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geant4/source/processes/hadronic/models/coherent_elastic/src/G4NuclNuclDiffuseElastic.cc
T
Gabriele Cosmo c9b32a6c0a Import Geant4 10.1.0 source tree
2016-06-10 12:08:39 +02:00

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//
// ********************************************************************
// * License and Disclaimer *
// * *
// * The Geant4 software is copyright of the Copyright Holders of *
// * the Geant4 Collaboration. It is provided under the terms and *
// * conditions of the Geant4 Software License, included in the file *
// * LICENSE and available at http://cern.ch/geant4/license . These *
// * include a list of copyright holders. *
// * *
// * Neither the authors of this software system, nor their employing *
// * institutes,nor the agencies providing financial support for this *
// * work make any representation or warranty, express or implied, *
// * regarding this software system or assume any liability for its *
// * use. Please see the license in the file LICENSE and URL above *
// * for the full disclaimer and the limitation of liability. *
// * *
// * This code implementation is the result of the scientific and *
// * technical work of the GEANT4 collaboration. *
// * By using, copying, modifying or distributing the software (or *
// * any work based on the software) you agree to acknowledge its *
// * use in resulting scientific publications, and indicate your *
// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
// $Id: G4NuclNuclDiffuseElastic.cc 83427 2014-08-21 15:44:43Z gcosmo $
//
//
// Physics model class G4NuclNuclDiffuseElastic
//
//
// G4 Model: optical diffuse elastic scattering with 4-momentum balance
//
// 24-May-07 V. Grichine
//
#include "G4NuclNuclDiffuseElastic.hh"
#include "G4ParticleTable.hh"
#include "G4ParticleDefinition.hh"
#include "G4IonTable.hh"
#include "G4NucleiProperties.hh"
#include "Randomize.hh"
#include "G4Integrator.hh"
#include "globals.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4Proton.hh"
#include "G4Neutron.hh"
#include "G4Deuteron.hh"
#include "G4Alpha.hh"
#include "G4PionPlus.hh"
#include "G4PionMinus.hh"
#include "G4Element.hh"
#include "G4ElementTable.hh"
#include "G4NistManager.hh"
#include "G4PhysicsTable.hh"
#include "G4PhysicsLogVector.hh"
#include "G4PhysicsFreeVector.hh"
/////////////////////////////////////////////////////////////////////////
//
// Test Constructor. Just to check xsc
G4NuclNuclDiffuseElastic::G4NuclNuclDiffuseElastic()
: G4HadronElastic("NNDiffuseElastic"), fParticle(0)
{
SetMinEnergy( 50*MeV );
SetMaxEnergy( 1.*TeV );
verboseLevel = 0;
lowEnergyRecoilLimit = 100.*keV;
lowEnergyLimitQ = 0.0*GeV;
lowEnergyLimitHE = 0.0*GeV;
lowestEnergyLimit= 0.0*keV;
plabLowLimit = 20.0*MeV;
theProton = G4Proton::Proton();
theNeutron = G4Neutron::Neutron();
theDeuteron = G4Deuteron::Deuteron();
theAlpha = G4Alpha::Alpha();
thePionPlus = G4PionPlus::PionPlus();
thePionMinus= G4PionMinus::PionMinus();
fEnergyBin = 200;
fAngleBin = 200;
fEnergyVector = new G4PhysicsLogVector( theMinEnergy, theMaxEnergy, fEnergyBin );
fAngleTable = 0;
fParticle = 0;
fWaveVector = 0.;
fAtomicWeight = 0.;
fAtomicNumber = 0.;
fNuclearRadius = 0.;
fBeta = 0.;
fZommerfeld = 0.;
fAm = 0.;
fAddCoulomb = false;
// Ranges of angle table relative to current Rutherford (Coulomb grazing) angle
// Empirical parameters
fCofAlphaMax = 1.5;
fCofAlphaCoulomb = 0.5;
fProfileDelta = 1.;
fProfileAlpha = 0.5;
fCofLambda = 1.0;
fCofDelta = 0.04;
fCofAlpha = 0.095;
fNuclearRadius1 = fNuclearRadius2 = fNuclearRadiusSquare
= fRutherfordRatio = fCoulombPhase0 = fHalfRutThetaTg = fHalfRutThetaTg2
= fRutherfordTheta = fProfileLambda = fCofPhase = fCofFar = fCofAlphaMax
= fCofAlphaCoulomb = fSumSigma = fEtaRatio = fReZ = 0.0;
fMaxL = 0;
fNuclearRadiusCof = 1.0;
}
//////////////////////////////////////////////////////////////////////////////
//
// Destructor
G4NuclNuclDiffuseElastic::~G4NuclNuclDiffuseElastic()
{
if ( fEnergyVector ) {
delete fEnergyVector;
fEnergyVector = 0;
}
for ( std::vector<G4PhysicsTable*>::iterator it = fAngleBank.begin();
it != fAngleBank.end(); ++it ) {
if ( (*it) ) (*it)->clearAndDestroy();
delete *it;
*it = 0;
}
fAngleTable = 0;
}
//////////////////////////////////////////////////////////////////////////////
//
// Initialisation for given particle using element table of application
void G4NuclNuclDiffuseElastic::Initialise()
{
// fEnergyVector = new G4PhysicsLogVector( theMinEnergy, theMaxEnergy, fEnergyBin );
const G4ElementTable* theElementTable = G4Element::GetElementTable();
size_t jEl, numOfEl = G4Element::GetNumberOfElements();
// projectile radius
G4double A1 = G4double( fParticle->GetBaryonNumber() );
G4double R1 = CalculateNuclearRad(A1);
for(jEl = 0 ; jEl < numOfEl; ++jEl) // application element loop
{
fAtomicNumber = (*theElementTable)[jEl]->GetZ(); // atomic number
fAtomicWeight = G4NistManager::Instance()->GetAtomicMassAmu( static_cast< G4int >( fAtomicNumber ) );
fNuclearRadius = CalculateNuclearRad(fAtomicWeight);
fNuclearRadius += R1;
if(verboseLevel > 0)
{
G4cout<<"G4NuclNuclDiffuseElastic::Initialise() the element: "
<<(*theElementTable)[jEl]->GetName()<<G4endl;
}
fElementNumberVector.push_back(fAtomicNumber);
fElementNameVector.push_back((*theElementTable)[jEl]->GetName());
BuildAngleTable();
fAngleBank.push_back(fAngleTable);
}
}
////////////////////////////////////////////////////////////////////////////
//
// return differential elastic cross section d(sigma)/d(omega)
G4double
G4NuclNuclDiffuseElastic::GetDiffuseElasticXsc( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A )
{
fParticle = particle;
fWaveVector = momentum/hbarc;
fAtomicWeight = A;
fAddCoulomb = false;
fNuclearRadius = CalculateNuclearRad(A);
G4double sigma = fNuclearRadius*fNuclearRadius*GetDiffElasticProb(theta);
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return invariant differential elastic cross section d(sigma)/d(tMand)
G4double
G4NuclNuclDiffuseElastic::GetInvElasticXsc( const G4ParticleDefinition* particle,
G4double tMand,
G4double plab,
G4double A, G4double Z )
{
G4double m1 = particle->GetPDGMass();
G4LorentzVector lv1(0.,0.,plab,std::sqrt(plab*plab+m1*m1));
G4int iZ = static_cast<G4int>(Z+0.5);
G4int iA = static_cast<G4int>(A+0.5);
G4ParticleDefinition * theDef = 0;
if (iZ == 1 && iA == 1) theDef = theProton;
else if (iZ == 1 && iA == 2) theDef = theDeuteron;
else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
else if (iZ == 2 && iA == 4) theDef = theAlpha;
else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
G4double tmass = theDef->GetPDGMass();
G4LorentzVector lv(0.0,0.0,0.0,tmass);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
lv1.boost(-bst);
G4ThreeVector p1 = lv1.vect();
G4double ptot = p1.mag();
G4double ptot2 = ptot*ptot;
G4double cost = 1 - 0.5*std::fabs(tMand)/ptot2;
if( cost >= 1.0 ) cost = 1.0;
else if( cost <= -1.0) cost = -1.0;
G4double thetaCMS = std::acos(cost);
G4double sigma = GetDiffuseElasticXsc( particle, thetaCMS, ptot, A);
sigma *= pi/ptot2;
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return differential elastic cross section d(sigma)/d(omega) with Coulomb
// correction
G4double
G4NuclNuclDiffuseElastic::GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A, G4double Z )
{
fParticle = particle;
fWaveVector = momentum/hbarc;
fAtomicWeight = A;
fAtomicNumber = Z;
fNuclearRadius = CalculateNuclearRad(A);
fAddCoulomb = false;
G4double z = particle->GetPDGCharge();
G4double kRt = fWaveVector*fNuclearRadius*theta;
G4double kRtC = 1.9;
if( z && (kRt > kRtC) )
{
fAddCoulomb = true;
fBeta = CalculateParticleBeta( particle, momentum);
fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
fAm = CalculateAm( momentum, fZommerfeld, fAtomicNumber);
}
G4double sigma = fNuclearRadius*fNuclearRadius*GetDiffElasticSumProb(theta);
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return invariant differential elastic cross section d(sigma)/d(tMand) with Coulomb
// correction
G4double
G4NuclNuclDiffuseElastic::GetInvElasticSumXsc( const G4ParticleDefinition* particle,
G4double tMand,
G4double plab,
G4double A, G4double Z )
{
G4double m1 = particle->GetPDGMass();
G4LorentzVector lv1(0.,0.,plab,std::sqrt(plab*plab+m1*m1));
G4int iZ = static_cast<G4int>(Z+0.5);
G4int iA = static_cast<G4int>(A+0.5);
G4ParticleDefinition* theDef = 0;
if (iZ == 1 && iA == 1) theDef = theProton;
else if (iZ == 1 && iA == 2) theDef = theDeuteron;
else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
else if (iZ == 2 && iA == 4) theDef = theAlpha;
else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
G4double tmass = theDef->GetPDGMass();
G4LorentzVector lv(0.0,0.0,0.0,tmass);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
lv1.boost(-bst);
G4ThreeVector p1 = lv1.vect();
G4double ptot = p1.mag();
G4double ptot2 = ptot*ptot;
G4double cost = 1 - 0.5*std::fabs(tMand)/ptot2;
if( cost >= 1.0 ) cost = 1.0;
else if( cost <= -1.0) cost = -1.0;
G4double thetaCMS = std::acos(cost);
G4double sigma = GetDiffuseElasticSumXsc( particle, thetaCMS, ptot, A, Z );
sigma *= pi/ptot2;
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return invariant differential elastic cross section d(sigma)/d(tMand) with Coulomb
// correction
G4double
G4NuclNuclDiffuseElastic::GetInvCoulombElasticXsc( const G4ParticleDefinition* particle,
G4double tMand,
G4double plab,
G4double A, G4double Z )
{
G4double m1 = particle->GetPDGMass();
G4LorentzVector lv1(0.,0.,plab,std::sqrt(plab*plab+m1*m1));
G4int iZ = static_cast<G4int>(Z+0.5);
G4int iA = static_cast<G4int>(A+0.5);
G4ParticleDefinition * theDef = 0;
if (iZ == 1 && iA == 1) theDef = theProton;
else if (iZ == 1 && iA == 2) theDef = theDeuteron;
else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
else if (iZ == 2 && iA == 4) theDef = theAlpha;
else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
G4double tmass = theDef->GetPDGMass();
G4LorentzVector lv(0.0,0.0,0.0,tmass);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
lv1.boost(-bst);
G4ThreeVector p1 = lv1.vect();
G4double ptot = p1.mag();
G4double ptot2 = ptot*ptot;
G4double cost = 1 - 0.5*std::fabs(tMand)/ptot2;
if( cost >= 1.0 ) cost = 1.0;
else if( cost <= -1.0) cost = -1.0;
G4double thetaCMS = std::acos(cost);
G4double sigma = GetCoulombElasticXsc( particle, thetaCMS, ptot, Z );
sigma *= pi/ptot2;
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability d(probability)/d(omega)
G4double
G4NuclNuclDiffuseElastic::GetDiffElasticProb( // G4ParticleDefinition* particle,
G4double theta
// G4double momentum,
// G4double A
)
{
G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
G4double delta, diffuse, gamma;
G4double e1, e2, bone, bone2;
// G4double wavek = momentum/hbarc; // wave vector
// G4double r0 = 1.08*fermi;
// G4double rad = r0*std::pow(A, 1./3.);
G4double kr = fWaveVector*fNuclearRadius; // wavek*rad;
G4double kr2 = kr*kr;
G4double krt = kr*theta;
bzero = BesselJzero(krt);
bzero2 = bzero*bzero;
bone = BesselJone(krt);
bone2 = bone*bone;
bonebyarg = BesselOneByArg(krt);
bonebyarg2 = bonebyarg*bonebyarg;
if (fParticle == theProton)
{
diffuse = 0.63*fermi;
gamma = 0.3*fermi;
delta = 0.1*fermi*fermi;
e1 = 0.3*fermi;
e2 = 0.35*fermi;
}
else // as proton, if were not defined
{
diffuse = 0.63*fermi;
gamma = 0.3*fermi;
delta = 0.1*fermi*fermi;
e1 = 0.3*fermi;
e2 = 0.35*fermi;
}
G4double lambda = 15.; // 15 ok
// G4double kgamma = fWaveVector*gamma; // wavek*delta;
G4double kgamma = lambda*(1.-std::exp(-fWaveVector*gamma/lambda)); // wavek*delta;
G4double kgamma2 = kgamma*kgamma;
// G4double dk2t = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
// G4double dk2t2 = dk2t*dk2t;
// G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;
G4double pikdt = lambda*(1.-std::exp(-pi*fWaveVector*diffuse*theta/lambda)); // wavek*delta;
damp = DampFactor(pikdt);
damp2 = damp*damp;
G4double mode2k2 = (e1*e1+e2*e2)*fWaveVector*fWaveVector;
G4double e2dk3t = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;
sigma = kgamma2;
// sigma += dk2t2;
sigma *= bzero2;
sigma += mode2k2*bone2 + e2dk3t*bzero*bone;
sigma += kr2*bonebyarg2;
sigma *= damp2; // *rad*rad;
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability d(probability)/d(omega) with
// Coulomb correction
G4double
G4NuclNuclDiffuseElastic::GetDiffElasticSumProb( // G4ParticleDefinition* particle,
G4double theta
// G4double momentum,
// G4double A
)
{
G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
G4double delta, diffuse, gamma;
G4double e1, e2, bone, bone2;
// G4double wavek = momentum/hbarc; // wave vector
// G4double r0 = 1.08*fermi;
// G4double rad = r0*std::pow(A, 1./3.);
G4double kr = fWaveVector*fNuclearRadius; // wavek*rad;
G4double kr2 = kr*kr;
G4double krt = kr*theta;
bzero = BesselJzero(krt);
bzero2 = bzero*bzero;
bone = BesselJone(krt);
bone2 = bone*bone;
bonebyarg = BesselOneByArg(krt);
bonebyarg2 = bonebyarg*bonebyarg;
if (fParticle == theProton)
{
diffuse = 0.63*fermi;
// diffuse = 0.6*fermi;
gamma = 0.3*fermi;
delta = 0.1*fermi*fermi;
e1 = 0.3*fermi;
e2 = 0.35*fermi;
}
else // as proton, if were not defined
{
diffuse = 0.63*fermi;
gamma = 0.3*fermi;
delta = 0.1*fermi*fermi;
e1 = 0.3*fermi;
e2 = 0.35*fermi;
}
G4double lambda = 15.; // 15 ok
// G4double kgamma = fWaveVector*gamma; // wavek*delta;
G4double kgamma = lambda*(1.-std::exp(-fWaveVector*gamma/lambda)); // wavek*delta;
// G4cout<<"kgamma = "<<kgamma<<G4endl;
if(fAddCoulomb) // add Coulomb correction
{
G4double sinHalfTheta = std::sin(0.5*theta);
G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
kgamma += 0.5*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
// kgamma += 0.65*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
}
G4double kgamma2 = kgamma*kgamma;
// G4double dk2t = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
// G4cout<<"dk2t = "<<dk2t<<G4endl;
// G4double dk2t2 = dk2t*dk2t;
// G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;
G4double pikdt = lambda*(1.-std::exp(-pi*fWaveVector*diffuse*theta/lambda)); // wavek*delta;
// G4cout<<"pikdt = "<<pikdt<<G4endl;
damp = DampFactor(pikdt);
damp2 = damp*damp;
G4double mode2k2 = (e1*e1+e2*e2)*fWaveVector*fWaveVector;
G4double e2dk3t = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;
sigma = kgamma2;
// sigma += dk2t2;
sigma *= bzero2;
sigma += mode2k2*bone2;
sigma += e2dk3t*bzero*bone;
// sigma += kr2*(1 + 8.*fZommerfeld*fZommerfeld/kr2)*bonebyarg2; // correction at J1()/()
sigma += kr2*bonebyarg2; // correction at J1()/()
sigma *= damp2; // *rad*rad;
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability d(probability)/d(t) with
// Coulomb correction
G4double
G4NuclNuclDiffuseElastic::GetDiffElasticSumProbA( G4double alpha )
{
G4double theta;
theta = std::sqrt(alpha);
// theta = std::acos( 1 - alpha/2. );
G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
G4double delta, diffuse, gamma;
G4double e1, e2, bone, bone2;
// G4double wavek = momentum/hbarc; // wave vector
// G4double r0 = 1.08*fermi;
// G4double rad = r0*std::pow(A, 1./3.);
G4double kr = fWaveVector*fNuclearRadius; // wavek*rad;
G4double kr2 = kr*kr;
G4double krt = kr*theta;
bzero = BesselJzero(krt);
bzero2 = bzero*bzero;
bone = BesselJone(krt);
bone2 = bone*bone;
bonebyarg = BesselOneByArg(krt);
bonebyarg2 = bonebyarg*bonebyarg;
if (fParticle == theProton)
{
diffuse = 0.63*fermi;
// diffuse = 0.6*fermi;
gamma = 0.3*fermi;
delta = 0.1*fermi*fermi;
e1 = 0.3*fermi;
e2 = 0.35*fermi;
}
else // as proton, if were not defined
{
diffuse = 0.63*fermi;
gamma = 0.3*fermi;
delta = 0.1*fermi*fermi;
e1 = 0.3*fermi;
e2 = 0.35*fermi;
}
G4double lambda = 15.; // 15 ok
// G4double kgamma = fWaveVector*gamma; // wavek*delta;
G4double kgamma = lambda*(1.-std::exp(-fWaveVector*gamma/lambda)); // wavek*delta;
// G4cout<<"kgamma = "<<kgamma<<G4endl;
if(fAddCoulomb) // add Coulomb correction
{
G4double sinHalfTheta = theta*0.5; // std::sin(0.5*theta);
G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
kgamma += 0.5*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
// kgamma += 0.65*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
}
G4double kgamma2 = kgamma*kgamma;
// G4double dk2t = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
// G4cout<<"dk2t = "<<dk2t<<G4endl;
// G4double dk2t2 = dk2t*dk2t;
// G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;
G4double pikdt = lambda*(1.-std::exp(-pi*fWaveVector*diffuse*theta/lambda)); // wavek*delta;
// G4cout<<"pikdt = "<<pikdt<<G4endl;
damp = DampFactor(pikdt);
damp2 = damp*damp;
G4double mode2k2 = (e1*e1+e2*e2)*fWaveVector*fWaveVector;
G4double e2dk3t = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;
sigma = kgamma2;
// sigma += dk2t2;
sigma *= bzero2;
sigma += mode2k2*bone2;
sigma += e2dk3t*bzero*bone;
// sigma += kr2*(1 + 8.*fZommerfeld*fZommerfeld/kr2)*bonebyarg2; // correction at J1()/()
sigma += kr2*bonebyarg2; // correction at J1()/()
sigma *= damp2; // *rad*rad;
return sigma;
}
////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability 2*pi*sin(theta)*d(probability)/d(omega)
G4double
G4NuclNuclDiffuseElastic::GetIntegrandFunction( G4double alpha )
{
G4double result;
result = GetDiffElasticSumProbA(alpha);
// result *= 2*pi*std::sin(theta);
return result;
}
////////////////////////////////////////////////////////////////////////////
//
// return integral elastic cross section d(sigma)/d(omega) integrated 0 - theta
G4double
G4NuclNuclDiffuseElastic::IntegralElasticProb( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A )
{
G4double result;
fParticle = particle;
fWaveVector = momentum/hbarc;
fAtomicWeight = A;
fNuclearRadius = CalculateNuclearRad(A);
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
// result = integral.Legendre10(this,&G4NuclNuclDiffuseElastic::GetIntegrandFunction, 0., theta );
result = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetIntegrandFunction, 0., theta );
return result;
}
////////////////////////////////////////////////////////////////////////////
//
// Return inv momentum transfer -t > 0
G4double G4NuclNuclDiffuseElastic::SampleT( const G4ParticleDefinition* aParticle,
G4double p, G4double A)
{
G4double theta = SampleThetaCMS( aParticle, p, A); // sample theta in cms
G4double t = 2*p*p*( 1 - std::cos(theta) ); // -t !!!
return t;
}
////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle sampled in cms
G4double
G4NuclNuclDiffuseElastic::SampleThetaCMS(const G4ParticleDefinition* particle,
G4double momentum, G4double A)
{
G4int i, iMax = 100;
G4double norm, result, theta1, theta2, thetaMax, sum = 0.;
fParticle = particle;
fWaveVector = momentum/hbarc;
fAtomicWeight = A;
fNuclearRadius = CalculateNuclearRad(A);
thetaMax = 10.174/fWaveVector/fNuclearRadius;
if (thetaMax > pi) thetaMax = pi;
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
// result = integral.Legendre10(this,&G4NuclNuclDiffuseElastic::GetIntegrandFunction, 0., theta );
norm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetIntegrandFunction, 0., thetaMax );
norm *= G4UniformRand();
for(i = 1; i <= iMax; i++)
{
theta1 = (i-1)*thetaMax/iMax;
theta2 = i*thetaMax/iMax;
sum += integral.Legendre10(this,&G4NuclNuclDiffuseElastic::GetIntegrandFunction, theta1, theta2);
if ( sum >= norm )
{
result = 0.5*(theta1 + theta2);
break;
}
}
if (i > iMax ) result = 0.5*(theta1 + theta2);
G4double sigma = pi*thetaMax/iMax;
result += G4RandGauss::shoot(0.,sigma);
if(result < 0.) result = 0.;
if(result > thetaMax) result = thetaMax;
return result;
}
/////////////////////////////////////////////////////////////////////////////
///////////////////// Table preparation and reading ////////////////////////
////////////////////////////////////////////////////////////////////////////
//
// Return inv momentum transfer -t > 0 from initialisation table
G4double G4NuclNuclDiffuseElastic::SampleInvariantT( const G4ParticleDefinition* aParticle, G4double p,
G4int Z, G4int A)
{
fParticle = aParticle;
G4double m1 = fParticle->GetPDGMass();
G4double totElab = std::sqrt(m1*m1+p*p);
G4double mass2 = G4NucleiProperties::GetNuclearMass(A, Z);
G4LorentzVector lv1(p,0.0,0.0,totElab);
G4LorentzVector lv(0.0,0.0,0.0,mass2);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
lv1.boost(-bst);
G4ThreeVector p1 = lv1.vect();
G4double momentumCMS = p1.mag();
G4double t = SampleTableT( aParticle, momentumCMS, G4double(Z), G4double(A) ); // sample theta2 in cms
return t;
}
////////////////////////////////////////////////////////////////////////////
//
// Return inv momentum transfer -t > 0 from initialisation table
G4double G4NuclNuclDiffuseElastic::SampleTableT( const G4ParticleDefinition* aParticle, G4double p,
G4double Z, G4double A)
{
G4double alpha = SampleTableThetaCMS( aParticle, p, Z, A); // sample theta2 in cms
// G4double t = 2*p*p*( 1 - std::cos(std::sqrt(alpha)) ); // -t !!!
G4double t = p*p*alpha; // -t !!!
return t;
}
////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle2 sampled in cms according to precalculated table.
G4double
G4NuclNuclDiffuseElastic::SampleTableThetaCMS(const G4ParticleDefinition* particle,
G4double momentum, G4double Z, G4double A)
{
size_t iElement;
G4int iMomentum, iAngle;
G4double randAngle, position, theta1, theta2, E1, E2, W1, W2, W;
G4double m1 = particle->GetPDGMass();
for(iElement = 0; iElement < fElementNumberVector.size(); iElement++)
{
if( std::fabs(Z - fElementNumberVector[iElement]) < 0.5) break;
}
if ( iElement == fElementNumberVector.size() )
{
InitialiseOnFly(Z,A); // table preparation, if needed
// iElement--;
// G4cout << "G4NuclNuclDiffuseElastic: Element with atomic number " << Z
// << " is not found, return zero angle" << G4endl;
// return 0.; // no table for this element
}
// G4cout<<"iElement = "<<iElement<<G4endl;
fAngleTable = fAngleBank[iElement];
G4double kinE = std::sqrt(momentum*momentum + m1*m1) - m1;
for( iMomentum = 0; iMomentum < fEnergyBin; iMomentum++)
{
// G4cout<<iMomentum<<", kinE = "<<kinE/MeV<<", vectorE = "<<fEnergyVector->GetLowEdgeEnergy(iMomentum)/MeV<<G4endl;
if( kinE < fEnergyVector->GetLowEdgeEnergy(iMomentum) ) break;
}
// G4cout<<"iMomentum = "<<iMomentum<<", fEnergyBin -1 = "<<fEnergyBin -1<<G4endl;
if ( iMomentum >= fEnergyBin ) iMomentum = fEnergyBin-1; // kinE is more then theMaxEnergy
if ( iMomentum < 0 ) iMomentum = 0; // against negative index, kinE < theMinEnergy
if (iMomentum == fEnergyBin -1 || iMomentum == 0 ) // the table edges
{
position = (*(*fAngleTable)(iMomentum))(fAngleBin-2)*G4UniformRand();
// G4cout<<"position = "<<position<<G4endl;
for(iAngle = 0; iAngle < fAngleBin-1; iAngle++)
{
if( position < (*(*fAngleTable)(iMomentum))(iAngle) ) break;
}
if (iAngle >= fAngleBin-1) iAngle = fAngleBin-2;
// G4cout<<"iAngle = "<<iAngle<<G4endl;
randAngle = GetScatteringAngle(iMomentum, iAngle, position);
// G4cout<<"randAngle = "<<randAngle<<G4endl;
}
else // kinE inside between energy table edges
{
// position = (*(*fAngleTable)(iMomentum))(fAngleBin-2)*G4UniformRand();
position = (*(*fAngleTable)(iMomentum))(0)*G4UniformRand();
// G4cout<<"position = "<<position<<G4endl;
for(iAngle = 0; iAngle < fAngleBin-1; iAngle++)
{
// if( position < (*(*fAngleTable)(iMomentum))(iAngle) ) break;
if( position > (*(*fAngleTable)(iMomentum))(iAngle) ) break;
}
if (iAngle >= fAngleBin-1) iAngle = fAngleBin-2;
// G4cout<<"iAngle = "<<iAngle<<G4endl;
theta2 = GetScatteringAngle(iMomentum, iAngle, position);
// G4cout<<"theta2 = "<<theta2<<G4endl;
E2 = fEnergyVector->GetLowEdgeEnergy(iMomentum);
// G4cout<<"E2 = "<<E2<<G4endl;
iMomentum--;
// position = (*(*fAngleTable)(iMomentum))(fAngleBin-2)*G4UniformRand();
// G4cout<<"position = "<<position<<G4endl;
for(iAngle = 0; iAngle < fAngleBin-1; iAngle++)
{
// if( position < (*(*fAngleTable)(iMomentum))(iAngle) ) break;
if( position > (*(*fAngleTable)(iMomentum))(iAngle) ) break;
}
if (iAngle >= fAngleBin-1) iAngle = fAngleBin-2;
theta1 = GetScatteringAngle(iMomentum, iAngle, position);
// G4cout<<"theta1 = "<<theta1<<G4endl;
E1 = fEnergyVector->GetLowEdgeEnergy(iMomentum);
// G4cout<<"E1 = "<<E1<<G4endl;
W = 1.0/(E2 - E1);
W1 = (E2 - kinE)*W;
W2 = (kinE - E1)*W;
randAngle = W1*theta1 + W2*theta2;
// randAngle = theta2;
}
// G4double angle = randAngle;
// if (randAngle > 0.) randAngle /= 2*pi*std::sin(angle);
// G4cout<<"randAngle = "<<randAngle/degree<<G4endl;
return randAngle;
}
//////////////////////////////////////////////////////////////////////////////
//
// Initialisation for given particle on fly using new element number
void G4NuclNuclDiffuseElastic::InitialiseOnFly(G4double Z, G4double A)
{
fAtomicNumber = Z; // atomic number
fAtomicWeight = G4NistManager::Instance()->GetAtomicMassAmu( static_cast< G4int >( Z ) );
G4double A1 = G4double( fParticle->GetBaryonNumber() );
G4double R1 = CalculateNuclearRad(A1);
fNuclearRadius = CalculateNuclearRad(fAtomicWeight) + R1;
if( verboseLevel > 0 )
{
G4cout<<"G4NuclNuclDiffuseElastic::Initialise() the element with Z = "
<<Z<<"; and A = "<<A<<G4endl;
}
fElementNumberVector.push_back(fAtomicNumber);
BuildAngleTable();
fAngleBank.push_back(fAngleTable);
return;
}
///////////////////////////////////////////////////////////////////////////////
//
// Build for given particle and element table of momentum, angle probability.
// For the moment in lab system.
void G4NuclNuclDiffuseElastic::BuildAngleTable()
{
G4int i, j;
G4double partMom, kinE, m1 = fParticle->GetPDGMass();
G4double alpha1, alpha2, alphaMax, alphaCoulomb, delta = 0., sum = 0.;
// G4cout<<"particle z = "<<z<<"; particle m1 = "<<m1/GeV<<" GeV"<<G4endl;
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
fAngleTable = new G4PhysicsTable(fEnergyBin);
for( i = 0; i < fEnergyBin; i++)
{
kinE = fEnergyVector->GetLowEdgeEnergy(i);
// G4cout<<G4endl;
// G4cout<<"kinE = "<<kinE/MeV<<" MeV"<<G4endl;
partMom = std::sqrt( kinE*(kinE + 2*m1) );
InitDynParameters(fParticle, partMom);
alphaMax = fRutherfordTheta*fCofAlphaMax;
if(alphaMax > pi) alphaMax = pi;
alphaCoulomb = fRutherfordTheta*fCofAlphaCoulomb;
// G4cout<<"alphaCoulomb = "<<alphaCoulomb/degree<<"; alphaMax = "<<alphaMax/degree<<G4endl;
G4PhysicsFreeVector* angleVector = new G4PhysicsFreeVector(fAngleBin-1);
// G4PhysicsLogVector* angleBins = new G4PhysicsLogVector( 0.001*alphaMax, alphaMax, fAngleBin );
G4double delth = (alphaMax-alphaCoulomb)/fAngleBin;
sum = 0.;
// fAddCoulomb = false;
fAddCoulomb = true;
// for(j = 1; j < fAngleBin; j++)
for(j = fAngleBin-1; j >= 1; j--)
{
// alpha1 = angleBins->GetLowEdgeEnergy(j-1);
// alpha2 = angleBins->GetLowEdgeEnergy(j);
// alpha1 = alphaMax*(j-1)/fAngleBin;
// alpha2 = alphaMax*( j )/fAngleBin;
alpha1 = alphaCoulomb + delth*(j-1);
// if(alpha1 < kRlim2) alpha1 = kRlim2;
alpha2 = alpha1 + delth;
delta = integral.Legendre10(this, &G4NuclNuclDiffuseElastic::GetFresnelIntegrandXsc, alpha1, alpha2);
// delta = integral.Legendre96(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction, alpha1, alpha2);
sum += delta;
angleVector->PutValue( j-1 , alpha1, sum ); // alpha2
// G4cout<<"j-1 = "<<j-1<<"; alpha2 = "<<alpha2/degree<<"; sum = "<<sum<<G4endl;
}
fAngleTable->insertAt(i,angleVector);
// delete[] angleVector;
// delete[] angleBins;
}
return;
}
/////////////////////////////////////////////////////////////////////////////////
//
//
G4double
G4NuclNuclDiffuseElastic:: GetScatteringAngle( G4int iMomentum, G4int iAngle, G4double position )
{
G4double x1, x2, y1, y2, randAngle;
if( iAngle == 0 )
{
randAngle = (*fAngleTable)(iMomentum)->GetLowEdgeEnergy(iAngle);
// iAngle++;
}
else
{
if ( iAngle >= G4int((*fAngleTable)(iMomentum)->GetVectorLength()) )
{
iAngle = (*fAngleTable)(iMomentum)->GetVectorLength() - 1;
}
y1 = (*(*fAngleTable)(iMomentum))(iAngle-1);
y2 = (*(*fAngleTable)(iMomentum))(iAngle);
x1 = (*fAngleTable)(iMomentum)->GetLowEdgeEnergy(iAngle-1);
x2 = (*fAngleTable)(iMomentum)->GetLowEdgeEnergy(iAngle);
if ( x1 == x2 ) randAngle = x2;
else
{
if ( y1 == y2 ) randAngle = x1 + ( x2 - x1 )*G4UniformRand();
else
{
randAngle = x1 + ( position - y1 )*( x2 - x1 )/( y2 - y1 );
}
}
}
return randAngle;
}
////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle sampled in lab system (target at rest)
G4double
G4NuclNuclDiffuseElastic::SampleThetaLab( const G4HadProjectile* aParticle,
G4double tmass, G4double A)
{
const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
G4double m1 = theParticle->GetPDGMass();
G4double plab = aParticle->GetTotalMomentum();
G4LorentzVector lv1 = aParticle->Get4Momentum();
G4LorentzVector lv(0.0,0.0,0.0,tmass);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
lv1.boost(-bst);
G4ThreeVector p1 = lv1.vect();
G4double ptot = p1.mag();
G4double tmax = 4.0*ptot*ptot;
G4double t = 0.0;
//
// Sample t
//
t = SampleT( theParticle, ptot, A);
// NaN finder
if(!(t < 0.0 || t >= 0.0))
{
if (verboseLevel > 0)
{
G4cout << "G4NuclNuclDiffuseElastic:WARNING: A = " << A
<< " mom(GeV)= " << plab/GeV
<< " S-wave will be sampled"
<< G4endl;
}
t = G4UniformRand()*tmax;
}
if(verboseLevel>1)
{
G4cout <<" t= " << t << " tmax= " << tmax
<< " ptot= " << ptot << G4endl;
}
// Sampling of angles in CM system
G4double phi = G4UniformRand()*twopi;
G4double cost = 1. - 2.0*t/tmax;
G4double sint;
if( cost >= 1.0 )
{
cost = 1.0;
sint = 0.0;
}
else if( cost <= -1.0)
{
cost = -1.0;
sint = 0.0;
}
else
{
sint = std::sqrt((1.0-cost)*(1.0+cost));
}
if (verboseLevel>1)
{
G4cout << "cos(t)=" << cost << " std::sin(t)=" << sint << G4endl;
}
G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
v1 *= ptot;
G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(ptot*ptot + m1*m1));
nlv1.boost(bst);
G4ThreeVector np1 = nlv1.vect();
// G4double theta = std::acos( np1.z()/np1.mag() ); // degree;
G4double theta = np1.theta();
return theta;
}
////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle in lab system (target at rest) knowing theta in CMS
G4double
G4NuclNuclDiffuseElastic::ThetaCMStoThetaLab( const G4DynamicParticle* aParticle,
G4double tmass, G4double thetaCMS)
{
const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
G4double m1 = theParticle->GetPDGMass();
// G4double plab = aParticle->GetTotalMomentum();
G4LorentzVector lv1 = aParticle->Get4Momentum();
G4LorentzVector lv(0.0,0.0,0.0,tmass);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
lv1.boost(-bst);
G4ThreeVector p1 = lv1.vect();
G4double ptot = p1.mag();
G4double phi = G4UniformRand()*twopi;
G4double cost = std::cos(thetaCMS);
G4double sint;
if( cost >= 1.0 )
{
cost = 1.0;
sint = 0.0;
}
else if( cost <= -1.0)
{
cost = -1.0;
sint = 0.0;
}
else
{
sint = std::sqrt((1.0-cost)*(1.0+cost));
}
if (verboseLevel>1)
{
G4cout << "cos(tcms)=" << cost << " std::sin(tcms)=" << sint << G4endl;
}
G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
v1 *= ptot;
G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(ptot*ptot + m1*m1));
nlv1.boost(bst);
G4ThreeVector np1 = nlv1.vect();
G4double thetaLab = np1.theta();
return thetaLab;
}
////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle in CMS system (target at rest) knowing theta in Lab
G4double
G4NuclNuclDiffuseElastic::ThetaLabToThetaCMS( const G4DynamicParticle* aParticle,
G4double tmass, G4double thetaLab)
{
const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
G4double m1 = theParticle->GetPDGMass();
G4double plab = aParticle->GetTotalMomentum();
G4LorentzVector lv1 = aParticle->Get4Momentum();
G4LorentzVector lv(0.0,0.0,0.0,tmass);
lv += lv1;
G4ThreeVector bst = lv.boostVector();
// lv1.boost(-bst);
// G4ThreeVector p1 = lv1.vect();
// G4double ptot = p1.mag();
G4double phi = G4UniformRand()*twopi;
G4double cost = std::cos(thetaLab);
G4double sint;
if( cost >= 1.0 )
{
cost = 1.0;
sint = 0.0;
}
else if( cost <= -1.0)
{
cost = -1.0;
sint = 0.0;
}
else
{
sint = std::sqrt((1.0-cost)*(1.0+cost));
}
if (verboseLevel>1)
{
G4cout << "cos(tlab)=" << cost << " std::sin(tlab)=" << sint << G4endl;
}
G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
v1 *= plab;
G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(plab*plab + m1*m1));
nlv1.boost(-bst);
G4ThreeVector np1 = nlv1.vect();
G4double thetaCMS = np1.theta();
return thetaCMS;
}
///////////////////////////////////////////////////////////////////////////////
//
// Test for given particle and element table of momentum, angle probability.
// For the moment in lab system.
void G4NuclNuclDiffuseElastic::TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom,
G4double Z, G4double A)
{
fAtomicNumber = Z; // atomic number
fAtomicWeight = A; // number of nucleons
fNuclearRadius = CalculateNuclearRad(fAtomicWeight);
G4cout<<"G4NuclNuclDiffuseElastic::TestAngleTable() init the element with Z = "
<<Z<<"; and A = "<<A<<G4endl;
fElementNumberVector.push_back(fAtomicNumber);
G4int i=0, j;
G4double a = 0., z = theParticle->GetPDGCharge(), m1 = fParticle->GetPDGMass();
G4double alpha1=0., alpha2=0., alphaMax=0., alphaCoulomb=0.;
G4double deltaL10 = 0., deltaL96 = 0., deltaAG = 0.;
G4double sumL10 = 0.,sumL96 = 0.,sumAG = 0.;
G4double epsilon = 0.001;
G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
fAngleTable = new G4PhysicsTable(fEnergyBin);
fWaveVector = partMom/hbarc;
G4double kR = fWaveVector*fNuclearRadius;
G4double kR2 = kR*kR;
G4double kRmax = 10.6; // 10.6, 18, 10.174; ~ 3 maxima of J1 or 15., 25.
G4double kRcoul = 1.2; // 1.4, 2.5; // on the first slope of J1
alphaMax = kRmax*kRmax/kR2;
if (alphaMax > 4.) alphaMax = 4.; // vmg05-02-09: was pi2
alphaCoulomb = kRcoul*kRcoul/kR2;
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);
}
G4PhysicsFreeVector* angleVector = new G4PhysicsFreeVector(fAngleBin-1);
// G4PhysicsLogVector* angleBins = new G4PhysicsLogVector( 0.001*alphaMax, alphaMax, fAngleBin );
fAddCoulomb = false;
for(j = 1; j < fAngleBin; j++)
{
// alpha1 = angleBins->GetLowEdgeEnergy(j-1);
// alpha2 = angleBins->GetLowEdgeEnergy(j);
alpha1 = alphaMax*(j-1)/fAngleBin;
alpha2 = alphaMax*( j )/fAngleBin;
if( ( alpha2 > alphaCoulomb ) && z ) fAddCoulomb = true;
deltaL10 = integral.Legendre10(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction, alpha1, alpha2);
deltaL96 = integral.Legendre96(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction, alpha1, alpha2);
deltaAG = integral.AdaptiveGauss(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction,
alpha1, alpha2,epsilon);
// G4cout<<alpha1<<"\t"<<std::sqrt(alpha1)/degree<<"\t"
// <<deltaL10<<"\t"<<deltaL96<<"\t"<<deltaAG<<G4endl;
sumL10 += deltaL10;
sumL96 += deltaL96;
sumAG += deltaAG;
G4cout<<alpha1<<"\t"<<std::sqrt(alpha1)/degree<<"\t"
<<sumL10<<"\t"<<sumL96<<"\t"<<sumAG<<G4endl;
angleVector->PutValue( j-1 , alpha1, sumL10 ); // alpha2
}
fAngleTable->insertAt(i,angleVector);
fAngleBank.push_back(fAngleTable);
/*
// Integral over all angle range - Bad accuracy !!!
sumL10 = integral.Legendre10(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction, 0., alpha2);
sumL96 = integral.Legendre96(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction, 0., alpha2);
sumAG = integral.AdaptiveGauss(this, &G4NuclNuclDiffuseElastic::GetIntegrandFunction,
0., alpha2,epsilon);
G4cout<<G4endl;
G4cout<<alpha2<<"\t"<<std::sqrt(alpha2)/degree<<"\t"
<<sumL10<<"\t"<<sumL96<<"\t"<<sumAG<<G4endl;
*/
return;
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
/////////////////////////////////////////////////////////////////
//
//
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);
}
/////////////////////////////////////////////////////////////////
//
//
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./std::sqrt(CLHEP::pi);
outIm *= 2./std::sqrt(CLHEP::pi);
outRe += GetErf(x);
return G4complex(outRe, outIm);
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
/////////////////////////////////////////////////////////////////
//
//
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;
}
///////////////////////////////////////////////////////////////////////////////
//
// Test for given particle and element table of momentum, angle probability.
// For the partMom in CMS.
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.
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.
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
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;
}
/////////////////////////////////////////////////////////////////
//
// The ratio el/ruth for Fresnel smooth nucleus profile
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;
}
///////////////////////////////////////////////////////////////////
//
// For the calculation of arg Gamma(z) one needs complex extension
// of ln(Gamma(z))
G4complex G4NuclNuclDiffuseElastic::GammaLogarithm(G4complex zz)
{
const G4double cof[6] = { 76.18009172947146, -86.50532032941677,
24.01409824083091, -1.231739572450155,
0.1208650973866179e-2, -0.5395239384953e-5 } ;
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);
}
/////////////////////////////////////////////////////////////
//
// Bessel J0 function based on rational approximation from
// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value)
{
G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
modvalue = std::fabs(value);
if ( value < 8.0 && value > -8.0 )
{
value2 = value*value;
fact1 = 57568490574.0 + value2*(-13362590354.0
+ value2*( 651619640.7
+ value2*(-11214424.18
+ value2*( 77392.33017
+ value2*(-184.9052456 ) ) ) ) );
fact2 = 57568490411.0 + value2*( 1029532985.0
+ value2*( 9494680.718
+ value2*(59272.64853
+ value2*(267.8532712
+ value2*1.0 ) ) ) );
bessel = fact1/fact2;
}
else
{
arg = 8.0/modvalue;
value2 = arg*arg;
shift = modvalue-0.785398164;
fact1 = 1.0 + value2*(-0.1098628627e-2
+ value2*(0.2734510407e-4
+ value2*(-0.2073370639e-5
+ value2*0.2093887211e-6 ) ) );
fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3
+ value2*(-0.6911147651e-5
+ value2*(0.7621095161e-6
- value2*0.934945152e-7 ) ) );
bessel = std::sqrt(0.636619772/modvalue)*(std::cos(shift)*fact1 - arg*std::sin(shift)*fact2 );
}
return bessel;
}
/////////////////////////////////////////////////////////////
//
// Bessel J1 function based on rational approximation from
// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value)
{
G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
modvalue = std::fabs(value);
if ( modvalue < 8.0 )
{
value2 = value*value;
fact1 = value*(72362614232.0 + value2*(-7895059235.0
+ value2*( 242396853.1
+ value2*(-2972611.439
+ value2*( 15704.48260
+ value2*(-30.16036606 ) ) ) ) ) );
fact2 = 144725228442.0 + value2*(2300535178.0
+ value2*(18583304.74
+ value2*(99447.43394
+ value2*(376.9991397
+ value2*1.0 ) ) ) );
bessel = fact1/fact2;
}
else
{
arg = 8.0/modvalue;
value2 = arg*arg;
shift = modvalue - 2.356194491;
fact1 = 1.0 + value2*( 0.183105e-2
+ value2*(-0.3516396496e-4
+ value2*(0.2457520174e-5
+ value2*(-0.240337019e-6 ) ) ) );
fact2 = 0.04687499995 + value2*(-0.2002690873e-3
+ value2*( 0.8449199096e-5
+ value2*(-0.88228987e-6
+ value2*0.105787412e-6 ) ) );
bessel = std::sqrt( 0.636619772/modvalue)*(std::cos(shift)*fact1 - arg*std::sin(shift)*fact2);
if (value < 0.0) bessel = -bessel;
}
return bessel;
}
//
//
/////////////////////////////////////////////////////////////////////////////////
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