Import Geant4 10.0.0 source tree
This commit is contained in:
Gabriele Cosmo
@@ -23,7 +23,7 @@
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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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// $Id$
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// $Id: G4NuclNuclDiffuseElastic.cc 71874 2013-06-27 13:39:59Z gunter $
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//
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//
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// Physics model class G4NuclNuclDiffuseElastic
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@@ -217,7 +217,7 @@ G4NuclNuclDiffuseElastic::GetInvElasticXsc( const G4ParticleDefinition* particle
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else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
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else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
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else if (iZ == 2 && iA == 4) theDef = theAlpha;
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else theDef = G4ParticleTable::GetParticleTable()->FindIon(iZ,iA,0,iZ);
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else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
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G4double tmass = theDef->GetPDGMass();
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@@ -304,7 +304,7 @@ G4NuclNuclDiffuseElastic::GetInvElasticSumXsc( const G4ParticleDefinition* parti
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else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
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else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
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else if (iZ == 2 && iA == 4) theDef = theAlpha;
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else theDef = G4ParticleTable::GetParticleTable()->FindIon(iZ,iA,0,iZ);
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else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
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G4double tmass = theDef->GetPDGMass();
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@@ -354,7 +354,7 @@ G4NuclNuclDiffuseElastic::GetInvCoulombElasticXsc( const G4ParticleDefinition* p
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else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
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else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
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else if (iZ == 2 && iA == 4) theDef = theAlpha;
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else theDef = G4ParticleTable::GetParticleTable()->FindIon(iZ,iA,0,iZ);
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else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
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G4double tmass = theDef->GetPDGMass();
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@@ -1382,6 +1382,703 @@ void G4NuclNuclDiffuseElastic::TestAngleTable(const G4ParticleDefinition* thePar
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return;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4double G4NuclNuclDiffuseElastic::GetLegendrePol(G4int n, G4double theta)
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{
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G4double legPol, epsilon = 1.e-6;
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G4double x = std::cos(theta);
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if ( n < 0 ) legPol = 0.;
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else if( n == 0 ) legPol = 1.;
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else if( n == 1 ) legPol = x;
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else if( n == 2 ) legPol = (3.*x*x-1.)/2.;
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else if( n == 3 ) legPol = (5.*x*x*x-3.*x)/2.;
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else if( n == 4 ) legPol = (35.*x*x*x*x-30.*x*x+3.)/8.;
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else if( n == 5 ) legPol = (63.*x*x*x*x*x-70.*x*x*x+15.*x)/8.;
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else if( n == 6 ) legPol = (231.*x*x*x*x*x*x-315.*x*x*x*x+105.*x*x-5.)/16.;
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else
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{
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// legPol = ( (2*n-1)*x*GetLegendrePol(n-1,x) - (n-1)*GetLegendrePol(n-2,x) )/n;
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legPol = std::sqrt( 2./(n*CLHEP::pi*std::sin(theta+epsilon)) )*std::sin( (n+0.5)*theta+0.25*CLHEP::pi );
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}
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return legPol;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::GetErfComp(G4complex z, G4int nMax)
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{
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G4int n;
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G4double n2, cofn, shny, chny, fn, gn;
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G4double x = z.real();
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G4double y = z.imag();
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G4double outRe = 0., outIm = 0.;
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G4double twox = 2.*x;
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G4double twoxy = twox*y;
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G4double twox2 = twox*twox;
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G4double cof1 = std::exp(-x*x)/CLHEP::pi;
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G4double cos2xy = std::cos(twoxy);
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G4double sin2xy = std::sin(twoxy);
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G4double twoxcos2xy = twox*cos2xy;
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G4double twoxsin2xy = twox*sin2xy;
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for( n = 1; n <= nMax; n++)
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{
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n2 = n*n;
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cofn = std::exp(-0.5*n2)/(n2+twox2); // /(n2+0.5*twox2);
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chny = std::cosh(n*y);
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shny = std::sinh(n*y);
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fn = twox - twoxcos2xy*chny + n*sin2xy*shny;
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gn = twoxsin2xy*chny + n*cos2xy*shny;
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fn *= cofn;
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gn *= cofn;
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outRe += fn;
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outIm += gn;
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}
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outRe *= 2*cof1;
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outIm *= 2*cof1;
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if(std::abs(x) < 0.0001)
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{
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outRe += GetErf(x);
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outIm += cof1*y;
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}
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else
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{
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outRe += GetErf(x) + cof1*(1-cos2xy)/twox;
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outIm += cof1*sin2xy/twox;
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}
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return G4complex(outRe, outIm);
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::GetErfInt(G4complex z) // , G4int nMax)
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{
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G4double outRe, outIm;
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G4double x = z.real();
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G4double y = z.imag();
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fReZ = x;
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G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
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outRe = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpSin, 0., y );
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outIm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpCos, 0., y );
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outRe *= 2./std::sqrt(CLHEP::pi);
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outIm *= 2./std::sqrt(CLHEP::pi);
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outRe += GetErf(x);
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return G4complex(outRe, outIm);
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta)
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{
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G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
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G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2);
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G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
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G4double kappa = u/std::sqrt(CLHEP::pi);
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G4double dTheta = theta - fRutherfordTheta;
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u *= dTheta;
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G4double u2 = u*u;
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G4double u2m2p3 = u2*2./3.;
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G4complex im = G4complex(0.,1.);
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G4complex order = G4complex(u,u);
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order /= std::sqrt(2.);
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G4complex gamma = CLHEP::pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*CLHEP::pi));
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G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
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G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
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G4complex out = gamma*(1. - a1*dTheta) - a0;
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return out;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::GammaMore(G4double theta)
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{
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G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
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G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2);
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G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
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G4double kappa = u/std::sqrt(CLHEP::pi);
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G4double dTheta = theta - fRutherfordTheta;
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u *= dTheta;
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G4double u2 = u*u;
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G4double u2m2p3 = u2*2./3.;
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G4complex im = G4complex(0.,1.);
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G4complex order = G4complex(u,u);
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order /= std::sqrt(2.);
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G4complex gamma = CLHEP::pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*CLHEP::pi));
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G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
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G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
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G4complex out = -gamma*(1. - a1*dTheta) - a0;
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return out;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::AmplitudeNear(G4double theta)
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{
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G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/CLHEP::pi);
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G4complex out = G4complex(kappa/fWaveVector,0.);
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out *= PhaseNear(theta);
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if( theta <= fRutherfordTheta )
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{
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out *= GammaLess(theta) + ProfileNear(theta);
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// out *= GammaMore(theta) + ProfileNear(theta);
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out += CoulombAmplitude(theta);
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}
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else
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{
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out *= GammaMore(theta) + ProfileNear(theta);
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// out *= GammaLess(theta) + ProfileNear(theta);
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}
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return out;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::AmplitudeSim(G4double theta)
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{
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G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
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G4double dTheta = 0.5*(theta - fRutherfordTheta);
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G4double sindTheta = std::sin(dTheta);
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G4double persqrt2 = std::sqrt(0.5);
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G4complex order = G4complex(persqrt2,persqrt2);
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order *= std::sqrt(0.5*fProfileLambda/sinThetaR)*2.*sindTheta;
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// order *= std::sqrt(0.5*fProfileLambda/sinThetaR)*2.*dTheta;
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G4complex out;
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if ( theta <= fRutherfordTheta )
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{
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out = 1. - 0.5*GetErfcInt(-order)*ProfileNear(theta);
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}
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else
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{
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out = 0.5*GetErfcInt(order)*ProfileNear(theta);
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}
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out *= CoulombAmplitude(theta);
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return out;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::AmplitudeGla(G4double theta)
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{
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G4int n;
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G4double T12b, b, b2; // cosTheta = std::cos(theta);
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G4complex out = G4complex(0.,0.), shiftC, shiftN;
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G4complex im = G4complex(0.,1.);
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for( n = 0; n < fMaxL; n++)
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{
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shiftC = std::exp( im*2.*CalculateCoulombPhase(n) );
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// b = ( fZommerfeld + std::sqrt( fZommerfeld*fZommerfeld + n*(n+1) ) )/fWaveVector;
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b = ( std::sqrt( G4double(n*(n+1)) ) )/fWaveVector;
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b2 = b*b;
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T12b = fSumSigma*std::exp(-b2/fNuclearRadiusSquare)/CLHEP::pi/fNuclearRadiusSquare;
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shiftN = std::exp( -0.5*(1.-im*fEtaRatio)*T12b ) - 1.;
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out += (2.*n+1.)*shiftC*shiftN*GetLegendrePol(n, theta);
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}
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out /= 2.*im*fWaveVector;
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out += CoulombAmplitude(theta);
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return out;
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}
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/////////////////////////////////////////////////////////////////
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//
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//
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G4complex G4NuclNuclDiffuseElastic::AmplitudeGG(G4double theta)
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{
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G4int n;
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G4double T12b, a, aTemp, b2, sinThetaH = std::sin(0.5*theta);
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G4double sinThetaH2 = sinThetaH*sinThetaH;
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G4complex out = G4complex(0.,0.);
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G4complex im = G4complex(0.,1.);
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a = -fSumSigma/CLHEP::twopi/fNuclearRadiusSquare;
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b2 = fWaveVector*fWaveVector*fNuclearRadiusSquare*sinThetaH2;
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aTemp = a;
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for( n = 1; n < fMaxL; n++)
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{
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T12b = aTemp*std::exp(-b2/n)/n;
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aTemp *= a;
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out += T12b;
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G4cout<<"out = "<<out<<G4endl;
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}
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out *= -4.*im*fWaveVector/CLHEP::pi;
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out += CoulombAmplitude(theta);
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return out;
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}
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///////////////////////////////////////////////////////////////////////////////
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//
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// Test for given particle and element table of momentum, angle probability.
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// For the partMom in CMS.
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void G4NuclNuclDiffuseElastic::InitParameters(const G4ParticleDefinition* theParticle,
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G4double partMom, G4double Z, G4double A)
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{
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fAtomicNumber = Z; // atomic number
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fAtomicWeight = A; // number of nucleons
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fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight);
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G4double A1 = G4double( theParticle->GetBaryonNumber() );
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fNuclearRadius1 = CalculateNuclearRad(A1);
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// fNuclearRadius = std::sqrt(fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2);
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fNuclearRadius = fNuclearRadius1 + fNuclearRadius2;
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G4double a = 0.;
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G4double z = theParticle->GetPDGCharge();
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G4double m1 = theParticle->GetPDGMass();
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fWaveVector = partMom/CLHEP::hbarc;
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G4double lambda = fCofLambda*fWaveVector*fNuclearRadius;
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G4cout<<"kR = "<<lambda<<G4endl;
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if( z )
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{
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a = partMom/m1; // beta*gamma for m1
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fBeta = a/std::sqrt(1+a*a);
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fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
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fRutherfordRatio = fZommerfeld/fWaveVector;
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fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
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}
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G4cout<<"fZommerfeld = "<<fZommerfeld<<G4endl;
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fProfileLambda = lambda; // *std::sqrt(1.-2*fZommerfeld/lambda);
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G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl;
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fProfileDelta = fCofDelta*fProfileLambda;
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fProfileAlpha = fCofAlpha*fProfileLambda;
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CalculateCoulombPhaseZero();
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CalculateRutherfordAnglePar();
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return;
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}
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///////////////////////////////////////////////////////////////////////////////
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//
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// Test for given particle and element table of momentum, angle probability.
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// For the partMom in CMS.
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void G4NuclNuclDiffuseElastic::InitDynParameters(const G4ParticleDefinition* theParticle,
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G4double partMom)
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{
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G4double a = 0.;
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G4double z = theParticle->GetPDGCharge();
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G4double m1 = theParticle->GetPDGMass();
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fWaveVector = partMom/CLHEP::hbarc;
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G4double lambda = fCofLambda*fWaveVector*fNuclearRadius;
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if( z )
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{
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a = partMom/m1; // beta*gamma for m1
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fBeta = a/std::sqrt(1+a*a);
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fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
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fRutherfordRatio = fZommerfeld/fWaveVector;
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fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
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}
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fProfileLambda = lambda; // *std::sqrt(1.-2*fZommerfeld/lambda);
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fProfileDelta = fCofDelta*fProfileLambda;
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fProfileAlpha = fCofAlpha*fProfileLambda;
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CalculateCoulombPhaseZero();
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CalculateRutherfordAnglePar();
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return;
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}
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///////////////////////////////////////////////////////////////////////////////
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//
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// Test for given particle and element table of momentum, angle probability.
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// For the partMom in CMS.
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void G4NuclNuclDiffuseElastic::InitParametersGla(const G4DynamicParticle* aParticle,
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G4double partMom, G4double Z, G4double A)
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{
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fAtomicNumber = Z; // target atomic number
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fAtomicWeight = A; // target number of nucleons
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fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight); // target nucleus radius
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G4double A1 = G4double( aParticle->GetDefinition()->GetBaryonNumber() );
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fNuclearRadius1 = CalculateNuclearRad(A1); // projectile nucleus radius
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fNuclearRadiusSquare = fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2;
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G4double a = 0., kR12;
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G4double z = aParticle->GetDefinition()->GetPDGCharge();
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G4double m1 = aParticle->GetDefinition()->GetPDGMass();
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fWaveVector = partMom/CLHEP::hbarc;
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G4double pN = A1 - z;
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if( pN < 0. ) pN = 0.;
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G4double tN = A - Z;
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if( tN < 0. ) tN = 0.;
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G4double pTkin = aParticle->GetKineticEnergy();
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pTkin /= A1;
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|
||||
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 } ;
|
||||
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);
|
||||
}
|
||||
|
||||
/////////////////////////////////////////////////////////////
|
||||
//
|
||||
// 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;
|
||||
}
|
||||
|
||||
//
|
||||
//
|
||||
/////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
Reference in New Issue
Block a user