Gabriele Cosmo
275 lines
10 KiB
C++
275 lines
10 KiB
C++
//
|
|
// ********************************************************************
|
|
// * 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. *
|
|
// ********************************************************************
|
|
//
|
|
// -------------------------------------------------------------------
|
|
//
|
|
// GEANT4 Class file
|
|
//
|
|
//
|
|
// File name: G4PolarizedMollerCrossSection
|
|
//
|
|
// Author: Andreas Schaelicke
|
|
//
|
|
// Creation date: 12.01.2006
|
|
//
|
|
// Modifications:
|
|
// 16-01-06 included cross section as calculated by P.Starovoitov
|
|
//
|
|
// Class Description:
|
|
// * calculates the differential cross section
|
|
// incomming electron K1(along positive z direction) scatters at an electron K2 at rest
|
|
// * phi denotes the angle between the scattering plane (defined by the
|
|
// outgoing electron) and X-axis
|
|
// * all stokes vectors refer to spins in the Global System (X,Y,Z)
|
|
//
|
|
|
|
#include "G4PolarizedMollerCrossSection.hh"
|
|
#include "G4PhysicalConstants.hh"
|
|
|
|
G4PolarizedMollerCrossSection::G4PolarizedMollerCrossSection() :
|
|
phi0(0.)
|
|
{
|
|
SetXmax(.5);
|
|
}
|
|
G4PolarizedMollerCrossSection::~G4PolarizedMollerCrossSection() {}
|
|
void G4PolarizedMollerCrossSection::Initialize(
|
|
G4double e,
|
|
G4double gamma,
|
|
G4double /*phi*/,
|
|
const G4StokesVector & pol0,
|
|
const G4StokesVector & pol1,
|
|
G4int flag)
|
|
{
|
|
G4double re2 = classic_electr_radius * classic_electr_radius;
|
|
G4double gamma2=gamma*gamma;
|
|
G4double gmo = (gamma - 1.);
|
|
G4double gmo2 = (gamma - 1.)*(gamma - 1.);
|
|
G4double gpo = (gamma + 1.);
|
|
G4double pref = gamma2*re2/(gmo2*(gamma + 1.0));
|
|
G4double sqrttwo=std::sqrt(2.);
|
|
G4double f = (-1. + e);
|
|
G4double e2 = e*e;
|
|
G4double f2 = f*f;
|
|
// G4double w = e*(1. - e);
|
|
|
|
G4bool polarized=(!pol0.IsZero())||(!pol1.IsZero());
|
|
|
|
if (flag==0) polarized=false;
|
|
// Unpolarised part of XS
|
|
phi0 = 0.;
|
|
phi0+= gmo2/gamma2;
|
|
phi0+= ((1. - 2.*gamma)/gamma2)*(1./e + 1./(1.-e));
|
|
phi0+= 1./(e*e) + 1./((1. - e)*(1. - e));
|
|
phi0*=0.25;
|
|
// Initial state polarisarion dependence
|
|
if (polarized) {
|
|
G4double usephi=1.;
|
|
if (flag<=1) usephi=0.;
|
|
// G4cout<<"Polarized differential moller cross section"<<G4endl;
|
|
// G4cout<<"Initial state polarisation contributions"<<G4endl;
|
|
// G4cout<<"Diagonal Matrix Elements"<<G4endl;
|
|
G4double xx = (gamma - f*e*gmo*(3. + gamma))/(4.*f*e*gamma2);
|
|
G4double yy = (-1. + f*e*gmo2 + 2.*gamma)/(4.*f*e*gamma2);
|
|
G4double zz = (-(e*gmo*(3. + gamma)) + e2*gmo*(3. + gamma) +
|
|
gamma*(-1. + 2.*gamma))/(4.*f*e*gamma2);
|
|
|
|
phi0 += xx*pol0.x()*pol1.x() + yy*pol0.y()*pol1.y() + zz*pol0.z()*pol1.z();
|
|
|
|
if (usephi==1.) {
|
|
// G4cout<<"Non-diagonal Matrix Elements"<<G4endl;
|
|
G4double xy = 0.;
|
|
G4double xz = -((-1. + 2.*e)*gmo)/(2.*sqrttwo*gamma2*
|
|
std::sqrt(-((f*e)/gpo)));
|
|
G4double yx = 0.;
|
|
G4double yz = 0.;
|
|
G4double zx = -((-1. + 2.*e)*gmo)/(2.*sqrttwo*gamma2*
|
|
std::sqrt(-((f*e)/gpo)));
|
|
G4double zy = 0.;
|
|
phi0+=yx*pol0.y()*pol1.x() + xy*pol0.x()*pol1.y();
|
|
phi0+=zx*pol0.z()*pol1.x() + xz*pol0.x()*pol1.z();
|
|
phi0+=zy*pol0.z()*pol1.y() + yz*pol0.y()*pol1.z();
|
|
}
|
|
}
|
|
// Final state polarisarion dependence
|
|
phi2=G4ThreeVector();
|
|
phi3=G4ThreeVector();
|
|
|
|
if (flag>=1) {
|
|
//
|
|
// Final Electron P1
|
|
//
|
|
|
|
// initial electron K1
|
|
if (!pol0.IsZero()) {
|
|
G4double xxP1K1 = (std::sqrt(gpo/(1. + e2*gmo + gamma - 2.*e*gamma))*
|
|
(gamma - e*gpo))/(4.*e2*gamma);
|
|
G4double xyP1K1 = 0.;
|
|
G4double xzP1K1 = (-1. + 2.*e*gamma)/(2.*sqrttwo*f*gamma*
|
|
std::sqrt(e*e2*(1. + e + gamma - e*gamma)));
|
|
G4double yxP1K1 = 0.;
|
|
G4double yyP1K1 = (-gamma2 + e*(-1. + gamma*(2. + gamma)))/(4.*f*e2*gamma2);
|
|
G4double yzP1K1 = 0.;
|
|
G4double zxP1K1 = (1. + 2.*e2*gmo - 2.*e*gamma)/(2.*sqrttwo*f*e*gamma*
|
|
std::sqrt(e*(1. + e + gamma - e*gamma)));
|
|
G4double zyP1K1 = 0.;
|
|
G4double zzP1K1 = (-gamma + e*(1. - 2.*e*gmo + gamma))/(4.*f*e2*gamma*
|
|
std::sqrt(1. - (2.*e)/(f*gpo)));
|
|
phi2[0] += xxP1K1*pol0.x() + xyP1K1*pol0.y() + xzP1K1*pol0.z();
|
|
phi2[1] += yxP1K1*pol0.x() + yyP1K1*pol0.y() + yzP1K1*pol0.z();
|
|
phi2[2] += zxP1K1*pol0.x() + zyP1K1*pol0.y() + zzP1K1*pol0.z();
|
|
}
|
|
// initial electron K2
|
|
if (!pol1.IsZero()) {
|
|
G4double xxP1K2 = ((1. + e*(-3. + gamma))*std::sqrt(gpo/(1. + e2*gmo + gamma -
|
|
2.*e*gamma)))/(4.*f*e*gamma);
|
|
G4double xyP1K2 = 0.;
|
|
G4double xzP1K2 = (-2. + 2.*e + gamma)/(2.*sqrttwo*f2*gamma*
|
|
std::sqrt(e*(1. + e + gamma - e*gamma)));
|
|
G4double yxP1K2 = 0.;
|
|
G4double yyP1K2 = (1. - 2.*gamma + e*(-1. + gamma*(2. + gamma)))/(4.*f2*e*gamma2);
|
|
G4double yzP1K2 = 0.;
|
|
G4double zxP1K2 = (2.*e*(1. + e*gmo - 2.*gamma) + gamma)/(2.*sqrttwo*f2*gamma*
|
|
std::sqrt(e*(1. + e + gamma - e*gamma)));
|
|
G4double zyP1K2 = 0.;
|
|
G4double zzP1K2 = (1. - 2.*gamma + e*(-1. - 2.*e*gmo + 3.*gamma))/
|
|
(4.*f2*e*gamma*std::sqrt(1. - (2.*e)/(f*gpo)));
|
|
phi2[0] += xxP1K2*pol1.x() + xyP1K2*pol1.y() + xzP1K2*pol1.z();
|
|
phi2[1] += yxP1K2*pol1.x() + yyP1K2*pol1.y() + yzP1K2*pol1.z();
|
|
phi2[2] += zxP1K2*pol1.x() + zyP1K2*pol1.y() + zzP1K2*pol1.z();
|
|
}
|
|
//
|
|
// Final Electron P2
|
|
//
|
|
|
|
// initial electron K1
|
|
if (!pol0.IsZero()) {
|
|
|
|
|
|
G4double xxP2K1 = (-1. + e + e*gamma)/(4.*f2*gamma*
|
|
std::sqrt((e*(2. + e*gmo))/gpo));
|
|
G4double xyP2K1 = 0.;
|
|
G4double xzP2K1 = -((1. + 2.*f*gamma)*std::sqrt(f/(-2. + e - e*gamma)))/
|
|
(2.*sqrttwo*f2*e*gamma);
|
|
G4double yxP2K1 = 0.;
|
|
G4double yyP2K1 = (1. - 2.*gamma + e*(-1. + gamma*(2. + gamma)))/(4.*f2*e*gamma2);
|
|
G4double yzP2K1 = 0.;
|
|
G4double zxP2K1 = (1. + 2.*e*(-2. + e + gamma - e*gamma))/(2.*sqrttwo*f*e*
|
|
std::sqrt(-(f*(2. + e*gmo)))*gamma);
|
|
G4double zyP2K1 = 0.;
|
|
G4double zzP2K1 = (std::sqrt((e*gpo)/(2. + e*gmo))*
|
|
(-3. + e*(5. + 2.*e*gmo - 3.*gamma) + 2.*gamma))/(4.*f2*e*gamma);
|
|
|
|
phi3[0] += xxP2K1*pol0.x() + xyP2K1*pol0.y() + xzP2K1*pol0.z();
|
|
phi3[1] += yxP2K1*pol0.x() + yyP2K1*pol0.y() + yzP2K1*pol0.z();
|
|
phi3[2] += zxP2K1*pol0.x() + zyP2K1*pol0.y() + zzP2K1*pol0.z();
|
|
}
|
|
// initial electron K2
|
|
if (!pol1.IsZero()) {
|
|
|
|
G4double xxP2K2 = (-2. - e*(-3. + gamma) + gamma)/
|
|
(4.*f*e*gamma* std::sqrt((e*(2. + e*gmo))/gpo));
|
|
G4double xyP2K2 = 0.;
|
|
G4double xzP2K2 = ((-2.*e + gamma)*std::sqrt(f/(-2. + e - e*gamma)))/
|
|
(2.*sqrttwo*f*e2*gamma);
|
|
G4double yxP2K2 = 0.;
|
|
G4double yyP2K2 = (-gamma2 + e*(-1. + gamma*(2. + gamma)))/(4.*f*e2*gamma2);
|
|
G4double yzP2K2 = 0.;
|
|
G4double zxP2K2 = (gamma + 2.*e*(-1. + e - e*gamma))/
|
|
(2.*sqrttwo*e2* std::sqrt(-(f*(2. + e*gmo)))*gamma);
|
|
G4double zyP2K2 = 0.;
|
|
G4double zzP2K2 = (std::sqrt((e*gpo)/(2. + e*gmo))*
|
|
(-2. + e*(3. + 2.*e*gmo - gamma) + gamma))/(4.*f*e2*gamma);
|
|
phi3[0] += xxP2K2*pol1.x() + xyP2K2*pol1.y() + xzP2K2*pol1.z();
|
|
phi3[1] += yxP2K2*pol1.x() + yyP2K2*pol1.y() + yzP2K2*pol1.z();
|
|
phi3[2] += zxP2K2*pol1.x() + zyP2K2*pol1.y() + zzP2K2*pol1.z();
|
|
}
|
|
}
|
|
phi0 *= pref;
|
|
phi2 *= pref;
|
|
phi3 *= pref;
|
|
}
|
|
|
|
G4double G4PolarizedMollerCrossSection::XSection(const G4StokesVector & pol2,
|
|
const G4StokesVector & pol3)
|
|
{
|
|
G4double xs=0.;
|
|
xs+=phi0;
|
|
|
|
G4bool polarized=(!pol2.IsZero())||(!pol3.IsZero());
|
|
if (polarized) {
|
|
xs+=phi2*pol2 + phi3*pol3;
|
|
}
|
|
return xs;
|
|
}
|
|
|
|
G4double G4PolarizedMollerCrossSection::TotalXSection(
|
|
G4double xmin, G4double xmax, G4double gamma,
|
|
const G4StokesVector & pol0,const G4StokesVector & pol1)
|
|
{
|
|
G4double xs=0.;
|
|
|
|
G4double x=xmin;
|
|
|
|
if (xmax != 1./2.) G4cout<<" warning xmax expected to be 1/2 but is "<<xmax<< G4endl;
|
|
|
|
// re -> electron radius^2;
|
|
G4double re2 = classic_electr_radius * classic_electr_radius;
|
|
G4double gamma2=gamma*gamma;
|
|
G4double gmo2 = (gamma - 1.)*(gamma - 1.);
|
|
G4double logMEM = std::log(1./x - 1.);
|
|
G4double pref = twopi*gamma2*re2/(gmo2*(gamma + 1.0));
|
|
// unpolarise XS
|
|
G4double sigma0 = 0.;
|
|
sigma0 += (gmo2/gamma2)*(0.5 - x);
|
|
sigma0 += ((1. - 2.*gamma)/gamma2)*logMEM;
|
|
sigma0 += 1./x - 1./(1. - x);
|
|
// longitudinal part
|
|
G4double sigma2=0.;
|
|
sigma2 += ((gamma2 + 2.*gamma - 3.)/gamma2)*(0.5 - x);
|
|
sigma2 += (1./gamma - 2.)*logMEM;
|
|
// transverse part
|
|
G4double sigma3=0.;
|
|
sigma3 += (2.*(1. - gamma)/gamma2)*(0.5 - x);
|
|
sigma3 += (1. - 3.*gamma)/(2.*gamma2)*logMEM;
|
|
// total cross section
|
|
xs+=pref*(sigma0 + sigma2*pol0.z()*pol1.z() + sigma3*(pol0.x()*pol1.x()+pol0.y()*pol1.y()));
|
|
|
|
return xs;
|
|
}
|
|
|
|
|
|
G4StokesVector G4PolarizedMollerCrossSection::GetPol2()
|
|
{
|
|
// Note, mean polarization can not contain correlation
|
|
// effects.
|
|
return 1./phi0 * phi2;
|
|
}
|
|
G4StokesVector G4PolarizedMollerCrossSection::GetPol3()
|
|
{
|
|
// Note, mean polarization can not contain correlation
|
|
// effects.
|
|
return 1./phi0 * phi3;
|
|
}
|