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25 //
26 // Geant4 Class file
27 //
28 // File name: G4PolarizedAnnihilationXS
29 //
30 // Author: Andreas Schaelicke
31 //
32 // Class Description:
33 // * calculates the differential cross section in e+e- -> gamma gamma
34
35 #include "G4PolarizedAnnihilationXS.hh"
36
37 #include "G4PhysicalConstants.hh"
38
39 G4PolarizedAnnihilationXS::G4PolarizedAnnihilationXS()
40 : polxx(0.)
41 , polyy(0.)
42 , polzz(0.)
43 , polxz(0.)
44 , polzx(0.)
45 , polxy(0.)
46 , polyx(0.)
47 , polyz(0.)
48 , polzy(0.)
49 , fPhi0(0.)
50 {
51 fPhi2 = G4ThreeVector(0., 0., 0.);
52 fPhi3 = G4ThreeVector(0., 0., 0.);
53 fDice = 0.;
54 fPolXS = 0.;
55 fUnpXS = 0.;
56 ISPxx = ISPyy = ISPzz = ISPnd = 0.;
57 }
58
59 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
60 G4PolarizedAnnihilationXS::~G4PolarizedAnnihilationXS() {}
61
62 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
63 void G4PolarizedAnnihilationXS::TotalXS()
64 {
65 // total cross section is sum of
66 // + unpol xsec "sigma0"
67 // + longitudinal polarised cross section "sigma_zz" times
68 // pol_3(e-)*pol_3(e+)
69 // + transverse contribution "(sigma_xx+sigma_yy)/2" times
70 // pol_T(e-)*pol_T(e+)
71 // (Note: if both beams are transversely polarised, i.e. pol_T(e-)!=0 and
72 // pol_T(e+)!=0, and sigma_xx!=sigma_yy, then the diff. cross section
73 // will exhibit a azimuthal asymmetry even if pol_T(e-)*pol_T(e+)==0)
74 }
75
76 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
77 void G4PolarizedAnnihilationXS::Initialize(
78 G4double eps, G4double gam,
79 G4double, // phi
80 const G4StokesVector& pol0, // positron polarization
81 const G4StokesVector& pol1, // electron polarization
82 G4int flag)
83 {
84 G4double diffXSFactor = re2 / (gam - 1.);
85 DefineCoefficients(pol0, pol1);
86
87 // prepare dicing
88 fDice = 0.;
89 G4double symmXS =
90 0.125 * ((-1. / sqr(gam + 1.)) / sqr(eps) +
91 ((sqr(gam) + 4. * gam - 1.) / sqr(gam + 1.)) / eps - 1.);
92
93 G4ThreeVector epsVector(1. / sqr(eps), 1. / eps, 1.);
94 G4ThreeVector oneEpsVector(1. / sqr(1. - eps), 1. / (1. - eps), 1.);
95 G4ThreeVector sumEpsVector(epsVector + oneEpsVector);
96 G4ThreeVector difEpsVector(epsVector - oneEpsVector);
97 G4ThreeVector calcVector(0., 0., 0.);
98
99 // temporary variables
100 G4double helpVar2 = 0., helpVar1 = 0.;
101
102 // unpolarised contribution
103 helpVar1 = (gam * gam + 4. * gam + 1.) / sqr(gam + 1.);
104 helpVar2 = -1. / sqr(gam + 1.);
105 calcVector = G4ThreeVector(helpVar2, helpVar1, -1.);
106 fUnpXS = 0.125 * calcVector * sumEpsVector;
107
108 // initial particles polarised contribution
109 helpVar2 = 1. / sqr(gam + 1.);
110 helpVar1 = -(gam * gam + 4. * gam + 1.) / sqr(gam + 1.);
111 calcVector = G4ThreeVector(helpVar2, helpVar1, 0.5 * (gam + 3.));
112 ISPxx = 0.25 * (calcVector * sumEpsVector) / (gam - 1.);
113
114 helpVar1 = 1. / sqr(gam + 1.);
115 calcVector = G4ThreeVector(-helpVar1, 2. * gam * helpVar1, -1.);
116 ISPyy = 0.125 * calcVector * sumEpsVector;
117
118 helpVar1 = 1. / (gam - 1.);
119 helpVar2 = 1. / sqr(gam + 1.);
120 calcVector = G4ThreeVector(
121 -(gam * gam + 1.) * helpVar2,
122 (gam * gam * (gam + 1.) + 7. * gam + 3.) * helpVar2, -(gam + 3.));
123 ISPzz = 0.125 * helpVar1 * (calcVector * sumEpsVector);
124
125 helpVar1 = std::sqrt(std::fabs(eps * (1. - eps) * 2. * (gam + 1.) - 1.));
126 calcVector = G4ThreeVector(-1. / (gam * gam - 1.), 2. / (gam - 1.), 0.);
127 ISPnd = 0.125 * (calcVector * difEpsVector) * helpVar1;
128
129 fPolXS = ISPxx * polxx + ISPyy * polyy + ISPzz * polzz;
130 fPolXS += ISPnd * (polzx + polxz);
131 fPhi0 = fUnpXS + fPolXS;
132 fDice = symmXS;
133
134 if(polzz != 0.)
135 {
136 fDice *= (1. + (polzz * ISPzz / fUnpXS));
137 if(fDice < 0.)
138 fDice = 0.;
139 }
140 // prepare final state coefficients
141 if(flag == 2)
142 {
143 // circular polarisation
144 G4double circ1 = 0., circ2 = 0., circ3 = 0.;
145 helpVar1 = 8. * sqr(1. - eps) * sqr(eps) * (gam - 1.) * sqr(gam + 1.) /
146 std::sqrt(gam * gam - 1.);
147 helpVar2 = sqr(gam + 1.) * sqr(eps) * (-2. * eps + 3.) -
148 (gam * gam + 3. * gam + 2.) * eps;
149 circ1 = helpVar2 + gam;
150 circ1 /= helpVar1;
151 circ2 = helpVar2 + 1.;
152 circ2 /= helpVar1;
153 helpVar1 = std::sqrt(std::fabs(eps * (1. - eps) * 2. * (gam + 1.) - 1.));
154 helpVar1 /= std::sqrt(gam * gam - 1.);
155 calcVector = G4ThreeVector(1., -2. * gam, 0.);
156 circ3 = 0.125 * (calcVector * sumEpsVector) / (gam + 1.);
157 circ3 *= helpVar1;
158
159 fPhi2.setZ(circ2 * pol1.z() + circ1 * pol0.z() +
160 circ3 * (pol1.x() + pol0.x()));
161 fPhi3.setZ(-circ1 * pol1.z() - circ2 * pol0.z() -
162 circ3 * (pol1.x() + pol0.x()));
163
164 // common to both linear polarisation
165 calcVector = G4ThreeVector(-1., 2. * gam, 0.);
166 G4double linearZero = 0.125 * (calcVector * sumEpsVector) / sqr(gam + 1.);
167
168 // Linear Polarisation #1
169 helpVar1 = std::sqrt(std::fabs(2. * (gam + 1.) * (1. - eps) * eps - 1.)) /
170 ((gam + 1.) * eps * (1. - eps));
171 helpVar2 = helpVar1 * helpVar1;
172
173 // photon 1
174 G4double diagContrib = 0.125 * helpVar2 * (polxx + polyy - polzz);
175 G4double nonDiagContrib =
176 0.125 * helpVar1 * (-polxz / (1. - eps) + polzx / eps);
177
178 fPhi2.setX(linearZero + diagContrib + nonDiagContrib);
179
180 // photon 2
181 nonDiagContrib = 0.125 * helpVar1 * (polxz / eps - polzx / (1. - eps));
182
183 fPhi3.setX(linearZero + diagContrib + nonDiagContrib);
184
185 // Linear Polarisation #2
186 helpVar1 =
187 std::sqrt(gam * gam - 1.) * (2. * (gam + 1.) * eps * (1. - eps) - 1.);
188 helpVar1 /= 8. * sqr(1. - eps) * sqr(eps) * sqr(gam + 1.) * (gam - 1.);
189 helpVar2 = std::sqrt((gam * gam - 1.) *
190 std::fabs(2. * (gam + 1.) * eps * (1. - eps) - 1.));
191 helpVar2 /= 8. * sqr(1. - eps) * sqr(eps) * sqr(gam + 1.) * (gam - 1.);
192
193 G4double contrib21 = (-polxy + polyx) * helpVar1;
194 G4double contrib32 =
195 -(eps * (gam + 1.) - 1.) * polyz + (eps * (gam + 1.) - gam) * polzy;
196
197 contrib32 *= helpVar2;
198 fPhi2.setY(contrib21 + contrib32);
199
200 contrib32 =
201 -(eps * (gam + 1.) - gam) * polyz + (eps * (gam + 1.) - 1.) * polzy;
202 contrib32 *= helpVar2;
203 fPhi3.setY(contrib21 + contrib32);
204 }
205 fPhi0 *= diffXSFactor;
206 fPhi2 *= diffXSFactor;
207 fPhi3 *= diffXSFactor;
208 }
209
210 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
211 G4double G4PolarizedAnnihilationXS::XSection(const G4StokesVector& pol2,
212 const G4StokesVector& pol3)
213 {
214 G4double xs = fPhi0 + pol2 * fPhi2 + pol3 * fPhi3;
215 return xs;
216 }
217
218 // calculate total cross section
219 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
220 G4double G4PolarizedAnnihilationXS::TotalXSection(G4double, G4double,
221 G4double gam,
222 const G4StokesVector& pol0,
223 const G4StokesVector& pol1)
224 {
225 G4double totalXSFactor = pi * re2 / (gam + 1.); // atomic number ignored
226 DefineCoefficients(pol0, pol1);
227
228 G4double xs = 0.;
229
230 G4double gam2 = gam * gam;
231 G4double sqrtgam1 = std::sqrt(gam2 - 1.);
232 G4double logMEM = std::log(gam + sqrtgam1);
233 G4double unpME = (gam * (gam + 4.) + 1.) * logMEM;
234 unpME += -(gam + 3.) * sqrtgam1;
235 unpME /= 4. * (gam2 - 1.);
236 G4double longPart = (3 + gam * (gam * (gam + 1.) + 7.)) * logMEM;
237 longPart += -(5. + gam * (3 * gam + 4.)) * sqrtgam1;
238 longPart /= 4. * sqr(gam - 1.) * (gam + 1.);
239 G4double tranPart = -(5 * gam + 1.) * logMEM;
240 tranPart += (gam + 5.) * sqrtgam1;
241 tranPart /= 4. * sqr(gam - 1.) * (gam + 1.);
242
243 xs += unpME;
244 xs += polzz * longPart;
245 xs += (polxx + polyy) * tranPart;
246
247 return xs * totalXSFactor;
248 }
249
250 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
251 G4StokesVector G4PolarizedAnnihilationXS::GetPol2()
252 {
253 // Note, mean polarization can not contain correlation effects.
254 return G4StokesVector(1. / fPhi0 * fPhi2);
255 }
256
257 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
258 G4StokesVector G4PolarizedAnnihilationXS::GetPol3()
259 {
260 // Note, mean polarization can not contain correlation effects.
261 return G4StokesVector(1. / fPhi0 * fPhi3);
262 }
263 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
264 void G4PolarizedAnnihilationXS::DefineCoefficients(const G4StokesVector& pol0,
265 const G4StokesVector& pol1)
266 {
267 polxx = pol0.x() * pol1.x();
268 polyy = pol0.y() * pol1.y();
269 polzz = pol0.z() * pol1.z();
270
271 polxz = pol0.x() * pol1.z();
272 polzx = pol0.z() * pol1.x();
273
274 polyz = pol0.y() * pol1.z();
275 polzy = pol0.z() * pol1.y();
276
277 polxy = pol0.x() * pol1.y();
278 polyx = pol0.y() * pol1.x();
279 }
280
281 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
282 G4double G4PolarizedAnnihilationXS::GetXmin(G4double y)
283 {
284 return 0.5 * (1. - std::sqrt((y - 1.) / (y + 1.)));
285 }
286
287 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
288 G4double G4PolarizedAnnihilationXS::GetXmax(G4double y)
289 {
290 return 0.5 * (1. + std::sqrt((y - 1.) / (y + 1.)));
291 }
292
293 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
294 G4double G4PolarizedAnnihilationXS::DiceEpsilon() { return fDice; }
295
296 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
297 G4double G4PolarizedAnnihilationXS::getVar(G4int choice)
298 {
299 if(choice == -1)
300 return fPolXS / fUnpXS;
301 if(choice == 0)
302 return fUnpXS;
303 if(choice == 1)
304 return ISPxx;
305 if(choice == 2)
306 return ISPyy;
307 if(choice == 3)
308 return ISPzz;
309 if(choice == 4)
310 return ISPnd;
311 return 0;
312 }
313