[824] | 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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