G4PolarizedMollerCrossSection.cc

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00026 // $Id: G4PolarizedMollerCrossSection.cc 69847 2013-05-16 09:36:18Z gcosmo $
00027 // -------------------------------------------------------------------
00028 //
00029 // GEANT4 Class file
00030 //
00031 //
00032 // File name:     G4PolarizedMollerCrossSection
00033 //
00034 // Author:        Andreas Schaelicke
00035 //
00036 // Creation date: 12.01.2006
00037 //
00038 // Modifications:
00039 //   16-01-06 included cross section as calculated by P.Starovoitov
00040 //
00041 // Class Description:
00042 //   * calculates the differential cross section
00043 //     incomming electron K1(along positive z direction) scatters at an electron K2 at rest
00044 //   * phi denotes the angle between the scattering plane (defined by the
00045 //     outgoing electron) and X-axis
00046 //   * all stokes vectors refer to spins in the Global System (X,Y,Z)
00047 //
00048 
00049 #include "G4PolarizedMollerCrossSection.hh"
00050 #include "G4PhysicalConstants.hh"
00051 
00052 G4PolarizedMollerCrossSection::G4PolarizedMollerCrossSection() :
00053   phi0(0.)
00054 {
00055   SetXmax(.5);
00056 }
00057 G4PolarizedMollerCrossSection::~G4PolarizedMollerCrossSection() {}
00058 void G4PolarizedMollerCrossSection::Initialize(
00059                                                G4double e,
00060                                                G4double gamma,
00061                                                G4double /*phi*/,
00062                                                const G4StokesVector & pol0,
00063                                                const G4StokesVector & pol1,
00064                                                G4int flag)
00065 {
00066   G4double re2 = classic_electr_radius * classic_electr_radius;
00067   G4double gamma2=gamma*gamma;
00068   G4double gmo = (gamma - 1.);
00069   G4double gmo2 = (gamma - 1.)*(gamma - 1.);
00070   G4double gpo = (gamma + 1.);
00071   G4double pref = gamma2*re2/(gmo2*(gamma + 1.0));
00072   G4double sqrttwo=std::sqrt(2.);
00073   G4double f = (-1. + e);
00074   G4double e2 = e*e;
00075   G4double f2 = f*f;
00076   //  G4double w = e*(1. - e);
00077 
00078   G4bool polarized=(!pol0.IsZero())||(!pol1.IsZero());
00079 
00080   if (flag==0) polarized=false;
00081   // Unpolarised part of XS
00082   phi0 = 0.;
00083   phi0+= gmo2/gamma2;
00084   phi0+= ((1. - 2.*gamma)/gamma2)*(1./e + 1./(1.-e));
00085   phi0+= 1./(e*e) + 1./((1. - e)*(1. - e));
00086   phi0*=0.25;
00087   // Initial state polarisarion dependence
00088   if (polarized) {
00089     G4double usephi=1.;
00090     if (flag<=1) usephi=0.;
00091     //    G4cout<<"Polarized differential moller cross section"<<G4endl;
00092     //    G4cout<<"Initial state polarisation contributions"<<G4endl;
00093     //    G4cout<<"Diagonal Matrix Elements"<<G4endl;
00094     G4double xx = (gamma - f*e*gmo*(3 + gamma))/(4*f*e*gamma2);
00095     G4double yy = (-1 + f*e*gmo2 + 2*gamma)/(4*f*e*gamma2);
00096     G4double zz = (-(e*gmo*(3 + gamma)) + e2*gmo*(3 + gamma) + 
00097                    gamma*(-1 + 2*gamma))/(4*f*e*gamma2);
00098 
00099     phi0 += xx*pol0.x()*pol1.x() + yy*pol0.y()*pol1.y() + zz*pol0.z()*pol1.z();
00100 
00101     if (usephi==1.) {
00102       //    G4cout<<"Non-diagonal Matrix Elements"<<G4endl;
00103       G4double xy = 0;
00104       G4double xz = -((-1 + 2*e)*gmo)/(2*sqrttwo*gamma2*
00105                                        std::sqrt(-((f*e)/gpo)));
00106       G4double yx = 0;
00107       G4double yz = 0;
00108       G4double zx = -((-1 + 2*e)*gmo)/(2*sqrttwo*gamma2*
00109                                        std::sqrt(-((f*e)/gpo)));
00110       G4double zy = 0;
00111       phi0+=yx*pol0.y()*pol1.x() + xy*pol0.x()*pol1.y();
00112       phi0+=zx*pol0.z()*pol1.x() + xz*pol0.x()*pol1.z();
00113       phi0+=zy*pol0.z()*pol1.y() + yz*pol0.y()*pol1.z();
00114     }
00115   }
00116   // Final state polarisarion dependence
00117   phi2=G4ThreeVector();
00118   phi3=G4ThreeVector();
00119 
00120   if (flag>=1) {
00121     //
00122     // Final Electron P1
00123     //
00124 
00125     // initial electron K1
00126     if (!pol0.IsZero()) {
00127       G4double xxP1K1 = (std::sqrt(gpo/(1 + e2*gmo + gamma - 2*e*gamma))*
00128                          (gamma - e*gpo))/(4*e2*gamma);
00129       G4double xyP1K1 = 0;
00130       G4double xzP1K1 = (-1 + 2*e*gamma)/(2*sqrttwo*f*gamma*
00131                                           std::sqrt(e*e2*(1 + e + gamma - e*gamma)));
00132       G4double yxP1K1 = 0;
00133       G4double yyP1K1 = (-gamma2 + e*(-1 + gamma*(2 + gamma)))/(4*f*e2*gamma2);
00134       G4double yzP1K1 = 0;
00135       G4double zxP1K1 = (1 + 2*e2*gmo - 2*e*gamma)/(2*sqrttwo*f*e*gamma*
00136                                                     std::sqrt(e*(1 + e + gamma - e*gamma)));
00137       G4double zyP1K1 = 0;
00138       G4double zzP1K1 = (-gamma + e*(1 - 2*e*gmo + gamma))/(4*f*e2*gamma*
00139                                                             std::sqrt(1 - (2*e)/(f*gpo)));
00140       phi2[0] += xxP1K1*pol0.x() + xyP1K1*pol0.y() + xzP1K1*pol0.z();
00141       phi2[1] += yxP1K1*pol0.x() + yyP1K1*pol0.y() + yzP1K1*pol0.z();
00142       phi2[2] += zxP1K1*pol0.x() + zyP1K1*pol0.y() + zzP1K1*pol0.z();
00143     }
00144     // initial electron K2
00145     if (!pol1.IsZero()) {
00146       G4double xxP1K2 = ((1 + e*(-3 + gamma))*std::sqrt(gpo/(1 + e2*gmo + gamma - 
00147                                                              2*e*gamma)))/(4*f*e*gamma);
00148       G4double xyP1K2 = 0;
00149       G4double xzP1K2 = (-2 + 2*e + gamma)/(2*sqrttwo*f2*gamma*
00150                                             std::sqrt(e*(1 + e + gamma - e*gamma)));
00151       G4double yxP1K2 = 0;
00152       G4double yyP1K2 = (1 - 2*gamma + e*(-1 + gamma*(2 + gamma)))/(4*f2*e*gamma2);
00153       G4double yzP1K2 = 0;
00154       G4double zxP1K2 = (2*e*(1 + e*gmo - 2*gamma) + gamma)/(2*sqrttwo*f2*gamma*
00155                                                              std::sqrt(e*(1 + e + gamma - e*gamma)));
00156       G4double zyP1K2 = 0;
00157       G4double zzP1K2 = (1 - 2*gamma + e*(-1 - 2*e*gmo + 3*gamma))/
00158         (4*f2*e*gamma*std::sqrt(1 - (2*e)/(f*gpo)));
00159       phi2[0] += xxP1K2*pol1.x() + xyP1K2*pol1.y() + xzP1K2*pol1.z();
00160       phi2[1] += yxP1K2*pol1.x() + yyP1K2*pol1.y() + yzP1K2*pol1.z();
00161       phi2[2] += zxP1K2*pol1.x() + zyP1K2*pol1.y() + zzP1K2*pol1.z();
00162     }
00163     //
00164     // Final Electron P2
00165     //
00166 
00167     // initial electron K1
00168     if (!pol0.IsZero()) {
00169 
00170 
00171       G4double xxP2K1 = (-1 + e + e*gamma)/(4*f2*gamma*
00172                                             std::sqrt((e*(2 + e*gmo))/gpo));
00173       G4double xyP2K1 = 0;
00174       G4double xzP2K1 = -((1 + 2*f*gamma)*std::sqrt(f/(-2 + e - e*gamma)))/
00175         (2*sqrttwo*f2*e*gamma);
00176       G4double yxP2K1 = 0;
00177       G4double yyP2K1 = (1 - 2*gamma + e*(-1 + gamma*(2 + gamma)))/(4*f2*e*gamma2);
00178       G4double yzP2K1 = 0;
00179       G4double zxP2K1 = (1 + 2*e*(-2 + e + gamma - e*gamma))/(2*sqrttwo*f*e*
00180                                                               std::sqrt(-(f*(2 + e*gmo)))*gamma);
00181       G4double zyP2K1 = 0;
00182       G4double zzP2K1 = (std::sqrt((e*gpo)/(2 + e*gmo))*
00183                          (-3 + e*(5 + 2*e*gmo - 3*gamma) + 2*gamma))/(4*f2*e*gamma);
00184 
00185       phi3[0] += xxP2K1*pol0.x() + xyP2K1*pol0.y() + xzP2K1*pol0.z();
00186       phi3[1] += yxP2K1*pol0.x() + yyP2K1*pol0.y() + yzP2K1*pol0.z();
00187       phi3[2] += zxP2K1*pol0.x() + zyP2K1*pol0.y() + zzP2K1*pol0.z();
00188     }
00189     // initial electron K2
00190     if (!pol1.IsZero()) {
00191 
00192       G4double xxP2K2 = (-2 - e*(-3 + gamma) + gamma)/
00193         (4*f*e*gamma* std::sqrt((e*(2 + e*gmo))/gpo));
00194       G4double xyP2K2 = 0;
00195       G4double xzP2K2 = ((-2*e + gamma)*std::sqrt(f/(-2 + e - e*gamma)))/
00196         (2*sqrttwo*f*e2*gamma);
00197       G4double yxP2K2 = 0;
00198       G4double yyP2K2 = (-gamma2 + e*(-1 + gamma*(2 + gamma)))/(4*f*e2*gamma2);
00199       G4double yzP2K2 = 0;
00200       G4double zxP2K2 = (gamma + 2*e*(-1 + e - e*gamma))/
00201         (2*sqrttwo*e2* std::sqrt(-(f*(2 + e*gmo)))*gamma);
00202       G4double zyP2K2 = 0;
00203       G4double zzP2K2 = (std::sqrt((e*gpo)/(2 + e*gmo))*
00204                          (-2 + e*(3 + 2*e*gmo - gamma) + gamma))/(4*f*e2*gamma);
00205       phi3[0] += xxP2K2*pol1.x() + xyP2K2*pol1.y() + xzP2K2*pol1.z();
00206       phi3[1] += yxP2K2*pol1.x() + yyP2K2*pol1.y() + yzP2K2*pol1.z();
00207       phi3[2] += zxP2K2*pol1.x() + zyP2K2*pol1.y() + zzP2K2*pol1.z();
00208     }
00209   }
00210   phi0 *= pref;
00211   phi2 *= pref;
00212   phi3 *= pref;
00213 }
00214 
00215 G4double G4PolarizedMollerCrossSection::XSection(const G4StokesVector & pol2,
00216                                                  const G4StokesVector & pol3)
00217 {
00218   G4double xs=0.;
00219   xs+=phi0;
00220 
00221   G4bool polarized=(!pol2.IsZero())||(!pol3.IsZero());
00222   if (polarized) {
00223     xs+=phi2*pol2 + phi3*pol3;
00224   }
00225   return xs;
00226 }
00227 
00228 G4double G4PolarizedMollerCrossSection::TotalXSection(
00229   G4double xmin, G4double xmax, G4double gamma,
00230   const G4StokesVector & pol0,const G4StokesVector & pol1)
00231 {
00232   G4double xs=0.;
00233 
00234   G4double x=xmin;
00235 
00236   if (xmax != 1./2.) G4cout<<" warning xmax expected to be 1/2 but is "<<xmax<< G4endl;
00237 
00238   //  re -> electron radius^2;
00239   G4double re2 = classic_electr_radius * classic_electr_radius;
00240   G4double gamma2=gamma*gamma;
00241   G4double gmo2 = (gamma - 1.)*(gamma - 1.);
00242   G4double logMEM = std::log(1./x - 1.);
00243   G4double pref = twopi*gamma2*re2/(gmo2*(gamma + 1.0));
00244   // unpolarise XS
00245   G4double sigma0 = 0.;
00246         sigma0 += (gmo2/gamma2)*(0.5 - x);
00247         sigma0 += ((1. - 2.*gamma)/gamma2)*logMEM;
00248         sigma0 += 1./x - 1./(1. - x);
00249   //    longitudinal part
00250   G4double sigma2=0.;
00251         sigma2 += ((gamma2 + 2.*gamma - 3.)/gamma2)*(0.5 - x);
00252         sigma2 += (1./gamma - 2.)*logMEM;
00253   //    transverse part
00254   G4double sigma3=0.;
00255         sigma3 += (2.*(1. - gamma)/gamma2)*(0.5 - x);
00256         sigma3 += (1. - 3.*gamma)/(2.*gamma2)*logMEM;
00257   // total cross section
00258   xs+=pref*(sigma0 + sigma2*pol0.z()*pol1.z() + sigma3*(pol0.x()*pol1.x()+pol0.y()*pol1.y()));
00259 
00260   return xs;
00261 }
00262 
00263 
00264 G4StokesVector G4PolarizedMollerCrossSection::GetPol2()
00265 {
00266   // Note, mean polarization can not contain correlation
00267   // effects.
00268   return 1./phi0 * phi2;
00269 }
00270 G4StokesVector G4PolarizedMollerCrossSection::GetPol3()
00271 {
00272   // Note, mean polarization can not contain correlation
00273   // effects.
00274   return 1./phi0 * phi3;
00275 }

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