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238 | G4double l7 = logVector[(G4int)r7]; |
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239 | G4double l8 = logVector[(G4int)r8]; |
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240 | G4double l9 = logVector[(G4int)r9]; |
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241 | |
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242 | G4double sigma1 = sigma + 1.; |
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243 | if (sigma1 < 0. || sigma1 > logEntries) |
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244 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::Wigner3J - Outside logVector boundaries, sigma"); |
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245 | |
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246 | G4double ls = logVector[static_cast<G4int>(sigma1+.00001)]; |
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247 | G4double hlp1 = (l2 + l3 + l4 +l7 -ls -l1 -l5 -l9 -l6 -l8) / 2.; |
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248 | G4int expon = static_cast<G4int>(r6 + r8+.00001); |
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249 | G4double sgn = std::pow(-1., expon); |
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250 | G4double coeff = std::exp(hlp1) * sgn; |
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251 | |
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252 | G4int n61 = static_cast<G4int>(r6 - r1+.00001); |
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253 | if (n61 < 0. || n61 > logEntries) |
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254 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::Wigner3J - Outside logVector boundaries, n61"); |
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255 | G4int n81 = static_cast<G4int>(r8 - r1+.00001); |
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256 | if (n81 < 0. || n81 > logEntries) |
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257 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::Wigner3J - Outside logVector boundaries, n81"); |
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258 | |
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259 | G4double hlp2 = l6 - logVector[n61] + l8 - logVector[n81]; |
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260 | G4double sum = std::exp(hlp2); |
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261 | std::vector<G4double> s; |
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262 | s.push_back(sum); |
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263 | n1 = (size_t)r1; |
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264 | for (i=1; i<=n1; i++) |
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265 | { |
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266 | G4double last = s.back(); |
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267 | G4double den = i * (r6 - r1 + i) * (r8 - r1 + i); |
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268 | if (den == 0) |
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269 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::Wigner3J - divide by zero"); |
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270 | G4double data = -last * (r1 + 1.0 - i) * (r5 + 1.0 - i) * (r9 + 1. - i) / den; |
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271 | s.push_back(data); |
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272 | sum += data; |
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273 | } |
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274 | value = coeff * sum * sign; |
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275 | } // endif ok |
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276 | else |
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277 | { |
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278 | } |
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279 | |
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280 | |
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281 | // G4cout << "Wigner3j(" |
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282 | // << j1 << "," << j2 << "," << j3 << "," |
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283 | // << m1 << "," << m2 << "," << m3 << ") = " |
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284 | // << value |
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285 | // << G4endl; |
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286 | |
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287 | return value; |
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288 | } |
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289 | |
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290 | |
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291 | |
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292 | std::vector<G4double> G4Clebsch::GenerateIso3(G4int isoIn1, G4int iso3In1, |
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293 | G4int isoIn2, G4int iso3In2, |
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294 | G4int isoA, G4int isoB) const |
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295 | { |
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296 | std::vector<G4double> temp; |
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297 | |
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298 | // ---- Special cases first ---- |
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299 | |
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300 | // Special case, both Jin are zero |
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301 | if (isoIn1 == 0 && isoIn2 == 0) |
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302 | { |
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303 | G4cout << "WARNING: G4Clebsch::GenerateIso3 - both isoIn are zero" << G4endl; |
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304 | temp.push_back(0.); |
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305 | temp.push_back(0.); |
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306 | return temp; |
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307 | } |
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308 | |
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309 | G4int iso3 = iso3In1 + iso3In2; |
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310 | |
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311 | // Special case, either Jout is zero |
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312 | if (isoA == 0) |
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313 | { |
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314 | temp.push_back(0.); |
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315 | temp.push_back(iso3); |
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316 | return temp; |
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317 | } |
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318 | if (isoB == 0) |
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319 | { |
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320 | temp.push_back(iso3); |
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321 | temp.push_back(0.); |
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322 | return temp; |
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323 | } |
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324 | |
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325 | // Number of possible states, in |
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326 | G4int jMinIn = std::max(std::abs(isoIn1 - isoIn2), std::abs(iso3)); |
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327 | G4int jMaxIn = isoIn1 + isoIn2; |
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328 | |
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329 | // Number of possible states, out |
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330 | |
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331 | G4int jMinOut = 9999; |
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332 | G4int jTmp, i, j; |
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333 | |
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334 | for(i=-1; i<=1; i+=2) |
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335 | { |
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336 | for(j=-1; j<=1; j+=2) |
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337 | { |
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338 | jTmp= std::abs(i*isoA + j*isoB); |
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339 | if(jTmp < jMinOut) jMinOut = jTmp; |
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340 | } |
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341 | } |
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342 | jMinOut = std::max(jMinOut, std::abs(iso3)); |
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343 | G4int jMaxOut = isoA + isoB; |
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344 | |
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345 | // Possible in and out common states |
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346 | G4int jMin = std::max(jMinIn, jMinOut); |
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347 | G4int jMax = std::min(jMaxIn, jMaxOut); |
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348 | if (jMin > jMax) |
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349 | { |
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350 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - jMin > JMax"); |
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351 | } |
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352 | |
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353 | // Number of possible isospins |
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354 | G4int nJ = (jMax - jMin) / 2 + 1; |
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355 | |
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356 | // A few consistency checks |
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357 | |
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358 | if ( (isoIn1 == 0 || isoIn2 == 0) && jMin != jMax ) |
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359 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - J1 or J2 = 0, but jMin != JMax"); |
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360 | |
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361 | // MGP ---- Shall it be a warning or an exception? |
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362 | if (nJ == 0) |
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363 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - nJ is zero, no overlap between in and out"); |
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364 | |
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365 | // Loop over all possible combinations of isoIn1, isoIn2, iso3In11, iso3In2, jTot |
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366 | // to get the probability of each of the in-channel couplings |
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367 | |
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368 | std::vector<G4double> clebsch; |
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369 | |
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370 | for(j=jMin; j<=jMax; j+=2) |
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371 | { |
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372 | G4double cg = ClebschGordan(isoIn1, iso3In1, isoIn2, iso3In2, j); |
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373 | clebsch.push_back(cg); |
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374 | } |
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375 | |
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376 | // Consistency check |
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377 | if (static_cast<G4int>(clebsch.size()) != nJ) |
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378 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - nJ inconsistency"); |
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379 | |
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380 | G4double sum = clebsch[0]; |
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381 | |
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382 | for (j=1; j<nJ; j++) |
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383 | { |
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384 | sum += clebsch[j]; |
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385 | } |
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386 | // Consistency check |
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387 | if (sum <= 0.) |
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388 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - Sum of Clebsch-Gordan probabilities <=0"); |
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389 | |
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390 | // Generate a normalized pdf |
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391 | |
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392 | std::vector<G4double> clebschPdf; |
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393 | G4double previous = clebsch[0]; |
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394 | clebschPdf.push_back(previous/sum); |
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395 | for (j=1; j<nJ; j++) |
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396 | { |
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397 | previous += clebsch[j]; |
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398 | G4double prob = previous / sum; |
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399 | clebschPdf.push_back(prob); |
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400 | } |
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401 | |
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402 | // Generate a random jTot according to the Clebsch-Gordan pdf |
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403 | G4double rand = G4UniformRand(); |
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404 | G4int jTot = 0; |
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405 | for (j=0; j<nJ; j++) |
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406 | { |
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407 | G4bool found = false; |
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408 | if (rand < clebschPdf[j]) |
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409 | { |
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410 | found = true; |
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411 | jTot = jMin + 2*j; |
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412 | } |
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413 | if (found) break; |
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414 | } |
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415 | |
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416 | // Generate iso3Out |
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417 | |
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418 | std::vector<G4double> mMin; |
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419 | mMin.push_back(-isoA); |
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420 | mMin.push_back(-isoB); |
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421 | |
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422 | std::vector<G4double> mMax; |
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423 | mMax.push_back(isoA); |
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424 | mMax.push_back(isoB); |
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425 | |
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426 | // Calculate the possible |J_i M_i> combinations and their probability |
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427 | |
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428 | std::vector<G4double> m1Out; |
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429 | std::vector<G4double> m2Out; |
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430 | |
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431 | const G4int size = 20; |
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432 | G4double prbout[size][size]; |
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433 | |
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434 | G4int m1pos(0), m2pos(0); |
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435 | G4int j12; |
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436 | G4int m1pr(0), m2pr(0); |
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437 | |
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438 | sum = 0.; |
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439 | for(j12 = std::abs(isoA-isoB); j12<=(isoA+isoB); j12+=2) |
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440 | { |
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441 | m1pos = -1; |
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442 | for (m1pr = static_cast<G4int>(mMin[0]+.00001); m1pr <= mMax[0]; m1pr+=2) |
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443 | { |
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444 | m1pos++; |
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445 | if (m1pos >= size) |
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446 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - m1pos > size"); |
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447 | m1Out.push_back(m1pr); |
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448 | m2pos = -1; |
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449 | for (m2pr = static_cast<G4int>(mMin[1]+.00001); m2pr <= mMax[1]; m2pr+=2) |
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450 | { |
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451 | m2pos++; |
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452 | if (m2pos >= size) |
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453 | { |
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454 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - m2pos > size"); |
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455 | } |
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456 | m2Out.push_back(m2pr); |
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457 | |
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458 | if(m1pr + m2pr == iso3) |
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459 | { |
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460 | G4int m12 = m1pr + m2pr; |
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461 | G4double c12 = ClebschGordan(isoA, m1pr, isoB,m2pr, j12); |
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462 | G4double c34 = ClebschGordan(0,0,0,0,0); |
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463 | G4double ctot = ClebschGordan(j12, m12, 0, 0, jTot); |
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464 | G4double cleb = c12*c34*ctot; |
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465 | prbout[m1pos][m2pos] = cleb; |
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466 | sum += cleb; |
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467 | } |
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468 | else |
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469 | { |
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470 | prbout[m1pos][m2pos] = 0.; |
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471 | } |
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472 | } |
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473 | } |
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474 | } |
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475 | |
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476 | if (sum <= 0.) |
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477 | throw G4HadronicException(__FILE__, __LINE__, "G4Clebsch::GenerateIso3 - sum (out) <=0"); |
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478 | |
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479 | for (i=0; i<size; i++) |
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480 | { |
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481 | for (j=0; j<size; j++) |
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482 | { |
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483 | prbout[i][j] /= sum; |
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484 | } |
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485 | } |
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486 | |
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487 | rand = G4UniformRand(); |
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488 | |
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489 | G4int m1p, m2p; |
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490 | |
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491 | for (m1p=0; m1p<m1pos; m1p++) |
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492 | { |
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493 | for (m2p=0; m2p<m2pos; m2p++) |
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494 | { |
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495 | if (rand < prbout[m1p][m2p]) |
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496 | { |
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497 | temp.push_back(m1Out[m1p]); |
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498 | temp.push_back(m2Out[m2p]); |
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499 | return temp; |
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500 | } |
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501 | else |
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502 | { |
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503 | rand -= prbout[m1p][m2p]; |
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504 | } |
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505 | } |
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506 | } |
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507 | |
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508 | throw G4HadronicException(__FILE__, __LINE__, "Should never get here "); |
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509 | return temp; |
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510 | } |
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511 | |
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512 | |
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513 | G4double G4Clebsch::NormalizedClebschGordan(G4int J, G4int m, |
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514 | G4int J1, G4int J2, |
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515 | G4int m1, G4int m2) const |
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516 | { |
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517 | // Calculate the normalized Clebsch-Gordan coefficient, that is the prob |
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518 | // of isospin decomposition of (J,m) into J1, J2, m1, m2 |
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519 | |
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520 | G4double cleb = 0.; |
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521 | |
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522 | if(J1 == 0 || J2 == 0) return cleb; |
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523 | |
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524 | G4double sum = 0.0; |
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525 | |
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526 | // Loop over all J1,J2,Jtot,m1,m2 combinations |
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527 | |
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528 | for(G4int m1Current=-J1; m1Current<=J1; m1Current+=2) |
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529 | { |
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530 | G4int m2Current = m - m1Current; |
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531 | |
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532 | G4double prob = ClebschGordan(J1, m1Current, J2, m2Current, J); |
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533 | sum += prob; |
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534 | if (m2Current == m2 && m1Current == m1) cleb += prob; |
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535 | } |
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536 | |
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537 | // Normalize probs to 1 |
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538 | if (sum > 0.) cleb /= sum; |
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539 | |
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540 | return cleb; |
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541 | } |
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