Gabriele Cosmo
1794 lines
50 KiB
C++
1794 lines
50 KiB
C++
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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//
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// $Id$
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//
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//
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// G4 Model: optical elastic scattering with 4-momentum balance
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//
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// Class Description
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// Final state production model for nucleus-nucleus elastic scattering;
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// Coulomb amplitude is not considered as correction
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// (as in G4DiffuseElastic)
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// Class Description - End
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//
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//
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// 17.03.09 V. Grichine implementation for Coulomb elastic scattering
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#ifndef G4NuclNuclDiffuseElastic_h
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#define G4NuclNuclDiffuseElastic_h 1
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#include <complex>
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#include <CLHEP/Units/PhysicalConstants.h>
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#include "globals.hh"
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#include "G4Integrator.hh"
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#include "G4HadronElastic.hh"
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#include "G4HadProjectile.hh"
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#include "G4Nucleus.hh"
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using namespace std;
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class G4ParticleDefinition;
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class G4PhysicsTable;
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class G4PhysicsLogVector;
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class G4NuclNuclDiffuseElastic : public G4HadronElastic // G4HadronicInteraction
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{
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public:
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G4NuclNuclDiffuseElastic();
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// G4NuclNuclDiffuseElastic(const G4ParticleDefinition* aParticle);
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virtual ~G4NuclNuclDiffuseElastic();
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void Initialise();
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void InitialiseOnFly(G4double Z, G4double A);
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void BuildAngleTable();
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// G4HadFinalState * ApplyYourself(const G4HadProjectile & aTrack, G4Nucleus & targetNucleus);
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virtual G4double SampleInvariantT(const G4ParticleDefinition* p,
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G4double plab,
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G4int Z, G4int A);
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void SetPlabLowLimit(G4double value);
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void SetHEModelLowLimit(G4double value);
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void SetQModelLowLimit(G4double value);
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void SetLowestEnergyLimit(G4double value);
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void SetRecoilKinEnergyLimit(G4double value);
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G4double SampleT(const G4ParticleDefinition* aParticle,
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G4double p, G4double A);
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G4double SampleTableT(const G4ParticleDefinition* aParticle,
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G4double p, G4double Z, G4double A);
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G4double SampleThetaCMS(const G4ParticleDefinition* aParticle, G4double p, G4double A);
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G4double SampleTableThetaCMS(const G4ParticleDefinition* aParticle, G4double p,
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G4double Z, G4double A);
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G4double GetScatteringAngle(G4int iMomentum, G4int iAngle, G4double position);
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G4double SampleThetaLab(const G4HadProjectile* aParticle,
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G4double tmass, G4double A);
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G4double GetDiffuseElasticXsc( const G4ParticleDefinition* particle,
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G4double theta,
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G4double momentum,
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G4double A );
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G4double GetInvElasticXsc( const G4ParticleDefinition* particle,
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G4double theta,
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G4double momentum,
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G4double A, G4double Z );
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G4double GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle,
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G4double theta,
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G4double momentum,
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G4double A, G4double Z );
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G4double GetInvElasticSumXsc( const G4ParticleDefinition* particle,
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G4double tMand,
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G4double momentum,
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G4double A, G4double Z );
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G4double IntegralElasticProb( const G4ParticleDefinition* particle,
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G4double theta,
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G4double momentum,
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G4double A );
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G4double GetCoulombElasticXsc( const G4ParticleDefinition* particle,
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G4double theta,
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G4double momentum,
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G4double Z );
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G4double GetRutherfordXsc( G4double theta );
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G4double GetInvCoulombElasticXsc( const G4ParticleDefinition* particle,
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G4double tMand,
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G4double momentum,
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G4double A, G4double Z );
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G4double GetCoulombTotalXsc( const G4ParticleDefinition* particle,
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G4double momentum, G4double Z );
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G4double GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
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G4double momentum, G4double Z,
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G4double theta1, G4double theta2 );
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G4double CalculateParticleBeta( const G4ParticleDefinition* particle,
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G4double momentum );
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G4double CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 );
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G4double CalculateAm( G4double momentum, G4double n, G4double Z);
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G4double CalculateNuclearRad( G4double A);
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G4double ThetaCMStoThetaLab(const G4DynamicParticle* aParticle,
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G4double tmass, G4double thetaCMS);
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G4double ThetaLabToThetaCMS(const G4DynamicParticle* aParticle,
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G4double tmass, G4double thetaLab);
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void TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom,
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G4double Z, G4double A);
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G4double BesselJzero(G4double z);
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G4double BesselJone(G4double z);
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G4double DampFactor(G4double z);
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G4double BesselOneByArg(G4double z);
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G4double GetDiffElasticProb(G4double theta);
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G4double GetDiffElasticSumProb(G4double theta);
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G4double GetDiffElasticSumProbA(G4double alpha);
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G4double GetIntegrandFunction(G4double theta);
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G4double GetNuclearRadius(){return fNuclearRadius;};
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// Technical math functions for strong Coulomb contribution
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G4complex GammaLogarithm(G4complex xx);
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G4complex GammaLogB2n(G4complex xx);
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G4double GetErf(G4double x);
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G4double GetCosHaPit2(G4double t){return std::cos(CLHEP::halfpi*t*t);};
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G4double GetSinHaPit2(G4double t){return std::sin(CLHEP::halfpi*t*t);};
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G4double GetCint(G4double x);
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G4double GetSint(G4double x);
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G4complex GetErfcComp(G4complex z, G4int nMax);
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G4complex GetErfcSer(G4complex z, G4int nMax);
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G4complex GetErfcInt(G4complex z); // , G4int nMax);
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G4complex GetErfComp(G4complex z, G4int nMax); // AandS algorithm != Ser, Int
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G4complex GetErfSer(G4complex z, G4int nMax);
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G4double GetExpCos(G4double x);
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G4double GetExpSin(G4double x);
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G4complex GetErfInt(G4complex z); // , G4int nMax);
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G4double GetLegendrePol(G4int n, G4double x);
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G4complex TestErfcComp(G4complex z, G4int nMax);
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G4complex TestErfcSer(G4complex z, G4int nMax);
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G4complex TestErfcInt(G4complex z); // , G4int nMax);
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G4complex CoulombAmplitude(G4double theta);
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G4double CoulombAmplitudeMod2(G4double theta);
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void CalculateCoulombPhaseZero();
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G4double CalculateCoulombPhase(G4int n);
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void CalculateRutherfordAnglePar();
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G4double ProfileNear(G4double theta);
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G4double ProfileFar(G4double theta);
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G4double Profile(G4double theta);
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G4complex PhaseNear(G4double theta);
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G4complex PhaseFar(G4double theta);
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G4complex GammaLess(G4double theta);
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G4complex GammaMore(G4double theta);
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G4complex AmplitudeNear(G4double theta);
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G4complex AmplitudeFar(G4double theta);
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G4complex Amplitude(G4double theta);
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G4double AmplitudeMod2(G4double theta);
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G4complex AmplitudeSim(G4double theta);
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G4double AmplitudeSimMod2(G4double theta);
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G4double GetRatioSim(G4double theta);
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G4double GetRatioGen(G4double theta);
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G4double GetFresnelDiffuseXsc(G4double theta);
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G4double GetFresnelIntegrandXsc(G4double alpha);
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G4complex AmplitudeGla(G4double theta);
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G4double AmplitudeGlaMod2(G4double theta);
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G4complex AmplitudeGG(G4double theta);
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G4double AmplitudeGGMod2(G4double theta);
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void InitParameters(const G4ParticleDefinition* theParticle,
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G4double partMom, G4double Z, G4double A);
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void InitDynParameters(const G4ParticleDefinition* theParticle,
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G4double partMom);
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void InitParametersGla(const G4DynamicParticle* aParticle,
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G4double partMom, G4double Z, G4double A);
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G4double GetHadronNucleonXscNS( G4ParticleDefinition* pParticle,
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G4double pTkin,
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G4ParticleDefinition* tParticle);
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G4double CalcMandelstamS( const G4double mp ,
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const G4double mt ,
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const G4double Plab );
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G4double GetProfileLambda(){return fProfileLambda;};
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void SetProfileLambda(G4double pl) {fProfileLambda = pl;};
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void SetProfileDelta(G4double pd) {fProfileDelta = pd;};
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void SetProfileAlpha(G4double pa){fProfileAlpha = pa;};
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void SetCofLambda(G4double pa){fCofLambda = pa;};
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void SetCofAlpha(G4double pa){fCofAlpha = pa;};
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void SetCofAlphaMax(G4double pa){fCofAlphaMax = pa;};
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void SetCofAlphaCoulomb(G4double pa){fCofAlphaCoulomb = pa;};
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void SetCofDelta(G4double pa){fCofDelta = pa;};
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void SetCofPhase(G4double pa){fCofPhase = pa;};
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void SetCofFar(G4double pa){fCofFar = pa;};
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void SetEtaRatio(G4double pa){fEtaRatio = pa;};
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void SetMaxL(G4int l){fMaxL = l;};
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void SetNuclearRadiusCof(G4double r){fNuclearRadiusCof = r;};
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G4double GetCofAlphaMax(){return fCofAlphaMax;};
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G4double GetCofAlphaCoulomb(){return fCofAlphaCoulomb;};
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private:
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G4ParticleDefinition* theProton;
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G4ParticleDefinition* theNeutron;
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G4ParticleDefinition* theDeuteron;
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G4ParticleDefinition* theAlpha;
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const G4ParticleDefinition* thePionPlus;
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const G4ParticleDefinition* thePionMinus;
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G4double lowEnergyRecoilLimit;
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G4double lowEnergyLimitHE;
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G4double lowEnergyLimitQ;
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G4double lowestEnergyLimit;
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G4double plabLowLimit;
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G4int fEnergyBin;
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G4int fAngleBin;
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G4PhysicsLogVector* fEnergyVector;
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G4PhysicsTable* fAngleTable;
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std::vector<G4PhysicsTable*> fAngleBank;
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std::vector<G4double> fElementNumberVector;
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std::vector<G4String> fElementNameVector;
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const G4ParticleDefinition* fParticle;
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G4double fWaveVector;
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G4double fAtomicWeight;
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G4double fAtomicNumber;
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G4double fNuclearRadius1;
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G4double fNuclearRadius2;
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G4double fNuclearRadius;
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G4double fNuclearRadiusSquare;
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G4double fNuclearRadiusCof;
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G4double fBeta;
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G4double fZommerfeld;
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G4double fRutherfordRatio;
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G4double fAm;
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G4bool fAddCoulomb;
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G4double fCoulombPhase0;
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G4double fHalfRutThetaTg;
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G4double fHalfRutThetaTg2;
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G4double fRutherfordTheta;
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G4double fProfileLambda;
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G4double fProfileDelta;
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G4double fProfileAlpha;
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G4double fCofLambda;
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G4double fCofAlpha;
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G4double fCofDelta;
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G4double fCofPhase;
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G4double fCofFar;
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G4double fCofAlphaMax;
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G4double fCofAlphaCoulomb;
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G4int fMaxL;
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G4double fSumSigma;
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G4double fEtaRatio;
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G4double fReZ;
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};
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inline void G4NuclNuclDiffuseElastic::SetRecoilKinEnergyLimit(G4double value)
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{
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lowEnergyRecoilLimit = value;
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}
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inline void G4NuclNuclDiffuseElastic::SetPlabLowLimit(G4double value)
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{
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plabLowLimit = value;
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}
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inline void G4NuclNuclDiffuseElastic::SetHEModelLowLimit(G4double value)
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{
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lowEnergyLimitHE = value;
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}
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inline void G4NuclNuclDiffuseElastic::SetQModelLowLimit(G4double value)
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{
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lowEnergyLimitQ = value;
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}
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inline void G4NuclNuclDiffuseElastic::SetLowestEnergyLimit(G4double value)
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{
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lowestEnergyLimit = value;
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}
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/////////////////////////////////////////////////////////////
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//
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// Bessel J0 function based on rational approximation from
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// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
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inline G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value)
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{
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G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
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modvalue = fabs(value);
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if ( value < 8.0 && value > -8.0 )
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{
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value2 = value*value;
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fact1 = 57568490574.0 + value2*(-13362590354.0
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+ value2*( 651619640.7
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+ value2*(-11214424.18
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+ value2*( 77392.33017
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+ value2*(-184.9052456 ) ) ) ) );
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fact2 = 57568490411.0 + value2*( 1029532985.0
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+ value2*( 9494680.718
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+ value2*(59272.64853
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+ value2*(267.8532712
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+ value2*1.0 ) ) ) );
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bessel = fact1/fact2;
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}
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else
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{
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arg = 8.0/modvalue;
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value2 = arg*arg;
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shift = modvalue-0.785398164;
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fact1 = 1.0 + value2*(-0.1098628627e-2
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+ value2*(0.2734510407e-4
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+ value2*(-0.2073370639e-5
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+ value2*0.2093887211e-6 ) ) );
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fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3
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+ value2*(-0.6911147651e-5
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+ value2*(0.7621095161e-6
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- value2*0.934945152e-7 ) ) );
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bessel = sqrt(0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2 );
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}
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return bessel;
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}
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/////////////////////////////////////////////////////////////
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//
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// Bessel J1 function based on rational approximation from
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// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
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inline G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value)
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{
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G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
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modvalue = fabs(value);
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if ( modvalue < 8.0 )
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{
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value2 = value*value;
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fact1 = value*(72362614232.0 + value2*(-7895059235.0
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+ value2*( 242396853.1
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+ value2*(-2972611.439
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+ value2*( 15704.48260
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+ value2*(-30.16036606 ) ) ) ) ) );
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fact2 = 144725228442.0 + value2*(2300535178.0
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+ value2*(18583304.74
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+ value2*(99447.43394
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+ value2*(376.9991397
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+ value2*1.0 ) ) ) );
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bessel = fact1/fact2;
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}
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else
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{
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arg = 8.0/modvalue;
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value2 = arg*arg;
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shift = modvalue - 2.356194491;
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fact1 = 1.0 + value2*( 0.183105e-2
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+ value2*(-0.3516396496e-4
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+ value2*(0.2457520174e-5
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+ value2*(-0.240337019e-6 ) ) ) );
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fact2 = 0.04687499995 + value2*(-0.2002690873e-3
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+ value2*( 0.8449199096e-5
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+ value2*(-0.88228987e-6
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+ value2*0.105787412e-6 ) ) );
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bessel = sqrt( 0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2);
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if (value < 0.0) bessel = -bessel;
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}
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return bessel;
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}
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////////////////////////////////////////////////////////////////////
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//
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// damp factor in diffraction x/sh(x), x was already *pi
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inline G4double G4NuclNuclDiffuseElastic::DampFactor(G4double x)
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{
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G4double df;
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G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials
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// x *= pi;
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if( std::fabs(x) < 0.01 )
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{
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df = 1./(1. + x/f2 + x*x/f3 + x*x*x/f4);
|
|
}
|
|
else
|
|
{
|
|
df = x/std::sinh(x);
|
|
}
|
|
return df;
|
|
}
|
|
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return J1(x)/x with special case for small x
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::BesselOneByArg(G4double x)
|
|
{
|
|
G4double x2, result;
|
|
|
|
if( std::fabs(x) < 0.01 )
|
|
{
|
|
x *= 0.5;
|
|
x2 = x*x;
|
|
result = 2. - x2 + x2*x2/6.;
|
|
}
|
|
else
|
|
{
|
|
result = BesselJone(x)/x;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return particle beta
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CalculateParticleBeta( const G4ParticleDefinition* particle,
|
|
G4double momentum )
|
|
{
|
|
G4double mass = particle->GetPDGMass();
|
|
G4double a = momentum/mass;
|
|
fBeta = a/std::sqrt(1+a*a);
|
|
|
|
return fBeta;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return Zommerfeld parameter for Coulomb scattering
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 )
|
|
{
|
|
fZommerfeld = CLHEP::fine_structure_const*Z1*Z2/beta;
|
|
|
|
return fZommerfeld;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return Wentzel correction for Coulomb scattering
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CalculateAm( G4double momentum, G4double n, G4double Z)
|
|
{
|
|
G4double k = momentum/CLHEP::hbarc;
|
|
G4double ch = 1.13 + 3.76*n*n;
|
|
G4double zn = 1.77*k*std::pow(Z,-1./3.)*CLHEP::Bohr_radius;
|
|
G4double zn2 = zn*zn;
|
|
fAm = ch/zn2;
|
|
|
|
return fAm;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// calculate nuclear radius for different atomic weights using different approximations
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CalculateNuclearRad( G4double A)
|
|
{
|
|
G4double r0 = 1.*CLHEP::fermi, radius;
|
|
// r0 *= 1.12;
|
|
// r0 *= 1.44;
|
|
r0 *= fNuclearRadiusCof;
|
|
|
|
/*
|
|
if( A < 50. )
|
|
{
|
|
if( A > 10. ) r0 = 1.16*( 1 - std::pow(A, -2./3.) )*CLHEP::fermi; // 1.08*fermi;
|
|
else r0 = 1.1*CLHEP::fermi;
|
|
|
|
radius = r0*std::pow(A, 1./3.);
|
|
}
|
|
else
|
|
{
|
|
r0 = 1.7*CLHEP::fermi; // 1.7*fermi;
|
|
|
|
radius = r0*std::pow(A, 0.27); // 0.27);
|
|
}
|
|
*/
|
|
radius = r0*std::pow(A, 1./3.);
|
|
|
|
return radius;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return Coulomb scattering differential xsc with Wentzel correction. Test function
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetCoulombElasticXsc( const G4ParticleDefinition* particle,
|
|
G4double theta,
|
|
G4double momentum,
|
|
G4double Z )
|
|
{
|
|
G4double sinHalfTheta = std::sin(0.5*theta);
|
|
G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
|
|
G4double beta = CalculateParticleBeta( particle, momentum);
|
|
G4double z = particle->GetPDGCharge();
|
|
G4double n = CalculateZommerfeld( beta, z, Z );
|
|
G4double am = CalculateAm( momentum, n, Z);
|
|
G4double k = momentum/CLHEP::hbarc;
|
|
G4double ch = 0.5*n/k;
|
|
G4double ch2 = ch*ch;
|
|
G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am);
|
|
|
|
return xsc;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return Rutherford scattering differential xsc with Wentzel correction. For Sampling.
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetRutherfordXsc( G4double theta )
|
|
{
|
|
G4double sinHalfTheta = std::sin(0.5*theta);
|
|
G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
|
|
|
|
G4double ch2 = fRutherfordRatio*fRutherfordRatio;
|
|
|
|
G4double xsc = ch2/(sinHalfTheta2+fAm)/(sinHalfTheta2+fAm);
|
|
|
|
return xsc;
|
|
}
|
|
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return Coulomb scattering total xsc with Wentzel correction
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetCoulombTotalXsc( const G4ParticleDefinition* particle,
|
|
G4double momentum, G4double Z )
|
|
{
|
|
G4double beta = CalculateParticleBeta( particle, momentum);
|
|
G4cout<<"beta = "<<beta<<G4endl;
|
|
G4double z = particle->GetPDGCharge();
|
|
G4double n = CalculateZommerfeld( beta, z, Z );
|
|
G4cout<<"fZomerfeld = "<<n<<G4endl;
|
|
G4double am = CalculateAm( momentum, n, Z);
|
|
G4cout<<"cof Am = "<<am<<G4endl;
|
|
G4double k = momentum/CLHEP::hbarc;
|
|
G4cout<<"k = "<<k*CLHEP::fermi<<" 1/fermi"<<G4endl;
|
|
G4cout<<"k*Bohr_radius = "<<k*CLHEP::Bohr_radius<<G4endl;
|
|
G4double ch = n/k;
|
|
G4double ch2 = ch*ch;
|
|
G4double xsc = ch2*CLHEP::pi/(am +am*am);
|
|
|
|
return xsc;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////
|
|
//
|
|
// return Coulomb scattering xsc with Wentzel correction integrated between
|
|
// theta1 and < theta2
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
|
|
G4double momentum, G4double Z,
|
|
G4double theta1, G4double theta2 )
|
|
{
|
|
G4double c1 = std::cos(theta1);
|
|
G4cout<<"c1 = "<<c1<<G4endl;
|
|
G4double c2 = std::cos(theta2);
|
|
G4cout<<"c2 = "<<c2<<G4endl;
|
|
G4double beta = CalculateParticleBeta( particle, momentum);
|
|
// G4cout<<"beta = "<<beta<<G4endl;
|
|
G4double z = particle->GetPDGCharge();
|
|
G4double n = CalculateZommerfeld( beta, z, Z );
|
|
// G4cout<<"fZomerfeld = "<<n<<G4endl;
|
|
G4double am = CalculateAm( momentum, n, Z);
|
|
// G4cout<<"cof Am = "<<am<<G4endl;
|
|
G4double k = momentum/CLHEP::hbarc;
|
|
// G4cout<<"k = "<<k*CLHEP::fermi<<" 1/fermi"<<G4endl;
|
|
// G4cout<<"k*Bohr_radius = "<<k*CLHEP::Bohr_radius<<G4endl;
|
|
G4double ch = n/k;
|
|
G4double ch2 = ch*ch;
|
|
am *= 2.;
|
|
G4double xsc = ch2*CLHEP::twopi*(c1-c2);
|
|
xsc /= (1 - c1 + am)*(1 - c2 + am);
|
|
|
|
return xsc;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////
|
|
//
|
|
// For the calculation of arg Gamma(z) one needs complex extension
|
|
// of ln(Gamma(z))
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GammaLogarithm(G4complex zz)
|
|
{
|
|
static G4double cof[6] = { 76.18009172947146, -86.50532032941677,
|
|
24.01409824083091, -1.231739572450155,
|
|
0.1208650973866179e-2, -0.5395239384953e-5 } ;
|
|
register G4int j;
|
|
G4complex z = zz - 1.0;
|
|
G4complex tmp = z + 5.5;
|
|
tmp -= (z + 0.5) * std::log(tmp);
|
|
G4complex ser = G4complex(1.000000000190015,0.);
|
|
|
|
for ( j = 0; j <= 5; j++ )
|
|
{
|
|
z += 1.0;
|
|
ser += cof[j]/z;
|
|
}
|
|
return -tmp + std::log(2.5066282746310005*ser);
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////
|
|
//
|
|
// For the calculation of arg Gamma(z) one needs complex extension
|
|
// of ln(Gamma(z)) here is approximate algorithm
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GammaLogB2n(G4complex z)
|
|
{
|
|
G4complex z1 = 12.*z;
|
|
G4complex z2 = z*z;
|
|
G4complex z3 = z2*z;
|
|
G4complex z5 = z2*z3;
|
|
G4complex z7 = z2*z5;
|
|
|
|
z3 *= 360.;
|
|
z5 *= 1260.;
|
|
z7 *= 1680.;
|
|
|
|
G4complex result = (z-0.5)*std::log(z)-z+0.5*std::log(CLHEP::twopi);
|
|
result += 1./z1 - 1./z3 +1./z5 -1./z7;
|
|
return result;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetErf(G4double x)
|
|
{
|
|
G4double t, z, tmp, result;
|
|
|
|
z = std::fabs(x);
|
|
t = 1.0/(1.0+0.5*z);
|
|
|
|
tmp = t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+
|
|
t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+
|
|
t*(-0.82215223+t*0.17087277)))))))));
|
|
|
|
if( x >= 0.) result = 1. - tmp;
|
|
else result = 1. + tmp;
|
|
|
|
return result;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GetErfcComp(G4complex z, G4int nMax)
|
|
{
|
|
G4complex erfcz = 1. - GetErfComp( z, nMax);
|
|
return erfcz;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GetErfcSer(G4complex z, G4int nMax)
|
|
{
|
|
G4complex erfcz = 1. - GetErfSer( z, nMax);
|
|
return erfcz;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GetErfcInt(G4complex z) // , G4int nMax)
|
|
{
|
|
G4complex erfcz = 1. - GetErfInt( z); // , nMax);
|
|
return erfcz;
|
|
}
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetLegendrePol(G4int n, G4double theta)
|
|
{
|
|
G4double legPol, epsilon = 1.e-6;
|
|
G4double x = std::cos(theta);
|
|
|
|
if ( n < 0 ) legPol = 0.;
|
|
else if( n == 0 ) legPol = 1.;
|
|
else if( n == 1 ) legPol = x;
|
|
else if( n == 2 ) legPol = (3.*x*x-1.)/2.;
|
|
else if( n == 3 ) legPol = (5.*x*x*x-3.*x)/2.;
|
|
else if( n == 4 ) legPol = (35.*x*x*x*x-30.*x*x+3.)/8.;
|
|
else if( n == 5 ) legPol = (63.*x*x*x*x*x-70.*x*x*x+15.*x)/8.;
|
|
else if( n == 6 ) legPol = (231.*x*x*x*x*x*x-315.*x*x*x*x+105.*x*x-5.)/16.;
|
|
else
|
|
{
|
|
// legPol = ( (2*n-1)*x*GetLegendrePol(n-1,x) - (n-1)*GetLegendrePol(n-2,x) )/n;
|
|
|
|
legPol = std::sqrt( 2./(n*CLHEP::pi*std::sin(theta+epsilon)) )*std::sin( (n+0.5)*theta+0.25*CLHEP::pi );
|
|
}
|
|
return legPol;
|
|
}
|
|
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::TestErfcComp(G4complex z, G4int nMax)
|
|
{
|
|
G4complex miz = G4complex( z.imag(), -z.real() );
|
|
G4complex erfcz = 1. - GetErfComp( miz, nMax);
|
|
G4complex w = std::exp(-z*z)*erfcz;
|
|
return w;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::TestErfcSer(G4complex z, G4int nMax)
|
|
{
|
|
G4complex miz = G4complex( z.imag(), -z.real() );
|
|
G4complex erfcz = 1. - GetErfSer( miz, nMax);
|
|
G4complex w = std::exp(-z*z)*erfcz;
|
|
return w;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::TestErfcInt(G4complex z) // , G4int nMax)
|
|
{
|
|
G4complex miz = G4complex( z.imag(), -z.real() );
|
|
G4complex erfcz = 1. - GetErfInt( miz); // , nMax);
|
|
G4complex w = std::exp(-z*z)*erfcz;
|
|
return w;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GetErfComp(G4complex z, G4int nMax)
|
|
{
|
|
G4int n;
|
|
G4double n2, cofn, shny, chny, fn, gn;
|
|
|
|
G4double x = z.real();
|
|
G4double y = z.imag();
|
|
|
|
G4double outRe = 0., outIm = 0.;
|
|
|
|
G4double twox = 2.*x;
|
|
G4double twoxy = twox*y;
|
|
G4double twox2 = twox*twox;
|
|
|
|
G4double cof1 = std::exp(-x*x)/CLHEP::pi;
|
|
|
|
G4double cos2xy = std::cos(twoxy);
|
|
G4double sin2xy = std::sin(twoxy);
|
|
|
|
G4double twoxcos2xy = twox*cos2xy;
|
|
G4double twoxsin2xy = twox*sin2xy;
|
|
|
|
for( n = 1; n <= nMax; n++)
|
|
{
|
|
n2 = n*n;
|
|
|
|
cofn = std::exp(-0.5*n2)/(n2+twox2); // /(n2+0.5*twox2);
|
|
|
|
chny = std::cosh(n*y);
|
|
shny = std::sinh(n*y);
|
|
|
|
fn = twox - twoxcos2xy*chny + n*sin2xy*shny;
|
|
gn = twoxsin2xy*chny + n*cos2xy*shny;
|
|
|
|
fn *= cofn;
|
|
gn *= cofn;
|
|
|
|
outRe += fn;
|
|
outIm += gn;
|
|
}
|
|
outRe *= 2*cof1;
|
|
outIm *= 2*cof1;
|
|
|
|
if(std::abs(x) < 0.0001)
|
|
{
|
|
outRe += GetErf(x);
|
|
outIm += cof1*y;
|
|
}
|
|
else
|
|
{
|
|
outRe += GetErf(x) + cof1*(1-cos2xy)/twox;
|
|
outIm += cof1*sin2xy/twox;
|
|
}
|
|
return G4complex(outRe, outIm);
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GetErfSer(G4complex z, G4int nMax)
|
|
{
|
|
G4int n;
|
|
G4double a =1., b = 1., tmp;
|
|
G4complex sum = z, d = z;
|
|
|
|
for( n = 1; n <= nMax; n++)
|
|
{
|
|
a *= 2.;
|
|
b *= 2.*n +1.;
|
|
d *= z*z;
|
|
|
|
tmp = a/b;
|
|
|
|
sum += tmp*d;
|
|
}
|
|
sum *= 2.*std::exp(-z*z)/std::sqrt(CLHEP::pi);
|
|
|
|
return sum;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////////
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetExpCos(G4double x)
|
|
{
|
|
G4double result;
|
|
|
|
result = std::exp(x*x-fReZ*fReZ);
|
|
result *= std::cos(2.*x*fReZ);
|
|
return result;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////////
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetExpSin(G4double x)
|
|
{
|
|
G4double result;
|
|
|
|
result = std::exp(x*x-fReZ*fReZ);
|
|
result *= std::sin(2.*x*fReZ);
|
|
return result;
|
|
}
|
|
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GetErfInt(G4complex z) // , G4int nMax)
|
|
{
|
|
G4double outRe, outIm;
|
|
|
|
G4double x = z.real();
|
|
G4double y = z.imag();
|
|
fReZ = x;
|
|
|
|
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
|
|
|
|
outRe = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpSin, 0., y );
|
|
outIm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpCos, 0., y );
|
|
|
|
outRe *= 2./sqrt(CLHEP::pi);
|
|
outIm *= 2./sqrt(CLHEP::pi);
|
|
|
|
outRe += GetErf(x);
|
|
|
|
return G4complex(outRe, outIm);
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetCint(G4double x)
|
|
{
|
|
G4double out;
|
|
|
|
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
|
|
|
|
out= integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetCosHaPit2, 0., x );
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetSint(G4double x)
|
|
{
|
|
G4double out;
|
|
|
|
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
|
|
|
|
out= integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetSinHaPit2, 0., x );
|
|
|
|
return out;
|
|
}
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::CoulombAmplitude(G4double theta)
|
|
{
|
|
G4complex ca;
|
|
|
|
G4double sinHalfTheta = std::sin(0.5*theta);
|
|
G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
|
|
sinHalfTheta2 += fAm;
|
|
|
|
G4double order = 2.*fCoulombPhase0 - fZommerfeld*std::log(sinHalfTheta2);
|
|
G4complex z = G4complex(0., order);
|
|
ca = std::exp(z);
|
|
|
|
ca *= -fZommerfeld/(2.*fWaveVector*sinHalfTheta2);
|
|
|
|
return ca;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CoulombAmplitudeMod2(G4double theta)
|
|
{
|
|
G4complex ca = CoulombAmplitude(theta);
|
|
G4double out = ca.real()*ca.real() + ca.imag()*ca.imag();
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
|
|
inline void G4NuclNuclDiffuseElastic::CalculateCoulombPhaseZero()
|
|
{
|
|
G4complex z = G4complex(1,fZommerfeld);
|
|
// G4complex gammalog = GammaLogarithm(z);
|
|
G4complex gammalog = GammaLogB2n(z);
|
|
fCoulombPhase0 = gammalog.imag();
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CalculateCoulombPhase(G4int n)
|
|
{
|
|
G4complex z = G4complex(1. + n, fZommerfeld);
|
|
// G4complex gammalog = GammaLogarithm(z);
|
|
G4complex gammalog = GammaLogB2n(z);
|
|
return gammalog.imag();
|
|
}
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
|
|
inline void G4NuclNuclDiffuseElastic::CalculateRutherfordAnglePar()
|
|
{
|
|
fHalfRutThetaTg = fZommerfeld/fProfileLambda; // (fWaveVector*fNuclearRadius);
|
|
fRutherfordTheta = 2.*std::atan(fHalfRutThetaTg);
|
|
fHalfRutThetaTg2 = fHalfRutThetaTg*fHalfRutThetaTg;
|
|
// G4cout<<"fRutherfordTheta = "<<fRutherfordTheta/degree<<" degree"<<G4endl;
|
|
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::ProfileNear(G4double theta)
|
|
{
|
|
G4double dTheta = fRutherfordTheta - theta;
|
|
G4double result = 0., argument = 0.;
|
|
|
|
if(std::abs(dTheta) < 0.001) result = fProfileAlpha*fProfileDelta;
|
|
else
|
|
{
|
|
argument = fProfileDelta*dTheta;
|
|
result = CLHEP::pi*argument*std::exp(fProfileAlpha*argument);
|
|
result /= std::sinh(CLHEP::pi*argument);
|
|
result -= 1.;
|
|
result /= dTheta;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::ProfileFar(G4double theta)
|
|
{
|
|
G4double dTheta = fRutherfordTheta + theta;
|
|
G4double argument = fProfileDelta*dTheta;
|
|
|
|
G4double result = CLHEP::pi*argument*std::exp(fProfileAlpha*argument);
|
|
result /= std::sinh(CLHEP::pi*argument);
|
|
result /= dTheta;
|
|
|
|
return result;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::Profile(G4double theta)
|
|
{
|
|
G4double dTheta = fRutherfordTheta - theta;
|
|
G4double result = 0., argument = 0.;
|
|
|
|
if(std::abs(dTheta) < 0.001) result = 1.;
|
|
else
|
|
{
|
|
argument = fProfileDelta*dTheta;
|
|
result = CLHEP::pi*argument;
|
|
result /= std::sinh(CLHEP::pi*argument);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::PhaseNear(G4double theta)
|
|
{
|
|
G4double twosigma = 2.*fCoulombPhase0;
|
|
twosigma -= fZommerfeld*std::log(fHalfRutThetaTg2/(1.+fHalfRutThetaTg2));
|
|
twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - CLHEP::halfpi;
|
|
twosigma -= fProfileLambda*theta - 0.25*CLHEP::pi;
|
|
|
|
twosigma *= fCofPhase;
|
|
|
|
G4complex z = G4complex(0., twosigma);
|
|
|
|
return std::exp(z);
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::PhaseFar(G4double theta)
|
|
{
|
|
G4double twosigma = 2.*fCoulombPhase0;
|
|
twosigma -= fZommerfeld*std::log(fHalfRutThetaTg2/(1.+fHalfRutThetaTg2));
|
|
twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - CLHEP::halfpi;
|
|
twosigma += fProfileLambda*theta - 0.25*CLHEP::pi;
|
|
|
|
twosigma *= fCofPhase;
|
|
|
|
G4complex z = G4complex(0., twosigma);
|
|
|
|
return std::exp(z);
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta)
|
|
{
|
|
G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
|
|
G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2);
|
|
|
|
G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
|
|
G4double kappa = u/std::sqrt(CLHEP::pi);
|
|
G4double dTheta = theta - fRutherfordTheta;
|
|
u *= dTheta;
|
|
G4double u2 = u*u;
|
|
G4double u2m2p3 = u2*2./3.;
|
|
|
|
G4complex im = G4complex(0.,1.);
|
|
G4complex order = G4complex(u,u);
|
|
order /= std::sqrt(2.);
|
|
|
|
G4complex gamma = CLHEP::pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*CLHEP::pi));
|
|
G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
|
|
G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
|
|
G4complex out = gamma*(1. - a1*dTheta) - a0;
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::GammaMore(G4double theta)
|
|
{
|
|
G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
|
|
G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2);
|
|
|
|
G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
|
|
G4double kappa = u/std::sqrt(CLHEP::pi);
|
|
G4double dTheta = theta - fRutherfordTheta;
|
|
u *= dTheta;
|
|
G4double u2 = u*u;
|
|
G4double u2m2p3 = u2*2./3.;
|
|
|
|
G4complex im = G4complex(0.,1.);
|
|
G4complex order = G4complex(u,u);
|
|
order /= std::sqrt(2.);
|
|
G4complex gamma = CLHEP::pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*CLHEP::pi));
|
|
G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
|
|
G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
|
|
G4complex out = -gamma*(1. - a1*dTheta) - a0;
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::AmplitudeNear(G4double theta)
|
|
{
|
|
G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/CLHEP::pi);
|
|
G4complex out = G4complex(kappa/fWaveVector,0.);
|
|
|
|
out *= PhaseNear(theta);
|
|
|
|
if( theta <= fRutherfordTheta )
|
|
{
|
|
out *= GammaLess(theta) + ProfileNear(theta);
|
|
// out *= GammaMore(theta) + ProfileNear(theta);
|
|
out += CoulombAmplitude(theta);
|
|
}
|
|
else
|
|
{
|
|
out *= GammaMore(theta) + ProfileNear(theta);
|
|
// out *= GammaLess(theta) + ProfileNear(theta);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::AmplitudeFar(G4double theta)
|
|
{
|
|
G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/CLHEP::pi);
|
|
G4complex out = G4complex(kappa/fWaveVector,0.);
|
|
out *= ProfileFar(theta);
|
|
out *= PhaseFar(theta);
|
|
return out;
|
|
}
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::Amplitude(G4double theta)
|
|
{
|
|
|
|
G4complex out = AmplitudeNear(theta) + fCofFar*AmplitudeFar(theta);
|
|
// G4complex out = AmplitudeNear(theta);
|
|
// G4complex out = AmplitudeFar(theta);
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::AmplitudeMod2(G4double theta)
|
|
{
|
|
G4complex out = Amplitude(theta);
|
|
G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
|
|
return mod2;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::AmplitudeSim(G4double theta)
|
|
{
|
|
G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
|
|
G4double dTheta = 0.5*(theta - fRutherfordTheta);
|
|
G4double sindTheta = std::sin(dTheta);
|
|
G4double persqrt2 = std::sqrt(0.5);
|
|
|
|
G4complex order = G4complex(persqrt2,persqrt2);
|
|
order *= std::sqrt(0.5*fProfileLambda/sinThetaR)*2.*sindTheta;
|
|
// order *= std::sqrt(0.5*fProfileLambda/sinThetaR)*2.*dTheta;
|
|
|
|
G4complex out;
|
|
|
|
if ( theta <= fRutherfordTheta )
|
|
{
|
|
out = 1. - 0.5*GetErfcInt(-order)*ProfileNear(theta);
|
|
}
|
|
else
|
|
{
|
|
out = 0.5*GetErfcInt(order)*ProfileNear(theta);
|
|
}
|
|
|
|
out *= CoulombAmplitude(theta);
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetRatioSim(G4double theta)
|
|
{
|
|
G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
|
|
G4double dTheta = 0.5*(theta - fRutherfordTheta);
|
|
G4double sindTheta = std::sin(dTheta);
|
|
|
|
G4double order = std::sqrt(fProfileLambda/sinThetaR/CLHEP::pi)*2.*sindTheta;
|
|
// G4cout<<"order = "<<order<<G4endl;
|
|
G4double cosFresnel = 0.5 - GetCint(order);
|
|
G4double sinFresnel = 0.5 - GetSint(order);
|
|
|
|
G4double out = 0.5*( cosFresnel*cosFresnel + sinFresnel*sinFresnel );
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
// The ratio el/ruth for Fresnel smooth nucleus profile
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetRatioGen(G4double theta)
|
|
{
|
|
G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
|
|
G4double dTheta = 0.5*(theta - fRutherfordTheta);
|
|
G4double sindTheta = std::sin(dTheta);
|
|
|
|
G4double prof = Profile(theta);
|
|
G4double prof2 = prof*prof;
|
|
// G4double profmod = std::abs(prof);
|
|
G4double order = std::sqrt(fProfileLambda/sinThetaR/CLHEP::pi)*2.*sindTheta;
|
|
|
|
order = std::abs(order); // since sin changes sign!
|
|
// G4cout<<"order = "<<order<<G4endl;
|
|
|
|
G4double cosFresnel = GetCint(order);
|
|
G4double sinFresnel = GetSint(order);
|
|
|
|
G4double out;
|
|
|
|
if ( theta <= fRutherfordTheta )
|
|
{
|
|
out = 1. + 0.5*( (0.5-cosFresnel)*(0.5-cosFresnel)+(0.5-sinFresnel)*(0.5-sinFresnel) )*prof2;
|
|
out += ( cosFresnel + sinFresnel - 1. )*prof;
|
|
}
|
|
else
|
|
{
|
|
out = 0.5*( (0.5-cosFresnel)*(0.5-cosFresnel)+(0.5-sinFresnel)*(0.5-sinFresnel) )*prof2;
|
|
}
|
|
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
// The xsc for Fresnel smooth nucleus profile
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetFresnelDiffuseXsc(G4double theta)
|
|
{
|
|
G4double ratio = GetRatioGen(theta);
|
|
G4double ruthXsc = GetRutherfordXsc(theta);
|
|
G4double xsc = ratio*ruthXsc;
|
|
return xsc;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
// The xsc for Fresnel smooth nucleus profile for integration
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::GetFresnelIntegrandXsc(G4double alpha)
|
|
{
|
|
G4double theta = std::sqrt(alpha);
|
|
G4double xsc = GetFresnelDiffuseXsc(theta);
|
|
return xsc;
|
|
}
|
|
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::AmplitudeSimMod2(G4double theta)
|
|
{
|
|
G4complex out = AmplitudeSim(theta);
|
|
G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
|
|
return mod2;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::AmplitudeGla(G4double theta)
|
|
{
|
|
G4int n;
|
|
G4double T12b, b, b2; // cosTheta = std::cos(theta);
|
|
G4complex out = G4complex(0.,0.), shiftC, shiftN;
|
|
G4complex im = G4complex(0.,1.);
|
|
|
|
for( n = 0; n < fMaxL; n++)
|
|
{
|
|
shiftC = std::exp( im*2.*CalculateCoulombPhase(n) );
|
|
// b = ( fZommerfeld + std::sqrt( fZommerfeld*fZommerfeld + n*(n+1) ) )/fWaveVector;
|
|
b = ( std::sqrt( G4double(n*(n+1)) ) )/fWaveVector;
|
|
b2 = b*b;
|
|
T12b = fSumSigma*std::exp(-b2/fNuclearRadiusSquare)/CLHEP::pi/fNuclearRadiusSquare;
|
|
shiftN = std::exp( -0.5*(1.-im*fEtaRatio)*T12b ) - 1.;
|
|
out += (2.*n+1.)*shiftC*shiftN*GetLegendrePol(n, theta);
|
|
}
|
|
out /= 2.*im*fWaveVector;
|
|
out += CoulombAmplitude(theta);
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::AmplitudeGlaMod2(G4double theta)
|
|
{
|
|
G4complex out = AmplitudeGla(theta);
|
|
G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
|
|
return mod2;
|
|
}
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4complex G4NuclNuclDiffuseElastic::AmplitudeGG(G4double theta)
|
|
{
|
|
G4int n;
|
|
G4double T12b, a, aTemp, b2, sinThetaH = std::sin(0.5*theta);
|
|
G4double sinThetaH2 = sinThetaH*sinThetaH;
|
|
G4complex out = G4complex(0.,0.);
|
|
G4complex im = G4complex(0.,1.);
|
|
|
|
a = -fSumSigma/CLHEP::twopi/fNuclearRadiusSquare;
|
|
b2 = fWaveVector*fWaveVector*fNuclearRadiusSquare*sinThetaH2;
|
|
|
|
aTemp = a;
|
|
|
|
for( n = 1; n < fMaxL; n++)
|
|
{
|
|
T12b = aTemp*std::exp(-b2/n)/n;
|
|
aTemp *= a;
|
|
out += T12b;
|
|
G4cout<<"out = "<<out<<G4endl;
|
|
}
|
|
out *= -4.*im*fWaveVector/CLHEP::pi;
|
|
out += CoulombAmplitude(theta);
|
|
return out;
|
|
}
|
|
|
|
/////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::AmplitudeGGMod2(G4double theta)
|
|
{
|
|
G4complex out = AmplitudeGG(theta);
|
|
G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
|
|
return mod2;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// Test for given particle and element table of momentum, angle probability.
|
|
// For the partMom in CMS.
|
|
|
|
inline void G4NuclNuclDiffuseElastic::InitParameters(const G4ParticleDefinition* theParticle,
|
|
G4double partMom, G4double Z, G4double A)
|
|
{
|
|
fAtomicNumber = Z; // atomic number
|
|
fAtomicWeight = A; // number of nucleons
|
|
|
|
fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight);
|
|
G4double A1 = G4double( theParticle->GetBaryonNumber() );
|
|
fNuclearRadius1 = CalculateNuclearRad(A1);
|
|
// fNuclearRadius = std::sqrt(fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2);
|
|
fNuclearRadius = fNuclearRadius1 + fNuclearRadius2;
|
|
|
|
G4double a = 0.;
|
|
G4double z = theParticle->GetPDGCharge();
|
|
G4double m1 = theParticle->GetPDGMass();
|
|
|
|
fWaveVector = partMom/CLHEP::hbarc;
|
|
|
|
G4double lambda = fCofLambda*fWaveVector*fNuclearRadius;
|
|
G4cout<<"kR = "<<lambda<<G4endl;
|
|
|
|
if( z )
|
|
{
|
|
a = partMom/m1; // beta*gamma for m1
|
|
fBeta = a/std::sqrt(1+a*a);
|
|
fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
|
|
fRutherfordRatio = fZommerfeld/fWaveVector;
|
|
fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
|
|
}
|
|
G4cout<<"fZommerfeld = "<<fZommerfeld<<G4endl;
|
|
fProfileLambda = lambda; // *std::sqrt(1.-2*fZommerfeld/lambda);
|
|
G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl;
|
|
fProfileDelta = fCofDelta*fProfileLambda;
|
|
fProfileAlpha = fCofAlpha*fProfileLambda;
|
|
|
|
CalculateCoulombPhaseZero();
|
|
CalculateRutherfordAnglePar();
|
|
|
|
return;
|
|
}
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// Test for given particle and element table of momentum, angle probability.
|
|
// For the partMom in CMS.
|
|
|
|
inline void G4NuclNuclDiffuseElastic::InitDynParameters(const G4ParticleDefinition* theParticle,
|
|
G4double partMom)
|
|
{
|
|
G4double a = 0.;
|
|
G4double z = theParticle->GetPDGCharge();
|
|
G4double m1 = theParticle->GetPDGMass();
|
|
|
|
fWaveVector = partMom/CLHEP::hbarc;
|
|
|
|
G4double lambda = fCofLambda*fWaveVector*fNuclearRadius;
|
|
|
|
if( z )
|
|
{
|
|
a = partMom/m1; // beta*gamma for m1
|
|
fBeta = a/std::sqrt(1+a*a);
|
|
fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
|
|
fRutherfordRatio = fZommerfeld/fWaveVector;
|
|
fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
|
|
}
|
|
fProfileLambda = lambda; // *std::sqrt(1.-2*fZommerfeld/lambda);
|
|
fProfileDelta = fCofDelta*fProfileLambda;
|
|
fProfileAlpha = fCofAlpha*fProfileLambda;
|
|
|
|
CalculateCoulombPhaseZero();
|
|
CalculateRutherfordAnglePar();
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// Test for given particle and element table of momentum, angle probability.
|
|
// For the partMom in CMS.
|
|
|
|
inline void G4NuclNuclDiffuseElastic::InitParametersGla(const G4DynamicParticle* aParticle,
|
|
G4double partMom, G4double Z, G4double A)
|
|
{
|
|
fAtomicNumber = Z; // target atomic number
|
|
fAtomicWeight = A; // target number of nucleons
|
|
|
|
fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight); // target nucleus radius
|
|
G4double A1 = G4double( aParticle->GetDefinition()->GetBaryonNumber() );
|
|
fNuclearRadius1 = CalculateNuclearRad(A1); // projectile nucleus radius
|
|
fNuclearRadiusSquare = fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2;
|
|
|
|
|
|
G4double a = 0., kR12;
|
|
G4double z = aParticle->GetDefinition()->GetPDGCharge();
|
|
G4double m1 = aParticle->GetDefinition()->GetPDGMass();
|
|
|
|
fWaveVector = partMom/CLHEP::hbarc;
|
|
|
|
G4double pN = A1 - z;
|
|
if( pN < 0. ) pN = 0.;
|
|
|
|
G4double tN = A - Z;
|
|
if( tN < 0. ) tN = 0.;
|
|
|
|
G4double pTkin = aParticle->GetKineticEnergy();
|
|
pTkin /= A1;
|
|
|
|
|
|
fSumSigma = (Z*z+pN*tN)*GetHadronNucleonXscNS(theProton, pTkin, theProton) +
|
|
(z*tN+pN*Z)*GetHadronNucleonXscNS(theProton, pTkin, theNeutron);
|
|
|
|
G4cout<<"fSumSigma = "<<fSumSigma/CLHEP::millibarn<<" mb"<<G4endl;
|
|
G4cout<<"pi*R2 = "<<CLHEP::pi*fNuclearRadiusSquare/CLHEP::millibarn<<" mb"<<G4endl;
|
|
kR12 = fWaveVector*std::sqrt(fNuclearRadiusSquare);
|
|
G4cout<<"k*sqrt(R2) = "<<kR12<<" "<<G4endl;
|
|
fMaxL = (G4int(kR12)+1)*4;
|
|
G4cout<<"fMaxL = "<<fMaxL<<" "<<G4endl;
|
|
|
|
if( z )
|
|
{
|
|
a = partMom/m1; // beta*gamma for m1
|
|
fBeta = a/std::sqrt(1+a*a);
|
|
fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
|
|
fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
|
|
}
|
|
|
|
CalculateCoulombPhaseZero();
|
|
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
/////////////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// Returns nucleon-nucleon cross-section based on N. Starkov parametrisation of
|
|
// data from mainly http://wwwppds.ihep.su:8001/c5-6A.html database
|
|
// projectile nucleon is pParticle with pTkin shooting target nucleon tParticle
|
|
|
|
inline G4double
|
|
G4NuclNuclDiffuseElastic::GetHadronNucleonXscNS( G4ParticleDefinition* pParticle,
|
|
G4double pTkin,
|
|
G4ParticleDefinition* tParticle)
|
|
{
|
|
G4double xsection(0), /*Delta,*/ A0, B0;
|
|
G4double hpXsc(0);
|
|
G4double hnXsc(0);
|
|
|
|
|
|
G4double targ_mass = tParticle->GetPDGMass();
|
|
G4double proj_mass = pParticle->GetPDGMass();
|
|
|
|
G4double proj_energy = proj_mass + pTkin;
|
|
G4double proj_momentum = std::sqrt(pTkin*(pTkin+2*proj_mass));
|
|
|
|
G4double sMand = CalcMandelstamS ( proj_mass , targ_mass , proj_momentum );
|
|
|
|
sMand /= CLHEP::GeV*CLHEP::GeV; // in GeV for parametrisation
|
|
proj_momentum /= CLHEP::GeV;
|
|
proj_energy /= CLHEP::GeV;
|
|
proj_mass /= CLHEP::GeV;
|
|
G4double logS = std::log(sMand);
|
|
|
|
// General PDG fit constants
|
|
|
|
|
|
// fEtaRatio=Re[f(0)]/Im[f(0)]
|
|
|
|
if( proj_momentum >= 1.2 )
|
|
{
|
|
fEtaRatio = 0.13*(logS - 5.8579332)*std::pow(sMand,-0.18);
|
|
}
|
|
else if( proj_momentum >= 0.6 )
|
|
{
|
|
fEtaRatio = -75.5*(std::pow(proj_momentum,0.25)-0.95)/
|
|
(std::pow(3*proj_momentum,2.2)+1);
|
|
}
|
|
else
|
|
{
|
|
fEtaRatio = 15.5*proj_momentum/(27*proj_momentum*proj_momentum*proj_momentum+2);
|
|
}
|
|
G4cout<<"fEtaRatio = "<<fEtaRatio<<G4endl;
|
|
|
|
// xsc
|
|
|
|
if( proj_momentum >= 10. ) // high energy: pp = nn = np
|
|
// if( proj_momentum >= 2.)
|
|
{
|
|
//Delta = 1.;
|
|
|
|
//if( proj_energy < 40. ) Delta = 0.916+0.0021*proj_energy;
|
|
|
|
if( proj_momentum >= 10.)
|
|
{
|
|
B0 = 7.5;
|
|
A0 = 100. - B0*std::log(3.0e7);
|
|
|
|
xsection = A0 + B0*std::log(proj_energy) - 11
|
|
+ 103*std::pow(2*0.93827*proj_energy + proj_mass*proj_mass+
|
|
0.93827*0.93827,-0.165); // mb
|
|
}
|
|
}
|
|
else // low energy pp = nn != np
|
|
{
|
|
if(pParticle == tParticle) // pp or nn // nn to be pp
|
|
{
|
|
if( proj_momentum < 0.73 )
|
|
{
|
|
hnXsc = 23 + 50*( std::pow( std::log(0.73/proj_momentum), 3.5 ) );
|
|
}
|
|
else if( proj_momentum < 1.05 )
|
|
{
|
|
hnXsc = 23 + 40*(std::log(proj_momentum/0.73))*
|
|
(std::log(proj_momentum/0.73));
|
|
}
|
|
else // if( proj_momentum < 10. )
|
|
{
|
|
hnXsc = 39.0 +
|
|
75*(proj_momentum - 1.2)/(std::pow(proj_momentum,3.0) + 0.15);
|
|
}
|
|
xsection = hnXsc;
|
|
}
|
|
else // pn to be np
|
|
{
|
|
if( proj_momentum < 0.8 )
|
|
{
|
|
hpXsc = 33+30*std::pow(std::log(proj_momentum/1.3),4.0);
|
|
}
|
|
else if( proj_momentum < 1.4 )
|
|
{
|
|
hpXsc = 33+30*std::pow(std::log(proj_momentum/0.95),2.0);
|
|
}
|
|
else // if( proj_momentum < 10. )
|
|
{
|
|
hpXsc = 33.3+
|
|
20.8*(std::pow(proj_momentum,2.0)-1.35)/
|
|
(std::pow(proj_momentum,2.50)+0.95);
|
|
}
|
|
xsection = hpXsc;
|
|
}
|
|
}
|
|
xsection *= CLHEP::millibarn; // parametrised in mb
|
|
G4cout<<"xsection = "<<xsection/CLHEP::millibarn<<" mb"<<G4endl;
|
|
return xsection;
|
|
}
|
|
|
|
////////////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
//
|
|
|
|
inline G4double G4NuclNuclDiffuseElastic::CalcMandelstamS( const G4double mp ,
|
|
const G4double mt ,
|
|
const G4double Plab )
|
|
{
|
|
G4double Elab = std::sqrt ( mp * mp + Plab * Plab );
|
|
G4double sMand = mp*mp + mt*mt + 2*Elab*mt ;
|
|
|
|
return sMand;
|
|
}
|
|
|
|
|
|
|
|
#endif
|