source: trunk/source/processes/electromagnetic/polarisation/src/G4PolarizedAnnihilationCrossSection.cc @ 1055

Last change on this file since 1055 was 1007, checked in by garnier, 15 years ago

update to geant4.9.2
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26// -------------------------------------------------------------------
27// $Id: G4PolarizedAnnihilationCrossSection.cc,v 1.6 2007/11/01 17:32:34 schaelic Exp $
28// GEANT4 tag $Name: geant4-09-02 $
29// -------------------------------------------------------------------
30//
31// GEANT4 Class file
32//
33//
34// File name:     G4PolarizedAnnihilationCrossSection
35//
36// Author:        Andreas Schaelicke
37//
38// Creation date: 22.03.2006
39//
40// Modifications:
41//   24-03-06 included cross section as given in W.McMaster, Nuovo Cimento 7, 1960, 395
42//   27-07-06 new calculation by P.Starovoitov
43//   15.10.07 introduced a more general framework for cross sections (AS)
44//   16.10.07 some minor corrections in formula longPart
45//
46// Class Description:
47//   * calculates the differential cross section in e+e- -> gamma gamma
48//
49
50#include "G4PolarizedAnnihilationCrossSection.hh"
51
52G4PolarizedAnnihilationCrossSection::G4PolarizedAnnihilationCrossSection() :
53  polxx(0.), polyy(0.), polzz(0.), polxz(0.), polzx(0.), polxy(0.), 
54  polyx(0.), polyz(0.), polzy(0.),
55  re2(1.), diffXSFactor(1.), totalXSFactor(1.),
56  phi0(0.)
57{
58  re2 = classic_electr_radius * classic_electr_radius;
59  phi2 = G4ThreeVector(0., 0., 0.);
60  phi3 = G4ThreeVector(0., 0., 0.);
61  dice = 0.;
62  polXS= 0.;
63  unpXS = 0.;
64  ISPxx=ISPyy=ISPzz=ISPnd=0.;
65}
66
67//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
68
69G4PolarizedAnnihilationCrossSection::~G4PolarizedAnnihilationCrossSection()
70{
71}
72
73//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
74
75void G4PolarizedAnnihilationCrossSection::TotalXS()
76{
77  // total cross section is sum of
78  //  + unpol xsec  "sigma0"
79  //  + longitudinal polarised cross section "sigma_zz" times pol_3(e-)*pol_3(e+)
80  //  + transverse contribution "(sigma_xx+sigma_yy)/2" times pol_T(e-)*pol_T(e+)
81  //     (Note: if both beams are transversely polarised, i.e. pol_T(e-)!=0 and
82  //      pol_T(e+)!=0, and sigma_xx!=sigma_yy, then the diff. cross section will
83  //      exhibit a azimuthal asymmetry even if pol_T(e-)*pol_T(e+)==0)
84
85
86}
87
88//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
89
90void G4PolarizedAnnihilationCrossSection::Initialize(
91                          G4double eps,
92                          G4double gam,
93                          G4double , // phi
94                    const G4StokesVector & pol0, // positron polarization
95                    const G4StokesVector & pol1, // electron polarization
96                          G4int flag)
97{
98
99  diffXSFactor=re2/(gam - 1.);
100  DefineCoefficients(pol0,pol1);
101  // 
102  // prepare dicing
103  //
104  dice = 0.;
105  G4double symmXS = 0.125*((-1./sqr(gam + 1.))/sqr(eps) + 
106                           ((sqr(gam) + 4.*gam - 1.)/sqr(gam + 1.))/eps - 1.);
107  //
108  //
109  //
110  G4ThreeVector epsVector(1./sqr(eps), 1./eps, 1.);
111  G4ThreeVector oneEpsVector(1./sqr(1. - eps), 1./(1.-eps), 1.);
112  G4ThreeVector sumEpsVector(epsVector + oneEpsVector);
113  G4ThreeVector difEpsVector(epsVector - oneEpsVector);
114  G4ThreeVector calcVector(0., 0., 0.);
115  //
116  // temporary variables
117  //
118  G4double helpVar2 = 0., helpVar1 = 0.;
119  //
120  // unpolarised contribution
121  //
122  helpVar1 = (gam*gam + 4.*gam + 1.)/sqr(gam + 1.);
123  helpVar2 = -1./sqr(gam + 1.);
124  calcVector = G4ThreeVector(helpVar2, helpVar1, -1.);
125  unpXS = 0.125 * calcVector * sumEpsVector;
126
127  // initial particles polarised contribution
128  helpVar2 = 1./sqr(gam + 1.);
129  helpVar1 = -(gam*gam + 4.*gam + 1.)/sqr(gam + 1.);
130  calcVector = G4ThreeVector(helpVar2, helpVar1, 0.5*(gam + 3.));
131  ISPxx = 0.25*(calcVector * sumEpsVector)/(gam - 1.);
132
133  helpVar1 = 1./sqr(gam + 1.);
134  calcVector = G4ThreeVector(-helpVar1, 2.*gam*helpVar1, -1.);
135  ISPyy = 0.125 * calcVector * sumEpsVector;
136
137  helpVar1 = 1./(gam - 1.);
138  helpVar2 = 1./sqr(gam + 1.);
139  calcVector = G4ThreeVector(-(gam*gam + 1.)*helpVar2,(gam*gam*(gam + 1.) + 7.*gam + 3.)*helpVar2, -(gam + 3.));
140  ISPzz = 0.125*helpVar1*(calcVector * sumEpsVector);
141
142  helpVar1 = std::sqrt(std::fabs(eps*(1. - eps)*2.*(gam + 1.) - 1.));
143  calcVector = G4ThreeVector(-1./(gam*gam - 1.), 2./(gam - 1.), 0.);
144  ISPnd = 0.125*(calcVector * difEpsVector) * helpVar1;
145
146  polXS = 0.; 
147  polXS += ISPxx*polxx;
148  polXS += ISPyy*polyy;
149  polXS += ISPzz*polzz;
150  polXS += ISPnd*(polzx + polxz);
151  phi0 = unpXS + polXS;
152  dice = symmXS;
153  //  if(polzz != 0.) dice *= (1. + std::fabs(polzz*ISPzz/unpXS));
154  if(polzz != 0.) {
155    dice *= (1. + (polzz*ISPzz/unpXS));
156    if (dice<0.) dice=0.;
157  }
158    // prepare final state coefficients
159  if (flag==2) {
160    //
161    // circular polarisation
162    //
163    G4double circ1 = 0., circ2 = 0., circ3 = 0.;
164    helpVar1 = 8.*sqr(1. - eps)*sqr(eps)*(gam - 1.)*sqr(gam + 1.)/std::sqrt(gam*gam - 1.);
165    helpVar2 =  sqr(gam + 1.)*sqr(eps)*(-2.*eps + 3.) - (gam*gam + 3.*gam + 2.)*eps;
166    circ1 = helpVar2 + gam;
167    circ1 /= helpVar1;
168    circ2 = helpVar2 + 1.;
169    circ2 /= helpVar1;
170    helpVar1 = std::sqrt(std::fabs(eps*(1. - eps)*2.*(gam + 1.) - 1.));
171    helpVar1 /= std::sqrt(gam*gam - 1.);
172    calcVector = G4ThreeVector(1., -2.*gam, 0.);
173    circ3 = 0.125*(calcVector * sumEpsVector)/(gam + 1.);
174    circ3 *= helpVar1;
175
176    phi2.setZ( circ2*pol1.z() + circ1*pol0.z() + circ3*(pol1.x() + pol0.x()));
177    phi3.setZ(-circ1*pol1.z() - circ2*pol0.z() - circ3*(pol1.x() + pol0.x()));
178    //
179    // common to both linear polarisation
180    //
181    calcVector = G4ThreeVector(-1., 2.*gam, 0.);
182    G4double linearZero = 0.125*(calcVector * sumEpsVector)/sqr(gam + 1.);
183    //   
184    //        Linear Polarisation #1
185    //
186    helpVar1 = std::sqrt(std::fabs(2.*(gam + 1.)*(1. - eps)*eps - 1.))/((gam + 1.)*eps*(1. - eps));
187    helpVar2 = helpVar1*helpVar1;
188    //
189    // photon 1
190    //
191    G4double diagContrib = 0.125*helpVar2*(polxx + polyy - polzz);
192    G4double nonDiagContrib = 0.125*helpVar1*(-polxz/(1. - eps) + polzx/eps);
193
194    phi2.setX(linearZero + diagContrib + nonDiagContrib);
195    //
196    // photon 2
197    //
198    nonDiagContrib = 0.125*helpVar1*(polxz/eps - polzx/(1. - eps));
199
200
201    phi3.setX(linearZero + diagContrib + nonDiagContrib);
202   //   
203   //        Linear Polarisation #2
204   //
205    helpVar1 = std::sqrt(gam*gam - 1.)*(2.*(gam + 1.)*eps*(1. - eps) - 1.);
206    helpVar1 /= 8.*sqr(1. - eps)*sqr(eps)*sqr(gam + 1.)*(gam - 1.);
207    helpVar2 = std::sqrt((gam*gam - 1.)*std::fabs(2.*(gam + 1.)*eps*(1. - eps) - 1.));
208    helpVar2 /= 8.*sqr(1. - eps)*sqr(eps)*sqr(gam + 1.)*(gam - 1.);
209
210    G4double contrib21 = (-polxy + polyx)*helpVar1;
211    G4double contrib32 = -(eps*(gam + 1.) - 1.)*polyz + (eps*(gam + 1.) - gam)*polzy;
212
213             contrib32 *=helpVar2;
214    phi2.setY(contrib21 + contrib32);
215
216             contrib32 = -(eps*(gam + 1.) - gam)*polyz + (eps*(gam + 1.) - 1.)*polzy;
217             contrib32 *=helpVar2;
218    phi3.setY(contrib21 + contrib32);
219
220  }
221  phi0 *= diffXSFactor;
222  phi2 *= diffXSFactor;
223  phi3 *= diffXSFactor;
224}
225
226
227//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
228
229G4double G4PolarizedAnnihilationCrossSection::XSection(const G4StokesVector & pol2,
230                                                       const G4StokesVector & pol3)
231{
232  G4double xs=phi0+pol2*phi2+pol3*phi3;
233  return xs;
234}
235//
236// calculate total cross section
237//
238G4double G4PolarizedAnnihilationCrossSection::TotalXSection(
239  G4double ,G4double ,G4double gam,
240  const G4StokesVector & pol0,const G4StokesVector & pol1)
241{
242  totalXSFactor =pi*re2/(gam + 1.);  // atomic number ignored 
243  DefineCoefficients(pol0,pol1);
244
245  G4double xs = 0.;
246
247
248  G4double gam2 = gam*gam;
249  G4double sqrtgam1 = std::sqrt(gam2 - 1.);
250  G4double logMEM  = std::log(gam+sqrtgam1);
251  G4double unpME = (gam*(gam + 4.) + 1.)*logMEM;
252  unpME += -(gam + 3.)*sqrtgam1;
253  unpME /= 4.*(gam2 - 1.);
254//   G4double longPart = - 2.*(gam*(gam + 4.) + 1.)*logMEM;
255//   longPart += (gam*(gam + 4.) + 7.)*sqrtgam1;
256//   longPart /= 4.*sqr(gam - 1.)*(gam + 1.);
257  G4double longPart = (3+gam*(gam*(gam + 1.) + 7.))*logMEM; 
258  longPart += - (5.+ gam*(3*gam + 4.))*sqrtgam1;
259  longPart /= 4.*sqr(gam - 1.)*(gam + 1.);
260  G4double tranPart = -(5*gam + 1.)*logMEM;
261  tranPart += (gam + 5.)*sqrtgam1;
262  tranPart /= 4.*sqr(gam - 1.)*(gam + 1.);
263                                   
264  xs += unpME;
265  xs += polzz*longPart;
266  xs += (polxx + polyy)*tranPart;
267
268  return xs*totalXSFactor;
269}
270
271//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
272G4StokesVector G4PolarizedAnnihilationCrossSection::GetPol2()
273{
274  // Note, mean polarization can not contain correlation
275  // effects.
276  return  1./phi0 * phi2;
277}
278
279//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
280
281G4StokesVector G4PolarizedAnnihilationCrossSection::GetPol3()
282{
283  // Note, mean polarization can not contain correlation
284  // effects.
285  return  1./phi0 * phi3;
286}
287//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
288void G4PolarizedAnnihilationCrossSection::DefineCoefficients(const G4StokesVector & pol0,
289                                                             const G4StokesVector & pol1)
290{
291  polxx=pol0.x()*pol1.x();
292  polyy=pol0.y()*pol1.y();
293  polzz=pol0.z()*pol1.z(); 
294
295  polxz=pol0.x()*pol1.z();
296  polzx=pol0.z()*pol1.x();
297
298  polyz=pol0.y()*pol1.z();
299  polzy=pol0.z()*pol1.y();
300
301  polxy=pol0.x()*pol1.y();
302  polyx=pol0.y()*pol1.x();
303}
304
305//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
306
307G4double G4PolarizedAnnihilationCrossSection::GetXmin(G4double y)
308{
309  return 0.5*(1.-std::sqrt((y-1.)/(y+1.)));
310}
311G4double G4PolarizedAnnihilationCrossSection::GetXmax(G4double y)
312{
313  return 0.5*(1.+std::sqrt((y-1.)/(y+1.)));
314}
315
316//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
317G4double G4PolarizedAnnihilationCrossSection::DiceEpsilon()
318{
319  return dice;
320}
321//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
322G4double G4PolarizedAnnihilationCrossSection::getVar(G4int choice)
323{
324  if (choice == -1) return polXS/unpXS;
325  if (choice == 0) return unpXS;
326  if (choice == 1) return ISPxx;
327  if (choice == 2) return ISPyy;
328  if (choice == 3) return ISPzz;
329  if (choice == 4) return ISPnd;
330  return 0;
331}
332//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
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