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74cad5e589f2f0ce98503e2246afb07c62ffbff0
geant4/source/processes/hadronic/models/coherent_elastic/include/G4NuclNuclDiffuseElastic.hh
T
Gabriele Cosmo 74cad5e589 Import Geant4 9.3.0 source tree
2016-06-09 16:15:05 +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.hh,v 1.8 2009/04/10 13:22:25 grichine Exp $
// GEANT4 tag $Name: geant4-09-03 $
//
//
// G4 Model: optical elastic scattering with 4-momentum balance
//
// Class Description
// Final state production model for nucleus-nucleus elastic scattering;
// Coulomb amplitude is not considered as correction
// (as in G4DiffuseElastic)
// Class Description - End
//
//
// 17.03.09 V. Grichine implementation for Coulomb elastic scattering
#ifndef G4NuclNuclDiffuseElastic_h
#define G4NuclNuclDiffuseElastic_h 1
#include "globals.hh"
#include <complex>
#include "G4Integrator.hh"
#include "G4HadronicInteraction.hh"
#include "G4HadProjectile.hh"
#include "G4Nucleus.hh"
using namespace std;
class G4ParticleDefinition;
class G4PhysicsTable;
class G4PhysicsLogVector;
class G4NuclNuclDiffuseElastic : public G4HadronicInteraction
{
public:
G4NuclNuclDiffuseElastic();
G4NuclNuclDiffuseElastic(const G4ParticleDefinition* aParticle);
virtual ~G4NuclNuclDiffuseElastic();
void Initialise();
void InitialiseOnFly(G4double Z, G4double A);
void BuildAngleTable();
G4HadFinalState * ApplyYourself(const G4HadProjectile & aTrack,
G4Nucleus & targetNucleus);
void SetPlabLowLimit(G4double value);
void SetHEModelLowLimit(G4double value);
void SetQModelLowLimit(G4double value);
void SetLowestEnergyLimit(G4double value);
void SetRecoilKinEnergyLimit(G4double value);
G4double SampleT(const G4ParticleDefinition* aParticle,
G4double p, G4double A);
G4double SampleTableT(const G4ParticleDefinition* aParticle,
G4double p, G4double Z, G4double A);
G4double SampleThetaCMS(const G4ParticleDefinition* aParticle, G4double p, G4double A);
G4double SampleTableThetaCMS(const G4ParticleDefinition* aParticle, G4double p,
G4double Z, G4double A);
G4double GetScatteringAngle(G4int iMomentum, G4int iAngle, G4double position);
G4double SampleThetaLab(const G4HadProjectile* aParticle,
G4double tmass, G4double A);
G4double GetDiffuseElasticXsc( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A );
G4double GetInvElasticXsc( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A, G4double Z );
G4double GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A, G4double Z );
G4double GetInvElasticSumXsc( const G4ParticleDefinition* particle,
G4double tMand,
G4double momentum,
G4double A, G4double Z );
G4double IntegralElasticProb( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double A );
G4double GetCoulombElasticXsc( const G4ParticleDefinition* particle,
G4double theta,
G4double momentum,
G4double Z );
G4double GetInvCoulombElasticXsc( const G4ParticleDefinition* particle,
G4double tMand,
G4double momentum,
G4double A, G4double Z );
G4double GetCoulombTotalXsc( const G4ParticleDefinition* particle,
G4double momentum, G4double Z );
G4double GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
G4double momentum, G4double Z,
G4double theta1, G4double theta2 );
G4double CalculateParticleBeta( const G4ParticleDefinition* particle,
G4double momentum );
G4double CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 );
G4double CalculateAm( G4double momentum, G4double n, G4double Z);
G4double CalculateNuclearRad( G4double A);
G4double ThetaCMStoThetaLab(const G4DynamicParticle* aParticle,
G4double tmass, G4double thetaCMS);
G4double ThetaLabToThetaCMS(const G4DynamicParticle* aParticle,
G4double tmass, G4double thetaLab);
void TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom,
G4double Z, G4double A);
G4double BesselJzero(G4double z);
G4double BesselJone(G4double z);
G4double DampFactor(G4double z);
G4double BesselOneByArg(G4double z);
G4double GetDiffElasticProb(G4double theta);
G4double GetDiffElasticSumProb(G4double theta);
G4double GetDiffElasticSumProbA(G4double alpha);
G4double GetIntegrandFunction(G4double theta);
G4double GetNuclearRadius(){return fNuclearRadius;};
// Technical math functions for strong Coulomb contribution
G4complex GammaLogarithm(G4complex xx);
G4double GetErf(G4double x);
G4complex GetErfcComp(G4complex z, G4int nMax);
G4complex GetErfcSer(G4complex z, G4int nMax);
G4complex GetErfcInt(G4complex z); // , G4int nMax);
G4complex GetErfComp(G4complex z, G4int nMax); // AandS algorithm != Ser, Int
G4complex GetErfSer(G4complex z, G4int nMax);
G4double GetExpCos(G4double x);
G4double GetExpSin(G4double x);
G4complex GetErfInt(G4complex z); // , G4int nMax);
G4complex TestErfcComp(G4complex z, G4int nMax);
G4complex TestErfcSer(G4complex z, G4int nMax);
G4complex TestErfcInt(G4complex z); // , G4int nMax);
G4complex CoulombAmplitude(G4double theta);
void CalculateCoulombPhaseZero();
void CalculateRutherfordAnglePar();
G4double ProfileNear(G4double theta);
G4double ProfileFar(G4double theta);
G4complex PhaseNear(G4double theta);
G4complex PhaseFar(G4double theta);
G4complex GammaLess(G4double theta);
G4complex GammaMore(G4double theta);
G4complex AmplitudeNear(G4double theta);
G4complex AmplitudeFar(G4double theta);
G4complex Amplitude(G4double theta);
G4double AmplitudeMod2(G4double theta);
void InitParameters(const G4ParticleDefinition* theParticle,
G4double partMom, G4double Z, G4double A);
G4double GetProfileLambda(){return fProfileLambda;};
void SetProfileLambda(G4double pl) {fProfileLambda = pl;};
void SetProfileDelta(G4double pd) {fProfileDelta = pd;};
void SetProfileAlpha(G4double pa){fProfileAlpha = pa;};
private:
G4ParticleDefinition* theProton;
G4ParticleDefinition* theNeutron;
G4ParticleDefinition* theDeuteron;
G4ParticleDefinition* theAlpha;
const G4ParticleDefinition* thePionPlus;
const G4ParticleDefinition* thePionMinus;
G4double lowEnergyRecoilLimit;
G4double lowEnergyLimitHE;
G4double lowEnergyLimitQ;
G4double lowestEnergyLimit;
G4double plabLowLimit;
G4int fEnergyBin;
G4int fAngleBin;
G4PhysicsLogVector* fEnergyVector;
G4PhysicsTable* fAngleTable;
std::vector<G4PhysicsTable*> fAngleBank;
std::vector<G4double> fElementNumberVector;
std::vector<G4String> fElementNameVector;
const G4ParticleDefinition* fParticle;
G4double fWaveVector;
G4double fAtomicWeight;
G4double fAtomicNumber;
G4double fNuclearRadius1;
G4double fNuclearRadius2;
G4double fNuclearRadius;
G4double fBeta;
G4double fZommerfeld;
G4double fAm;
G4bool fAddCoulomb;
G4double fCoulombPhase0;
G4double fHalfRutThetaTg;
G4double fRutherfordTheta;
G4double fProfileLambda;
G4double fProfileDelta;
G4double fProfileAlpha;
G4double fReZ;
};
inline void G4NuclNuclDiffuseElastic::SetRecoilKinEnergyLimit(G4double value)
{
lowEnergyRecoilLimit = value;
}
inline void G4NuclNuclDiffuseElastic::SetPlabLowLimit(G4double value)
{
plabLowLimit = value;
}
inline void G4NuclNuclDiffuseElastic::SetHEModelLowLimit(G4double value)
{
lowEnergyLimitHE = value;
}
inline void G4NuclNuclDiffuseElastic::SetQModelLowLimit(G4double value)
{
lowEnergyLimitQ = value;
}
inline void G4NuclNuclDiffuseElastic::SetLowestEnergyLimit(G4double value)
{
lowestEnergyLimit = value;
}
/////////////////////////////////////////////////////////////
//
// Bessel J0 function based on rational approximation from
// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
inline G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value)
{
G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
modvalue = 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 = sqrt(0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2 );
}
return bessel;
}
/////////////////////////////////////////////////////////////
//
// Bessel J1 function based on rational approximation from
// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
inline G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value)
{
G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
modvalue = 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 = sqrt( 0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2);
if (value < 0.0) bessel = -bessel;
}
return bessel;
}
////////////////////////////////////////////////////////////////////
//
// damp factor in diffraction x/sh(x), x was already *pi
inline G4double G4NuclNuclDiffuseElastic::DampFactor(G4double x)
{
G4double df;
G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials
// x *= pi;
if( std::fabs(x) < 0.01 )
{
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 = 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/hbarc;
G4double ch = 1.13 + 3.76*n*n;
G4double zn = 1.77*k*std::pow(Z,-1./3.)*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, radius;
if( A < 50. )
{
if( A > 10. ) r0 = 1.16*( 1 - std::pow(A, -2./3.) )*fermi; // 1.08*fermi;
else r0 = 1.1*fermi;
radius = r0*std::pow(A, 1./3.);
}
else
{
r0 = 1.7*fermi; // 1.7*fermi;
radius = r0*std::pow(A, 0.27); // 0.27);
}
return radius;
}
////////////////////////////////////////////////////////////////////
//
// return Coulomb scattering differential xsc with Wentzel correction
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/hbarc;
G4double ch = 0.5*n/k;
G4double ch2 = ch*ch;
G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am);
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/hbarc;
G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl;
G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl;
G4double ch = n/k;
G4double ch2 = ch*ch;
G4double xsc = ch2*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/hbarc;
// G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl;
// G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl;
G4double ch = n/k;
G4double ch2 = ch*ch;
am *= 2.;
G4double xsc = ch2*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);
}
/////////////////////////////////////////////////////////////////
//
//
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 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)/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(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(pi);
outIm *= 2./sqrt(pi);
outRe += GetErf(x);
return G4complex(outRe, outIm);
}
/////////////////////////////////////////////////////////////////
//
//
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 void G4NuclNuclDiffuseElastic::CalculateCoulombPhaseZero()
{
G4complex z = G4complex(1,fZommerfeld);
G4complex gammalog = GammaLogarithm(z);
fCoulombPhase0 = gammalog.imag();
}
/////////////////////////////////////////////////////////////////
//
//
inline void G4NuclNuclDiffuseElastic::CalculateRutherfordAnglePar()
{
fHalfRutThetaTg = fZommerfeld/(fWaveVector*fNuclearRadius);
fRutherfordTheta = 2.*std::atan(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 = pi*argument*std::exp(fProfileAlpha*argument);
result /= std::sinh(pi*argument);
result -= 1.;
result /= dTheta;
}
return result;
}
/////////////////////////////////////////////////////////////////
//
//
inline G4double G4NuclNuclDiffuseElastic::ProfileFar(G4double theta)
{
G4double dTheta = fRutherfordTheta + theta;
G4double argument = fProfileDelta*dTheta;
G4double result = pi*argument*std::exp(fProfileAlpha*argument);
result /= std::sinh(pi*argument);
result /= dTheta;
return result;
}
/////////////////////////////////////////////////////////////////
//
//
inline G4complex G4NuclNuclDiffuseElastic::PhaseNear(G4double theta)
{
G4double twosigma = 2.*fCoulombPhase0;
twosigma -= fZommerfeld*std::log(fHalfRutThetaTg/(1.+fHalfRutThetaTg*fHalfRutThetaTg));
twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi;
twosigma -= fProfileLambda*theta - 0.25*pi;
G4complex z = G4complex(0., twosigma);
return std::exp(z);
}
/////////////////////////////////////////////////////////////////
//
//
inline G4complex G4NuclNuclDiffuseElastic::PhaseFar(G4double theta)
{
G4double twosigma = 2.*fCoulombPhase0;
twosigma -= fZommerfeld*std::log(fHalfRutThetaTg/(1.+fHalfRutThetaTg*fHalfRutThetaTg));
twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi;
twosigma += fProfileLambda*theta - 0.25*pi;
G4complex z = G4complex(0., twosigma);
return std::exp(z);
}
/////////////////////////////////////////////////////////////////
//
//
inline G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta)
{
G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg*fHalfRutThetaTg);
G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg*fHalfRutThetaTg);
G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
G4double kappa = u/std::sqrt(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 = pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*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. + fHalfRutThetaTg*fHalfRutThetaTg);
G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg*fHalfRutThetaTg);
G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
G4double kappa = u/std::sqrt(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 = pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*pi));
G4complex a0 = 0.5*(1. + 3.*(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)/pi);
G4complex out = G4complex(kappa/fWaveVector,0.);
out *= PhaseNear(theta);
if(theta <= fRutherfordTheta)
{
out *= GammaLess(theta) + ProfileNear(theta);
out += CoulombAmplitude(theta);
}
else
{
out *= GammaMore(theta) + ProfileNear(theta);
}
return out;
}
/////////////////////////////////////////////////////////////////
//
//
inline G4complex G4NuclNuclDiffuseElastic::AmplitudeFar(G4double theta)
{
G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi);
G4complex out = G4complex(kappa/fWaveVector,0.);
out *= ProfileFar(theta)*PhaseFar(theta);
return out;
}
/////////////////////////////////////////////////////////////////
//
//
inline G4complex G4NuclNuclDiffuseElastic::Amplitude(G4double theta)
{
G4complex out = AmplitudeNear(theta) + 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;
}
///////////////////////////////////////////////////////////////////////////////
//
// Test for given particle and element table of momentum, angle probability.
// For the moment in lab system.
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/hbarc;
G4double lambda = fWaveVector*fNuclearRadius;
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);
}
fProfileLambda = lambda*std::sqrt(1.-2*fZommerfeld/lambda);
G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl;
fProfileDelta = 0.1*fProfileLambda;
fProfileAlpha = 0.05*fProfileLambda;
CalculateCoulombPhaseZero();
CalculateRutherfordAnglePar();
return;
}
#endif
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