[1197] | 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 | // $Id: G4NuclNuclDiffuseElastic.hh,v 1.8 2009/04/10 13:22:25 grichine Exp $ |
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[1337] | 28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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[1197] | 29 | // |
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| 30 | // |
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| 31 | // G4 Model: optical elastic scattering with 4-momentum balance |
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| 32 | // |
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| 33 | // Class Description |
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| 34 | // Final state production model for nucleus-nucleus elastic scattering; |
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| 35 | // Coulomb amplitude is not considered as correction |
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| 36 | // (as in G4DiffuseElastic) |
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| 37 | // Class Description - End |
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| 38 | // |
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| 39 | // |
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| 40 | // 17.03.09 V. Grichine implementation for Coulomb elastic scattering |
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| 41 | |
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| 42 | |
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| 43 | #ifndef G4NuclNuclDiffuseElastic_h |
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| 44 | #define G4NuclNuclDiffuseElastic_h 1 |
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| 45 | |
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| 46 | #include "globals.hh" |
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| 47 | #include <complex> |
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| 48 | #include "G4Integrator.hh" |
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| 49 | |
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| 50 | #include "G4HadronicInteraction.hh" |
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| 51 | #include "G4HadProjectile.hh" |
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| 52 | #include "G4Nucleus.hh" |
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| 53 | |
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| 54 | using namespace std; |
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| 55 | |
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| 56 | class G4ParticleDefinition; |
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| 57 | class G4PhysicsTable; |
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| 58 | class G4PhysicsLogVector; |
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| 59 | |
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| 60 | class G4NuclNuclDiffuseElastic : public G4HadronicInteraction |
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| 61 | { |
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| 62 | public: |
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| 63 | |
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| 64 | G4NuclNuclDiffuseElastic(); |
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| 65 | |
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| 66 | G4NuclNuclDiffuseElastic(const G4ParticleDefinition* aParticle); |
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| 67 | |
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| 68 | |
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| 69 | |
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| 70 | |
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| 71 | |
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| 72 | virtual ~G4NuclNuclDiffuseElastic(); |
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| 73 | |
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| 74 | void Initialise(); |
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| 75 | |
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| 76 | void InitialiseOnFly(G4double Z, G4double A); |
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| 77 | |
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| 78 | void BuildAngleTable(); |
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| 79 | |
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| 80 | |
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| 81 | G4HadFinalState * ApplyYourself(const G4HadProjectile & aTrack, |
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| 82 | G4Nucleus & targetNucleus); |
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| 83 | |
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| 84 | |
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| 85 | void SetPlabLowLimit(G4double value); |
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| 86 | |
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| 87 | void SetHEModelLowLimit(G4double value); |
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| 88 | |
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| 89 | void SetQModelLowLimit(G4double value); |
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| 90 | |
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| 91 | void SetLowestEnergyLimit(G4double value); |
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| 92 | |
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| 93 | void SetRecoilKinEnergyLimit(G4double value); |
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| 94 | |
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| 95 | G4double SampleT(const G4ParticleDefinition* aParticle, |
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| 96 | G4double p, G4double A); |
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| 97 | |
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| 98 | G4double SampleTableT(const G4ParticleDefinition* aParticle, |
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| 99 | G4double p, G4double Z, G4double A); |
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| 100 | |
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| 101 | G4double SampleThetaCMS(const G4ParticleDefinition* aParticle, G4double p, G4double A); |
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| 102 | |
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| 103 | G4double SampleTableThetaCMS(const G4ParticleDefinition* aParticle, G4double p, |
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| 104 | G4double Z, G4double A); |
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| 105 | |
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| 106 | G4double GetScatteringAngle(G4int iMomentum, G4int iAngle, G4double position); |
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| 107 | |
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| 108 | G4double SampleThetaLab(const G4HadProjectile* aParticle, |
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| 109 | G4double tmass, G4double A); |
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| 110 | |
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| 111 | G4double GetDiffuseElasticXsc( const G4ParticleDefinition* particle, |
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| 112 | G4double theta, |
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| 113 | G4double momentum, |
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| 114 | G4double A ); |
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| 115 | |
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| 116 | G4double GetInvElasticXsc( const G4ParticleDefinition* particle, |
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| 117 | G4double theta, |
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| 118 | G4double momentum, |
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| 119 | G4double A, G4double Z ); |
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| 120 | |
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| 121 | G4double GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle, |
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| 122 | G4double theta, |
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| 123 | G4double momentum, |
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| 124 | G4double A, G4double Z ); |
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| 125 | |
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| 126 | G4double GetInvElasticSumXsc( const G4ParticleDefinition* particle, |
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| 127 | G4double tMand, |
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| 128 | G4double momentum, |
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| 129 | G4double A, G4double Z ); |
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| 130 | |
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| 131 | G4double IntegralElasticProb( const G4ParticleDefinition* particle, |
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| 132 | G4double theta, |
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| 133 | G4double momentum, |
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| 134 | G4double A ); |
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| 135 | |
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| 136 | |
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| 137 | G4double GetCoulombElasticXsc( const G4ParticleDefinition* particle, |
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| 138 | G4double theta, |
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| 139 | G4double momentum, |
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| 140 | G4double Z ); |
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| 141 | |
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| 142 | G4double GetInvCoulombElasticXsc( const G4ParticleDefinition* particle, |
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| 143 | G4double tMand, |
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| 144 | G4double momentum, |
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| 145 | G4double A, G4double Z ); |
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| 146 | |
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| 147 | G4double GetCoulombTotalXsc( const G4ParticleDefinition* particle, |
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| 148 | G4double momentum, G4double Z ); |
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| 149 | |
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| 150 | G4double GetCoulombIntegralXsc( const G4ParticleDefinition* particle, |
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| 151 | G4double momentum, G4double Z, |
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| 152 | G4double theta1, G4double theta2 ); |
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| 153 | |
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| 154 | |
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| 155 | G4double CalculateParticleBeta( const G4ParticleDefinition* particle, |
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| 156 | G4double momentum ); |
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| 157 | |
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| 158 | G4double CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 ); |
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| 159 | |
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| 160 | G4double CalculateAm( G4double momentum, G4double n, G4double Z); |
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| 161 | |
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| 162 | G4double CalculateNuclearRad( G4double A); |
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| 163 | |
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| 164 | G4double ThetaCMStoThetaLab(const G4DynamicParticle* aParticle, |
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| 165 | G4double tmass, G4double thetaCMS); |
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| 166 | |
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| 167 | G4double ThetaLabToThetaCMS(const G4DynamicParticle* aParticle, |
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| 168 | G4double tmass, G4double thetaLab); |
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| 169 | |
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| 170 | void TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom, |
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| 171 | G4double Z, G4double A); |
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| 172 | |
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| 173 | |
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| 174 | |
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| 175 | G4double BesselJzero(G4double z); |
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| 176 | G4double BesselJone(G4double z); |
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| 177 | G4double DampFactor(G4double z); |
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| 178 | G4double BesselOneByArg(G4double z); |
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| 179 | |
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| 180 | G4double GetDiffElasticProb(G4double theta); |
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| 181 | G4double GetDiffElasticSumProb(G4double theta); |
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| 182 | G4double GetDiffElasticSumProbA(G4double alpha); |
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| 183 | G4double GetIntegrandFunction(G4double theta); |
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| 184 | |
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| 185 | G4double GetNuclearRadius(){return fNuclearRadius;}; |
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| 186 | |
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| 187 | |
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| 188 | // Technical math functions for strong Coulomb contribution |
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| 189 | |
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| 190 | G4complex GammaLogarithm(G4complex xx); |
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| 191 | |
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| 192 | G4double GetErf(G4double x); |
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| 193 | |
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| 194 | G4complex GetErfcComp(G4complex z, G4int nMax); |
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| 195 | G4complex GetErfcSer(G4complex z, G4int nMax); |
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| 196 | G4complex GetErfcInt(G4complex z); // , G4int nMax); |
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| 197 | |
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| 198 | G4complex GetErfComp(G4complex z, G4int nMax); // AandS algorithm != Ser, Int |
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| 199 | G4complex GetErfSer(G4complex z, G4int nMax); |
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| 200 | |
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| 201 | G4double GetExpCos(G4double x); |
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| 202 | G4double GetExpSin(G4double x); |
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| 203 | G4complex GetErfInt(G4complex z); // , G4int nMax); |
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| 204 | |
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| 205 | |
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| 206 | G4complex TestErfcComp(G4complex z, G4int nMax); |
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| 207 | G4complex TestErfcSer(G4complex z, G4int nMax); |
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| 208 | G4complex TestErfcInt(G4complex z); // , G4int nMax); |
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| 209 | |
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| 210 | G4complex CoulombAmplitude(G4double theta); |
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| 211 | void CalculateCoulombPhaseZero(); |
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| 212 | void CalculateRutherfordAnglePar(); |
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| 213 | |
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| 214 | G4double ProfileNear(G4double theta); |
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| 215 | G4double ProfileFar(G4double theta); |
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| 216 | |
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| 217 | G4complex PhaseNear(G4double theta); |
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| 218 | G4complex PhaseFar(G4double theta); |
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| 219 | |
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| 220 | G4complex GammaLess(G4double theta); |
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| 221 | G4complex GammaMore(G4double theta); |
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| 222 | |
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| 223 | G4complex AmplitudeNear(G4double theta); |
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| 224 | G4complex AmplitudeFar(G4double theta); |
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| 225 | G4complex Amplitude(G4double theta); |
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| 226 | G4double AmplitudeMod2(G4double theta); |
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| 227 | void InitParameters(const G4ParticleDefinition* theParticle, |
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| 228 | G4double partMom, G4double Z, G4double A); |
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| 229 | |
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| 230 | G4double GetProfileLambda(){return fProfileLambda;}; |
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| 231 | |
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| 232 | void SetProfileLambda(G4double pl) {fProfileLambda = pl;}; |
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| 233 | void SetProfileDelta(G4double pd) {fProfileDelta = pd;}; |
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| 234 | void SetProfileAlpha(G4double pa){fProfileAlpha = pa;}; |
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| 235 | |
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| 236 | private: |
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| 237 | |
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| 238 | |
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| 239 | G4ParticleDefinition* theProton; |
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| 240 | G4ParticleDefinition* theNeutron; |
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| 241 | G4ParticleDefinition* theDeuteron; |
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| 242 | G4ParticleDefinition* theAlpha; |
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| 243 | |
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| 244 | const G4ParticleDefinition* thePionPlus; |
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| 245 | const G4ParticleDefinition* thePionMinus; |
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| 246 | |
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| 247 | G4double lowEnergyRecoilLimit; |
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| 248 | G4double lowEnergyLimitHE; |
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| 249 | G4double lowEnergyLimitQ; |
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| 250 | G4double lowestEnergyLimit; |
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| 251 | G4double plabLowLimit; |
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| 252 | |
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| 253 | G4int fEnergyBin; |
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| 254 | G4int fAngleBin; |
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| 255 | |
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| 256 | G4PhysicsLogVector* fEnergyVector; |
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| 257 | G4PhysicsTable* fAngleTable; |
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| 258 | std::vector<G4PhysicsTable*> fAngleBank; |
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| 259 | |
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| 260 | std::vector<G4double> fElementNumberVector; |
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| 261 | std::vector<G4String> fElementNameVector; |
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| 262 | |
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| 263 | const G4ParticleDefinition* fParticle; |
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| 264 | G4double fWaveVector; |
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| 265 | G4double fAtomicWeight; |
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| 266 | G4double fAtomicNumber; |
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| 267 | |
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| 268 | G4double fNuclearRadius1; |
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| 269 | G4double fNuclearRadius2; |
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| 270 | G4double fNuclearRadius; |
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| 271 | |
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| 272 | G4double fBeta; |
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| 273 | G4double fZommerfeld; |
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| 274 | G4double fAm; |
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| 275 | G4bool fAddCoulomb; |
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| 276 | |
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| 277 | G4double fCoulombPhase0; |
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| 278 | G4double fHalfRutThetaTg; |
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| 279 | G4double fRutherfordTheta; |
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| 280 | |
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| 281 | G4double fProfileLambda; |
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| 282 | G4double fProfileDelta; |
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| 283 | G4double fProfileAlpha; |
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| 284 | |
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| 285 | G4double fReZ; |
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| 286 | |
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| 287 | }; |
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| 288 | |
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| 289 | |
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| 290 | inline void G4NuclNuclDiffuseElastic::SetRecoilKinEnergyLimit(G4double value) |
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| 291 | { |
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| 292 | lowEnergyRecoilLimit = value; |
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| 293 | } |
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| 294 | |
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| 295 | inline void G4NuclNuclDiffuseElastic::SetPlabLowLimit(G4double value) |
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| 296 | { |
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| 297 | plabLowLimit = value; |
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| 298 | } |
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| 299 | |
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| 300 | inline void G4NuclNuclDiffuseElastic::SetHEModelLowLimit(G4double value) |
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| 301 | { |
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| 302 | lowEnergyLimitHE = value; |
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| 303 | } |
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| 304 | |
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| 305 | inline void G4NuclNuclDiffuseElastic::SetQModelLowLimit(G4double value) |
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| 306 | { |
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| 307 | lowEnergyLimitQ = value; |
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| 308 | } |
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| 309 | |
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| 310 | inline void G4NuclNuclDiffuseElastic::SetLowestEnergyLimit(G4double value) |
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| 311 | { |
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| 312 | lowestEnergyLimit = value; |
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| 313 | } |
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| 314 | |
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| 315 | |
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| 316 | ///////////////////////////////////////////////////////////// |
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| 317 | // |
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| 318 | // Bessel J0 function based on rational approximation from |
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| 319 | // J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141 |
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| 320 | |
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| 321 | inline G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value) |
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| 322 | { |
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| 323 | G4double modvalue, value2, fact1, fact2, arg, shift, bessel; |
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| 324 | |
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| 325 | modvalue = fabs(value); |
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| 326 | |
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| 327 | if ( value < 8.0 && value > -8.0 ) |
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| 328 | { |
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| 329 | value2 = value*value; |
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| 330 | |
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| 331 | fact1 = 57568490574.0 + value2*(-13362590354.0 |
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| 332 | + value2*( 651619640.7 |
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| 333 | + value2*(-11214424.18 |
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| 334 | + value2*( 77392.33017 |
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| 335 | + value2*(-184.9052456 ) ) ) ) ); |
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| 336 | |
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| 337 | fact2 = 57568490411.0 + value2*( 1029532985.0 |
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| 338 | + value2*( 9494680.718 |
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| 339 | + value2*(59272.64853 |
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| 340 | + value2*(267.8532712 |
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| 341 | + value2*1.0 ) ) ) ); |
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| 342 | |
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| 343 | bessel = fact1/fact2; |
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| 344 | } |
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| 345 | else |
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| 346 | { |
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| 347 | arg = 8.0/modvalue; |
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| 348 | |
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| 349 | value2 = arg*arg; |
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| 350 | |
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| 351 | shift = modvalue-0.785398164; |
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| 352 | |
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| 353 | fact1 = 1.0 + value2*(-0.1098628627e-2 |
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| 354 | + value2*(0.2734510407e-4 |
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| 355 | + value2*(-0.2073370639e-5 |
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| 356 | + value2*0.2093887211e-6 ) ) ); |
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| 357 | |
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| 358 | fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3 |
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| 359 | + value2*(-0.6911147651e-5 |
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| 360 | + value2*(0.7621095161e-6 |
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| 361 | - value2*0.934945152e-7 ) ) ); |
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| 362 | |
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| 363 | bessel = sqrt(0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2 ); |
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| 364 | } |
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| 365 | return bessel; |
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| 366 | } |
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| 367 | |
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| 368 | ///////////////////////////////////////////////////////////// |
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| 369 | // |
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| 370 | // Bessel J1 function based on rational approximation from |
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| 371 | // J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141 |
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| 372 | |
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| 373 | inline G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value) |
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| 374 | { |
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| 375 | G4double modvalue, value2, fact1, fact2, arg, shift, bessel; |
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| 376 | |
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| 377 | modvalue = fabs(value); |
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| 378 | |
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| 379 | if ( modvalue < 8.0 ) |
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| 380 | { |
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| 381 | value2 = value*value; |
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| 382 | |
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| 383 | fact1 = value*(72362614232.0 + value2*(-7895059235.0 |
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| 384 | + value2*( 242396853.1 |
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| 385 | + value2*(-2972611.439 |
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| 386 | + value2*( 15704.48260 |
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| 387 | + value2*(-30.16036606 ) ) ) ) ) ); |
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| 388 | |
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| 389 | fact2 = 144725228442.0 + value2*(2300535178.0 |
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| 390 | + value2*(18583304.74 |
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| 391 | + value2*(99447.43394 |
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| 392 | + value2*(376.9991397 |
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| 393 | + value2*1.0 ) ) ) ); |
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| 394 | bessel = fact1/fact2; |
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| 395 | } |
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| 396 | else |
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| 397 | { |
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| 398 | arg = 8.0/modvalue; |
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| 399 | |
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| 400 | value2 = arg*arg; |
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| 401 | |
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| 402 | shift = modvalue - 2.356194491; |
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| 403 | |
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| 404 | fact1 = 1.0 + value2*( 0.183105e-2 |
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| 405 | + value2*(-0.3516396496e-4 |
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| 406 | + value2*(0.2457520174e-5 |
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| 407 | + value2*(-0.240337019e-6 ) ) ) ); |
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| 408 | |
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| 409 | fact2 = 0.04687499995 + value2*(-0.2002690873e-3 |
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| 410 | + value2*( 0.8449199096e-5 |
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| 411 | + value2*(-0.88228987e-6 |
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| 412 | + value2*0.105787412e-6 ) ) ); |
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| 413 | |
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| 414 | bessel = sqrt( 0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2); |
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| 415 | |
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| 416 | if (value < 0.0) bessel = -bessel; |
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| 417 | } |
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| 418 | return bessel; |
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| 419 | } |
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| 420 | |
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| 421 | //////////////////////////////////////////////////////////////////// |
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| 422 | // |
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| 423 | // damp factor in diffraction x/sh(x), x was already *pi |
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| 424 | |
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| 425 | inline G4double G4NuclNuclDiffuseElastic::DampFactor(G4double x) |
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| 426 | { |
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| 427 | G4double df; |
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| 428 | G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials |
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| 429 | |
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| 430 | // x *= pi; |
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| 431 | |
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| 432 | if( std::fabs(x) < 0.01 ) |
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| 433 | { |
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| 434 | df = 1./(1. + x/f2 + x*x/f3 + x*x*x/f4); |
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| 435 | } |
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| 436 | else |
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| 437 | { |
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| 438 | df = x/std::sinh(x); |
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| 439 | } |
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| 440 | return df; |
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| 441 | } |
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| 442 | |
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| 443 | |
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| 444 | //////////////////////////////////////////////////////////////////// |
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| 445 | // |
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| 446 | // return J1(x)/x with special case for small x |
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| 447 | |
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| 448 | inline G4double G4NuclNuclDiffuseElastic::BesselOneByArg(G4double x) |
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| 449 | { |
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| 450 | G4double x2, result; |
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| 451 | |
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| 452 | if( std::fabs(x) < 0.01 ) |
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| 453 | { |
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| 454 | x *= 0.5; |
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| 455 | x2 = x*x; |
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| 456 | result = 2. - x2 + x2*x2/6.; |
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| 457 | } |
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| 458 | else |
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| 459 | { |
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| 460 | result = BesselJone(x)/x; |
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| 461 | } |
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| 462 | return result; |
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| 463 | } |
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| 464 | |
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| 465 | //////////////////////////////////////////////////////////////////// |
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| 466 | // |
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| 467 | // return particle beta |
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| 468 | |
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| 469 | inline G4double G4NuclNuclDiffuseElastic::CalculateParticleBeta( const G4ParticleDefinition* particle, |
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| 470 | G4double momentum ) |
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| 471 | { |
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| 472 | G4double mass = particle->GetPDGMass(); |
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| 473 | G4double a = momentum/mass; |
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| 474 | fBeta = a/std::sqrt(1+a*a); |
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| 475 | |
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| 476 | return fBeta; |
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| 477 | } |
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| 478 | |
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| 479 | //////////////////////////////////////////////////////////////////// |
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| 480 | // |
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| 481 | // return Zommerfeld parameter for Coulomb scattering |
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| 482 | |
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| 483 | inline G4double G4NuclNuclDiffuseElastic::CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 ) |
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| 484 | { |
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| 485 | fZommerfeld = fine_structure_const*Z1*Z2/beta; |
---|
| 486 | |
---|
| 487 | return fZommerfeld; |
---|
| 488 | } |
---|
| 489 | |
---|
| 490 | //////////////////////////////////////////////////////////////////// |
---|
| 491 | // |
---|
| 492 | // return Wentzel correction for Coulomb scattering |
---|
| 493 | |
---|
| 494 | inline G4double G4NuclNuclDiffuseElastic::CalculateAm( G4double momentum, G4double n, G4double Z) |
---|
| 495 | { |
---|
| 496 | G4double k = momentum/hbarc; |
---|
| 497 | G4double ch = 1.13 + 3.76*n*n; |
---|
| 498 | G4double zn = 1.77*k*std::pow(Z,-1./3.)*Bohr_radius; |
---|
| 499 | G4double zn2 = zn*zn; |
---|
| 500 | fAm = ch/zn2; |
---|
| 501 | |
---|
| 502 | return fAm; |
---|
| 503 | } |
---|
| 504 | |
---|
| 505 | //////////////////////////////////////////////////////////////////// |
---|
| 506 | // |
---|
| 507 | // calculate nuclear radius for different atomic weights using different approximations |
---|
| 508 | |
---|
| 509 | inline G4double G4NuclNuclDiffuseElastic::CalculateNuclearRad( G4double A) |
---|
| 510 | { |
---|
| 511 | G4double r0, radius; |
---|
| 512 | |
---|
| 513 | if( A < 50. ) |
---|
| 514 | { |
---|
| 515 | if( A > 10. ) r0 = 1.16*( 1 - std::pow(A, -2./3.) )*fermi; // 1.08*fermi; |
---|
| 516 | else r0 = 1.1*fermi; |
---|
| 517 | |
---|
| 518 | radius = r0*std::pow(A, 1./3.); |
---|
| 519 | } |
---|
| 520 | else |
---|
| 521 | { |
---|
| 522 | r0 = 1.7*fermi; // 1.7*fermi; |
---|
| 523 | |
---|
| 524 | radius = r0*std::pow(A, 0.27); // 0.27); |
---|
| 525 | } |
---|
| 526 | return radius; |
---|
| 527 | } |
---|
| 528 | |
---|
| 529 | //////////////////////////////////////////////////////////////////// |
---|
| 530 | // |
---|
| 531 | // return Coulomb scattering differential xsc with Wentzel correction |
---|
| 532 | |
---|
| 533 | inline G4double G4NuclNuclDiffuseElastic::GetCoulombElasticXsc( const G4ParticleDefinition* particle, |
---|
| 534 | G4double theta, |
---|
| 535 | G4double momentum, |
---|
| 536 | G4double Z ) |
---|
| 537 | { |
---|
| 538 | G4double sinHalfTheta = std::sin(0.5*theta); |
---|
| 539 | G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta; |
---|
| 540 | G4double beta = CalculateParticleBeta( particle, momentum); |
---|
| 541 | G4double z = particle->GetPDGCharge(); |
---|
| 542 | G4double n = CalculateZommerfeld( beta, z, Z ); |
---|
| 543 | G4double am = CalculateAm( momentum, n, Z); |
---|
| 544 | G4double k = momentum/hbarc; |
---|
| 545 | G4double ch = 0.5*n/k; |
---|
| 546 | G4double ch2 = ch*ch; |
---|
| 547 | G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am); |
---|
| 548 | |
---|
| 549 | return xsc; |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | |
---|
| 553 | //////////////////////////////////////////////////////////////////// |
---|
| 554 | // |
---|
| 555 | // return Coulomb scattering total xsc with Wentzel correction |
---|
| 556 | |
---|
| 557 | inline G4double G4NuclNuclDiffuseElastic::GetCoulombTotalXsc( const G4ParticleDefinition* particle, |
---|
| 558 | G4double momentum, G4double Z ) |
---|
| 559 | { |
---|
| 560 | G4double beta = CalculateParticleBeta( particle, momentum); |
---|
| 561 | G4cout<<"beta = "<<beta<<G4endl; |
---|
| 562 | G4double z = particle->GetPDGCharge(); |
---|
| 563 | G4double n = CalculateZommerfeld( beta, z, Z ); |
---|
| 564 | G4cout<<"fZomerfeld = "<<n<<G4endl; |
---|
| 565 | G4double am = CalculateAm( momentum, n, Z); |
---|
| 566 | G4cout<<"cof Am = "<<am<<G4endl; |
---|
| 567 | G4double k = momentum/hbarc; |
---|
| 568 | G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl; |
---|
| 569 | G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl; |
---|
| 570 | G4double ch = n/k; |
---|
| 571 | G4double ch2 = ch*ch; |
---|
| 572 | G4double xsc = ch2*pi/(am +am*am); |
---|
| 573 | |
---|
| 574 | return xsc; |
---|
| 575 | } |
---|
| 576 | |
---|
| 577 | //////////////////////////////////////////////////////////////////// |
---|
| 578 | // |
---|
| 579 | // return Coulomb scattering xsc with Wentzel correction integrated between |
---|
| 580 | // theta1 and < theta2 |
---|
| 581 | |
---|
| 582 | inline G4double G4NuclNuclDiffuseElastic::GetCoulombIntegralXsc( const G4ParticleDefinition* particle, |
---|
| 583 | G4double momentum, G4double Z, |
---|
| 584 | G4double theta1, G4double theta2 ) |
---|
| 585 | { |
---|
| 586 | G4double c1 = std::cos(theta1); |
---|
| 587 | G4cout<<"c1 = "<<c1<<G4endl; |
---|
| 588 | G4double c2 = std::cos(theta2); |
---|
| 589 | G4cout<<"c2 = "<<c2<<G4endl; |
---|
| 590 | G4double beta = CalculateParticleBeta( particle, momentum); |
---|
| 591 | // G4cout<<"beta = "<<beta<<G4endl; |
---|
| 592 | G4double z = particle->GetPDGCharge(); |
---|
| 593 | G4double n = CalculateZommerfeld( beta, z, Z ); |
---|
| 594 | // G4cout<<"fZomerfeld = "<<n<<G4endl; |
---|
| 595 | G4double am = CalculateAm( momentum, n, Z); |
---|
| 596 | // G4cout<<"cof Am = "<<am<<G4endl; |
---|
| 597 | G4double k = momentum/hbarc; |
---|
| 598 | // G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl; |
---|
| 599 | // G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl; |
---|
| 600 | G4double ch = n/k; |
---|
| 601 | G4double ch2 = ch*ch; |
---|
| 602 | am *= 2.; |
---|
| 603 | G4double xsc = ch2*twopi*(c1-c2); |
---|
| 604 | xsc /= (1 - c1 + am)*(1 - c2 + am); |
---|
| 605 | |
---|
| 606 | return xsc; |
---|
| 607 | } |
---|
| 608 | |
---|
| 609 | /////////////////////////////////////////////////////////////////// |
---|
| 610 | // |
---|
| 611 | // For the calculation of arg Gamma(z) one needs complex extension |
---|
| 612 | // of ln(Gamma(z)) |
---|
| 613 | |
---|
| 614 | inline G4complex G4NuclNuclDiffuseElastic::GammaLogarithm(G4complex zz) |
---|
| 615 | { |
---|
| 616 | static G4double cof[6] = { 76.18009172947146, -86.50532032941677, |
---|
| 617 | 24.01409824083091, -1.231739572450155, |
---|
| 618 | 0.1208650973866179e-2, -0.5395239384953e-5 } ; |
---|
| 619 | register G4int j; |
---|
| 620 | G4complex z = zz - 1.0; |
---|
| 621 | G4complex tmp = z + 5.5; |
---|
| 622 | tmp -= (z + 0.5) * std::log(tmp); |
---|
| 623 | G4complex ser = G4complex(1.000000000190015,0.); |
---|
| 624 | |
---|
| 625 | for ( j = 0; j <= 5; j++ ) |
---|
| 626 | { |
---|
| 627 | z += 1.0; |
---|
| 628 | ser += cof[j]/z; |
---|
| 629 | } |
---|
| 630 | return -tmp + std::log(2.5066282746310005*ser); |
---|
| 631 | } |
---|
| 632 | |
---|
| 633 | ///////////////////////////////////////////////////////////////// |
---|
| 634 | // |
---|
| 635 | // |
---|
| 636 | |
---|
| 637 | inline G4double G4NuclNuclDiffuseElastic::GetErf(G4double x) |
---|
| 638 | { |
---|
| 639 | G4double t, z, tmp, result; |
---|
| 640 | |
---|
| 641 | z = std::fabs(x); |
---|
| 642 | t = 1.0/(1.0+0.5*z); |
---|
| 643 | |
---|
| 644 | tmp = t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+ |
---|
| 645 | t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+ |
---|
| 646 | t*(-0.82215223+t*0.17087277))))))))); |
---|
| 647 | |
---|
| 648 | if( x >= 0.) result = 1. - tmp; |
---|
| 649 | else result = 1. + tmp; |
---|
| 650 | |
---|
| 651 | return result; |
---|
| 652 | } |
---|
| 653 | |
---|
| 654 | ///////////////////////////////////////////////////////////////// |
---|
| 655 | // |
---|
| 656 | // |
---|
| 657 | |
---|
| 658 | inline G4complex G4NuclNuclDiffuseElastic::GetErfcComp(G4complex z, G4int nMax) |
---|
| 659 | { |
---|
| 660 | G4complex erfcz = 1. - GetErfComp( z, nMax); |
---|
| 661 | return erfcz; |
---|
| 662 | } |
---|
| 663 | |
---|
| 664 | ///////////////////////////////////////////////////////////////// |
---|
| 665 | // |
---|
| 666 | // |
---|
| 667 | |
---|
| 668 | inline G4complex G4NuclNuclDiffuseElastic::GetErfcSer(G4complex z, G4int nMax) |
---|
| 669 | { |
---|
| 670 | G4complex erfcz = 1. - GetErfSer( z, nMax); |
---|
| 671 | return erfcz; |
---|
| 672 | } |
---|
| 673 | |
---|
| 674 | ///////////////////////////////////////////////////////////////// |
---|
| 675 | // |
---|
| 676 | // |
---|
| 677 | |
---|
| 678 | inline G4complex G4NuclNuclDiffuseElastic::GetErfcInt(G4complex z) // , G4int nMax) |
---|
| 679 | { |
---|
| 680 | G4complex erfcz = 1. - GetErfInt( z); // , nMax); |
---|
| 681 | return erfcz; |
---|
| 682 | } |
---|
| 683 | |
---|
| 684 | ///////////////////////////////////////////////////////////////// |
---|
| 685 | // |
---|
| 686 | // |
---|
| 687 | |
---|
| 688 | inline G4complex G4NuclNuclDiffuseElastic::TestErfcComp(G4complex z, G4int nMax) |
---|
| 689 | { |
---|
| 690 | G4complex miz = G4complex( z.imag(), -z.real() ); |
---|
| 691 | G4complex erfcz = 1. - GetErfComp( miz, nMax); |
---|
| 692 | G4complex w = std::exp(-z*z)*erfcz; |
---|
| 693 | return w; |
---|
| 694 | } |
---|
| 695 | |
---|
| 696 | ///////////////////////////////////////////////////////////////// |
---|
| 697 | // |
---|
| 698 | // |
---|
| 699 | |
---|
| 700 | inline G4complex G4NuclNuclDiffuseElastic::TestErfcSer(G4complex z, G4int nMax) |
---|
| 701 | { |
---|
| 702 | G4complex miz = G4complex( z.imag(), -z.real() ); |
---|
| 703 | G4complex erfcz = 1. - GetErfSer( miz, nMax); |
---|
| 704 | G4complex w = std::exp(-z*z)*erfcz; |
---|
| 705 | return w; |
---|
| 706 | } |
---|
| 707 | |
---|
| 708 | ///////////////////////////////////////////////////////////////// |
---|
| 709 | // |
---|
| 710 | // |
---|
| 711 | |
---|
| 712 | inline G4complex G4NuclNuclDiffuseElastic::TestErfcInt(G4complex z) // , G4int nMax) |
---|
| 713 | { |
---|
| 714 | G4complex miz = G4complex( z.imag(), -z.real() ); |
---|
| 715 | G4complex erfcz = 1. - GetErfInt( miz); // , nMax); |
---|
| 716 | G4complex w = std::exp(-z*z)*erfcz; |
---|
| 717 | return w; |
---|
| 718 | } |
---|
| 719 | |
---|
| 720 | ///////////////////////////////////////////////////////////////// |
---|
| 721 | // |
---|
| 722 | // |
---|
| 723 | |
---|
| 724 | inline G4complex G4NuclNuclDiffuseElastic::GetErfComp(G4complex z, G4int nMax) |
---|
| 725 | { |
---|
| 726 | G4int n; |
---|
| 727 | G4double n2, cofn, shny, chny, fn, gn; |
---|
| 728 | |
---|
| 729 | G4double x = z.real(); |
---|
| 730 | G4double y = z.imag(); |
---|
| 731 | |
---|
| 732 | G4double outRe = 0., outIm = 0.; |
---|
| 733 | |
---|
| 734 | G4double twox = 2.*x; |
---|
| 735 | G4double twoxy = twox*y; |
---|
| 736 | G4double twox2 = twox*twox; |
---|
| 737 | |
---|
| 738 | G4double cof1 = std::exp(-x*x)/pi; |
---|
| 739 | |
---|
| 740 | G4double cos2xy = std::cos(twoxy); |
---|
| 741 | G4double sin2xy = std::sin(twoxy); |
---|
| 742 | |
---|
| 743 | G4double twoxcos2xy = twox*cos2xy; |
---|
| 744 | G4double twoxsin2xy = twox*sin2xy; |
---|
| 745 | |
---|
| 746 | for( n = 1; n <= nMax; n++) |
---|
| 747 | { |
---|
| 748 | n2 = n*n; |
---|
| 749 | |
---|
| 750 | cofn = std::exp(-0.5*n2)/(n2+twox2); // /(n2+0.5*twox2); |
---|
| 751 | |
---|
| 752 | chny = std::cosh(n*y); |
---|
| 753 | shny = std::sinh(n*y); |
---|
| 754 | |
---|
| 755 | fn = twox - twoxcos2xy*chny + n*sin2xy*shny; |
---|
| 756 | gn = twoxsin2xy*chny + n*cos2xy*shny; |
---|
| 757 | |
---|
| 758 | fn *= cofn; |
---|
| 759 | gn *= cofn; |
---|
| 760 | |
---|
| 761 | outRe += fn; |
---|
| 762 | outIm += gn; |
---|
| 763 | } |
---|
| 764 | outRe *= 2*cof1; |
---|
| 765 | outIm *= 2*cof1; |
---|
| 766 | |
---|
| 767 | if(std::abs(x) < 0.0001) |
---|
| 768 | { |
---|
| 769 | outRe += GetErf(x); |
---|
| 770 | outIm += cof1*y; |
---|
| 771 | } |
---|
| 772 | else |
---|
| 773 | { |
---|
| 774 | outRe += GetErf(x) + cof1*(1-cos2xy)/twox; |
---|
| 775 | outIm += cof1*sin2xy/twox; |
---|
| 776 | } |
---|
| 777 | return G4complex(outRe, outIm); |
---|
| 778 | } |
---|
| 779 | |
---|
| 780 | ///////////////////////////////////////////////////////////////// |
---|
| 781 | // |
---|
| 782 | // |
---|
| 783 | |
---|
| 784 | inline G4complex G4NuclNuclDiffuseElastic::GetErfSer(G4complex z, G4int nMax) |
---|
| 785 | { |
---|
| 786 | G4int n; |
---|
| 787 | G4double a =1., b = 1., tmp; |
---|
| 788 | G4complex sum = z, d = z; |
---|
| 789 | |
---|
| 790 | for( n = 1; n <= nMax; n++) |
---|
| 791 | { |
---|
| 792 | a *= 2.; |
---|
| 793 | b *= 2.*n +1.; |
---|
| 794 | d *= z*z; |
---|
| 795 | |
---|
| 796 | tmp = a/b; |
---|
| 797 | |
---|
| 798 | sum += tmp*d; |
---|
| 799 | } |
---|
| 800 | sum *= 2.*std::exp(-z*z)/std::sqrt(pi); |
---|
| 801 | |
---|
| 802 | return sum; |
---|
| 803 | } |
---|
| 804 | |
---|
| 805 | ///////////////////////////////////////////////////////////////////// |
---|
| 806 | |
---|
| 807 | inline G4double G4NuclNuclDiffuseElastic::GetExpCos(G4double x) |
---|
| 808 | { |
---|
| 809 | G4double result; |
---|
| 810 | |
---|
| 811 | result = std::exp(x*x-fReZ*fReZ); |
---|
| 812 | result *= std::cos(2.*x*fReZ); |
---|
| 813 | return result; |
---|
| 814 | } |
---|
| 815 | |
---|
| 816 | ///////////////////////////////////////////////////////////////////// |
---|
| 817 | |
---|
| 818 | inline G4double G4NuclNuclDiffuseElastic::GetExpSin(G4double x) |
---|
| 819 | { |
---|
| 820 | G4double result; |
---|
| 821 | |
---|
| 822 | result = std::exp(x*x-fReZ*fReZ); |
---|
| 823 | result *= std::sin(2.*x*fReZ); |
---|
| 824 | return result; |
---|
| 825 | } |
---|
| 826 | |
---|
| 827 | |
---|
| 828 | |
---|
| 829 | ///////////////////////////////////////////////////////////////// |
---|
| 830 | // |
---|
| 831 | // |
---|
| 832 | |
---|
| 833 | inline G4complex G4NuclNuclDiffuseElastic::GetErfInt(G4complex z) // , G4int nMax) |
---|
| 834 | { |
---|
| 835 | G4double outRe, outIm; |
---|
| 836 | |
---|
| 837 | G4double x = z.real(); |
---|
| 838 | G4double y = z.imag(); |
---|
| 839 | fReZ = x; |
---|
| 840 | |
---|
| 841 | G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral; |
---|
| 842 | |
---|
| 843 | outRe = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpSin, 0., y ); |
---|
| 844 | outIm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpCos, 0., y ); |
---|
| 845 | |
---|
| 846 | outRe *= 2./sqrt(pi); |
---|
| 847 | outIm *= 2./sqrt(pi); |
---|
| 848 | |
---|
| 849 | outRe += GetErf(x); |
---|
| 850 | |
---|
| 851 | return G4complex(outRe, outIm); |
---|
| 852 | } |
---|
| 853 | |
---|
| 854 | |
---|
| 855 | ///////////////////////////////////////////////////////////////// |
---|
| 856 | // |
---|
| 857 | // |
---|
| 858 | |
---|
| 859 | inline G4complex G4NuclNuclDiffuseElastic::CoulombAmplitude(G4double theta) |
---|
| 860 | { |
---|
| 861 | G4complex ca; |
---|
| 862 | |
---|
| 863 | G4double sinHalfTheta = std::sin(0.5*theta); |
---|
| 864 | G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta; |
---|
| 865 | sinHalfTheta2 += fAm; |
---|
| 866 | G4double order = 2.*fCoulombPhase0 - fZommerfeld*std::log(sinHalfTheta2); |
---|
| 867 | G4complex z = G4complex(0., order); |
---|
| 868 | ca = std::exp(z); |
---|
| 869 | ca *= -fZommerfeld/(2.*fWaveVector*sinHalfTheta2); |
---|
| 870 | |
---|
| 871 | return ca; |
---|
| 872 | } |
---|
| 873 | |
---|
| 874 | ///////////////////////////////////////////////////////////////// |
---|
| 875 | // |
---|
| 876 | // |
---|
| 877 | |
---|
| 878 | |
---|
| 879 | inline void G4NuclNuclDiffuseElastic::CalculateCoulombPhaseZero() |
---|
| 880 | { |
---|
| 881 | G4complex z = G4complex(1,fZommerfeld); |
---|
| 882 | G4complex gammalog = GammaLogarithm(z); |
---|
| 883 | fCoulombPhase0 = gammalog.imag(); |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | |
---|
| 887 | ///////////////////////////////////////////////////////////////// |
---|
| 888 | // |
---|
| 889 | // |
---|
| 890 | |
---|
| 891 | |
---|
| 892 | inline void G4NuclNuclDiffuseElastic::CalculateRutherfordAnglePar() |
---|
| 893 | { |
---|
| 894 | fHalfRutThetaTg = fZommerfeld/(fWaveVector*fNuclearRadius); |
---|
| 895 | fRutherfordTheta = 2.*std::atan(fHalfRutThetaTg); |
---|
| 896 | G4cout<<"fRutherfordTheta = "<<fRutherfordTheta/degree<<" degree"<<G4endl; |
---|
| 897 | |
---|
| 898 | } |
---|
| 899 | |
---|
| 900 | ///////////////////////////////////////////////////////////////// |
---|
| 901 | // |
---|
| 902 | // |
---|
| 903 | |
---|
| 904 | inline G4double G4NuclNuclDiffuseElastic::ProfileNear(G4double theta) |
---|
| 905 | { |
---|
| 906 | G4double dTheta = fRutherfordTheta - theta; |
---|
| 907 | G4double result = 0., argument = 0.; |
---|
| 908 | |
---|
| 909 | if(std::abs(dTheta) < 0.001) result = fProfileAlpha*fProfileDelta; |
---|
| 910 | else |
---|
| 911 | { |
---|
| 912 | argument = fProfileDelta*dTheta; |
---|
| 913 | result = pi*argument*std::exp(fProfileAlpha*argument); |
---|
| 914 | result /= std::sinh(pi*argument); |
---|
| 915 | result -= 1.; |
---|
| 916 | result /= dTheta; |
---|
| 917 | } |
---|
| 918 | return result; |
---|
| 919 | } |
---|
| 920 | |
---|
| 921 | ///////////////////////////////////////////////////////////////// |
---|
| 922 | // |
---|
| 923 | // |
---|
| 924 | |
---|
| 925 | inline G4double G4NuclNuclDiffuseElastic::ProfileFar(G4double theta) |
---|
| 926 | { |
---|
| 927 | G4double dTheta = fRutherfordTheta + theta; |
---|
| 928 | G4double argument = fProfileDelta*dTheta; |
---|
| 929 | |
---|
| 930 | G4double result = pi*argument*std::exp(fProfileAlpha*argument); |
---|
| 931 | result /= std::sinh(pi*argument); |
---|
| 932 | result /= dTheta; |
---|
| 933 | |
---|
| 934 | return result; |
---|
| 935 | } |
---|
| 936 | |
---|
| 937 | ///////////////////////////////////////////////////////////////// |
---|
| 938 | // |
---|
| 939 | // |
---|
| 940 | |
---|
| 941 | inline G4complex G4NuclNuclDiffuseElastic::PhaseNear(G4double theta) |
---|
| 942 | { |
---|
| 943 | G4double twosigma = 2.*fCoulombPhase0; |
---|
| 944 | twosigma -= fZommerfeld*std::log(fHalfRutThetaTg/(1.+fHalfRutThetaTg*fHalfRutThetaTg)); |
---|
| 945 | twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi; |
---|
| 946 | twosigma -= fProfileLambda*theta - 0.25*pi; |
---|
| 947 | |
---|
| 948 | G4complex z = G4complex(0., twosigma); |
---|
| 949 | |
---|
| 950 | return std::exp(z); |
---|
| 951 | } |
---|
| 952 | |
---|
| 953 | ///////////////////////////////////////////////////////////////// |
---|
| 954 | // |
---|
| 955 | // |
---|
| 956 | |
---|
| 957 | inline G4complex G4NuclNuclDiffuseElastic::PhaseFar(G4double theta) |
---|
| 958 | { |
---|
| 959 | G4double twosigma = 2.*fCoulombPhase0; |
---|
| 960 | twosigma -= fZommerfeld*std::log(fHalfRutThetaTg/(1.+fHalfRutThetaTg*fHalfRutThetaTg)); |
---|
| 961 | twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi; |
---|
| 962 | twosigma += fProfileLambda*theta - 0.25*pi; |
---|
| 963 | |
---|
| 964 | G4complex z = G4complex(0., twosigma); |
---|
| 965 | |
---|
| 966 | return std::exp(z); |
---|
| 967 | } |
---|
| 968 | |
---|
| 969 | ///////////////////////////////////////////////////////////////// |
---|
| 970 | // |
---|
| 971 | // |
---|
| 972 | |
---|
| 973 | |
---|
| 974 | inline G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta) |
---|
| 975 | { |
---|
| 976 | G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg*fHalfRutThetaTg); |
---|
| 977 | G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg*fHalfRutThetaTg); |
---|
| 978 | |
---|
| 979 | G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR); |
---|
| 980 | G4double kappa = u/std::sqrt(pi); |
---|
| 981 | G4double dTheta = theta - fRutherfordTheta; |
---|
| 982 | u *= dTheta; |
---|
| 983 | G4double u2 = u*u; |
---|
| 984 | G4double u2m2p3 = u2*2./3.; |
---|
| 985 | |
---|
| 986 | G4complex im = G4complex(0.,1.); |
---|
| 987 | G4complex order = G4complex(u,u); |
---|
| 988 | order /= std::sqrt(2.); |
---|
| 989 | G4complex gamma = pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*pi)); |
---|
| 990 | G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR; |
---|
| 991 | G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR; |
---|
| 992 | G4complex out = gamma*(1. - a1*dTheta) - a0; |
---|
| 993 | return out; |
---|
| 994 | } |
---|
| 995 | |
---|
| 996 | ///////////////////////////////////////////////////////////////// |
---|
| 997 | // |
---|
| 998 | // |
---|
| 999 | |
---|
| 1000 | inline G4complex G4NuclNuclDiffuseElastic::GammaMore(G4double theta) |
---|
| 1001 | { |
---|
| 1002 | G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg*fHalfRutThetaTg); |
---|
| 1003 | G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg*fHalfRutThetaTg); |
---|
| 1004 | |
---|
| 1005 | G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR); |
---|
| 1006 | G4double kappa = u/std::sqrt(pi); |
---|
| 1007 | G4double dTheta = theta - fRutherfordTheta; |
---|
| 1008 | u *= dTheta; |
---|
| 1009 | G4double u2 = u*u; |
---|
| 1010 | G4double u2m2p3 = u2*2./3.; |
---|
| 1011 | |
---|
| 1012 | G4complex im = G4complex(0.,1.); |
---|
| 1013 | G4complex order = G4complex(u,u); |
---|
| 1014 | order /= std::sqrt(2.); |
---|
| 1015 | G4complex gamma = pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*pi)); |
---|
| 1016 | G4complex a0 = 0.5*(1. + 3.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR; |
---|
| 1017 | G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR; |
---|
| 1018 | G4complex out = -gamma*(1. - a1*dTheta) - a0; |
---|
| 1019 | return out; |
---|
| 1020 | } |
---|
| 1021 | |
---|
| 1022 | ///////////////////////////////////////////////////////////////// |
---|
| 1023 | // |
---|
| 1024 | // |
---|
| 1025 | |
---|
| 1026 | inline G4complex G4NuclNuclDiffuseElastic::AmplitudeNear(G4double theta) |
---|
| 1027 | { |
---|
| 1028 | G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi); |
---|
| 1029 | G4complex out = G4complex(kappa/fWaveVector,0.); |
---|
| 1030 | out *= PhaseNear(theta); |
---|
| 1031 | |
---|
| 1032 | if(theta <= fRutherfordTheta) |
---|
| 1033 | { |
---|
| 1034 | out *= GammaLess(theta) + ProfileNear(theta); |
---|
| 1035 | out += CoulombAmplitude(theta); |
---|
| 1036 | } |
---|
| 1037 | else |
---|
| 1038 | { |
---|
| 1039 | out *= GammaMore(theta) + ProfileNear(theta); |
---|
| 1040 | } |
---|
| 1041 | return out; |
---|
| 1042 | } |
---|
| 1043 | |
---|
| 1044 | ///////////////////////////////////////////////////////////////// |
---|
| 1045 | // |
---|
| 1046 | // |
---|
| 1047 | |
---|
| 1048 | inline G4complex G4NuclNuclDiffuseElastic::AmplitudeFar(G4double theta) |
---|
| 1049 | { |
---|
| 1050 | G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi); |
---|
| 1051 | G4complex out = G4complex(kappa/fWaveVector,0.); |
---|
| 1052 | out *= ProfileFar(theta)*PhaseFar(theta); |
---|
| 1053 | return out; |
---|
| 1054 | } |
---|
| 1055 | |
---|
| 1056 | |
---|
| 1057 | ///////////////////////////////////////////////////////////////// |
---|
| 1058 | // |
---|
| 1059 | // |
---|
| 1060 | |
---|
| 1061 | inline G4complex G4NuclNuclDiffuseElastic::Amplitude(G4double theta) |
---|
| 1062 | { |
---|
| 1063 | |
---|
| 1064 | G4complex out = AmplitudeNear(theta) + AmplitudeFar(theta); |
---|
| 1065 | return out; |
---|
| 1066 | } |
---|
| 1067 | |
---|
| 1068 | ///////////////////////////////////////////////////////////////// |
---|
| 1069 | // |
---|
| 1070 | // |
---|
| 1071 | |
---|
| 1072 | inline G4double G4NuclNuclDiffuseElastic::AmplitudeMod2(G4double theta) |
---|
| 1073 | { |
---|
| 1074 | G4complex out = Amplitude(theta); |
---|
| 1075 | G4double mod2 = out.real()*out.real() + out.imag()*out.imag(); |
---|
| 1076 | return mod2; |
---|
| 1077 | } |
---|
| 1078 | |
---|
| 1079 | |
---|
| 1080 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 1081 | // |
---|
| 1082 | // Test for given particle and element table of momentum, angle probability. |
---|
| 1083 | // For the moment in lab system. |
---|
| 1084 | |
---|
| 1085 | inline void G4NuclNuclDiffuseElastic::InitParameters(const G4ParticleDefinition* theParticle, |
---|
| 1086 | G4double partMom, G4double Z, G4double A) |
---|
| 1087 | { |
---|
| 1088 | fAtomicNumber = Z; // atomic number |
---|
| 1089 | fAtomicWeight = A; // number of nucleons |
---|
| 1090 | |
---|
| 1091 | fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight); |
---|
| 1092 | G4double A1 = G4double( theParticle->GetBaryonNumber() ); |
---|
| 1093 | fNuclearRadius1 = CalculateNuclearRad(A1); |
---|
| 1094 | // fNuclearRadius = std::sqrt(fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2); |
---|
| 1095 | fNuclearRadius = fNuclearRadius1 + fNuclearRadius2; |
---|
| 1096 | |
---|
| 1097 | G4double a = 0.; |
---|
| 1098 | G4double z = theParticle->GetPDGCharge(); |
---|
| 1099 | G4double m1 = theParticle->GetPDGMass(); |
---|
| 1100 | |
---|
| 1101 | fWaveVector = partMom/hbarc; |
---|
| 1102 | |
---|
| 1103 | G4double lambda = fWaveVector*fNuclearRadius; |
---|
| 1104 | |
---|
| 1105 | if( z ) |
---|
| 1106 | { |
---|
| 1107 | a = partMom/m1; // beta*gamma for m1 |
---|
| 1108 | fBeta = a/std::sqrt(1+a*a); |
---|
| 1109 | fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber); |
---|
| 1110 | fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber); |
---|
| 1111 | } |
---|
| 1112 | fProfileLambda = lambda*std::sqrt(1.-2*fZommerfeld/lambda); |
---|
| 1113 | G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl; |
---|
| 1114 | fProfileDelta = 0.1*fProfileLambda; |
---|
| 1115 | fProfileAlpha = 0.05*fProfileLambda; |
---|
| 1116 | |
---|
| 1117 | CalculateCoulombPhaseZero(); |
---|
| 1118 | CalculateRutherfordAnglePar(); |
---|
| 1119 | |
---|
| 1120 | return; |
---|
| 1121 | } |
---|
| 1122 | |
---|
| 1123 | |
---|
| 1124 | |
---|
| 1125 | |
---|
| 1126 | |
---|
| 1127 | #endif |
---|