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28 //
29 // GEANT4 Class file
30 //
31 //
32 // File name: G4eplusTo3GammaOKVIModel
33 //
34 // Authors: Andrei Alkin, Vladimir Ivanchenko, Omrame Kadri
35 //
36 // Creation date: 29.03.2018
37 //
38 // -------------------------------------------------------------------
39 //
40 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
41 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
42
43 #include "G4eplusTo3GammaOKVIModel.hh"
44 #include "G4PhysicalConstants.hh"
45 #include "G4SystemOfUnits.hh"
46 #include "G4EmParameters.hh"
47 #include "G4TrackStatus.hh"
48 #include "G4Electron.hh"
49 #include "G4Positron.hh"
50 #include "G4Gamma.hh"
51 #include "Randomize.hh"
52 #include "G4ParticleChangeForGamma.hh"
53 #include "G4Log.hh"
54 #include "G4Exp.hh"
55
56 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
57
58 using namespace std;
59
60 G4eplusTo3GammaOKVIModel::G4eplusTo3GammaOKVIModel(const G4ParticleDefinition*,
61 const G4String& nam)
62 : G4VEmModel(nam), fDelta(0.001)
63 {
64 theGamma = G4Gamma::Gamma();
65 }
66
67 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
68
69 G4eplusTo3GammaOKVIModel::~G4eplusTo3GammaOKVIModel() = default;
70
71 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
72
73 void G4eplusTo3GammaOKVIModel::Initialise(const G4ParticleDefinition*,
74 const G4DataVector&)
75 {}
76
77 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
78
79 // (A.A.) F_{ijk} calculation method
80 G4double G4eplusTo3GammaOKVIModel::ComputeF(G4double fr1, G4double fr2,
81 G4double fr3, G4double kinEnergy)
82 {
83 G4double ekin = std::max(eV,kinEnergy);
84 G4double tau = ekin/electron_mass_c2;
85 G4double gam = tau + 1.0;
86 G4double gamma2 = gam*gam;
87 G4double bg2 = tau * (tau+2.0);
88 G4double bg = sqrt(bg2);
89
90 G4double rho = (gamma2+4.*gam+1.)*G4Log(gam+bg)/(gamma2-1.)
91 - (gam+3.)/(sqrt(gam*gam - 1.)) + 1.;
92 G4double border;
93
94 if(ekin < 500*MeV) {
95 border = 1. - (electron_mass_c2)/(2*(ekin + electron_mass_c2));
96 } else {
97 border = 1. - (100*electron_mass_c2)/(2*(ekin + electron_mass_c2));
98 }
99
100 border = std::min(border, 0.9999);
101
102 if (fr1>border) { fr1 = border; }
103 if (fr2>border) { fr2 = border; }
104 if (fr3>border) { fr3 = border; }
105
106 G4double fr1s = fr1*fr1; // "s" for "squared"
107 G4double fr2s = fr2*fr2;
108 G4double fr3s = fr3*fr3;
109
110 G4double aa = (1.-fr1)*(1.-fr2);
111 G4double ab = fr3s + (fr1-fr2)*(fr1-fr2);
112 G4double add= ((1.-fr1)*(1.-fr1) + (1.-fr2)*(1.-fr2))/(fr3s*aa);
113
114 G4double fres = -rho*(1./fr1s + 1./fr2s)
115 + (ab/(2.*(fr1*fr2*aa)))*(G4Log(2.*gam*aa/(fr1*fr2)))
116 + (ab/(2.*fr1*fr2*(1-fr3)))*G4Log(2.*gam*(1.-fr3)/(fr1*fr2)) - add;
117
118 return fres;
119 }
120
121 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
122
123 // (A.A.) F_{ijk} calculation method
124 G4double G4eplusTo3GammaOKVIModel::ComputeF0(G4double fr1, G4double fr2,
125 G4double fr3)
126 {
127 G4double tau = 0.0;
128 G4double gam = tau + 1.0;
129 G4double gamma2 = gam*gam;
130 G4double bg2 = tau * (tau+2.0);
131 G4double bg = sqrt(bg2);
132
133 G4double rho = (gamma2+4.*gam+1.)*G4Log(gam+bg)/(gamma2-1.)
134 - (gam+3.)/(sqrt(gam*gam - 1.)) + 1.;
135 G4double border = 0.5;
136
137 if (fr1>border) { fr1 = border; }
138 if (fr2>border) { fr2 = border; }
139 if (fr3>border) { fr3 = border; }
140
141 G4double fr1s = fr1*fr1; // "s" for "squared"
142 G4double fr2s = fr2*fr2;
143 G4double fr3s = fr3*fr3;
144
145 G4double aa = (1.-fr1)*(1.-fr2);
146 G4double ab = fr3s + (fr1-fr2)*(fr1-fr2);
147 G4double add= ((1.-fr1)*(1.-fr1) + (1.-fr2)*(1.-fr2))/(fr3s*aa);
148
149 G4double fres = -rho*(1./fr1s + 1./fr2s)
150 + (ab/(2.*(fr1*fr2*aa)))*(G4Log(2.*gam*aa/(fr1*fr2)))
151 + (ab/(2.*fr1*fr2*(1-fr3)))*G4Log(2.*gam*(1.-fr3)/(fr1*fr2)) - add;
152
153 return fres;
154 }
155
156 //(A.A.) diff x-sections for maximum search and rejection
157 G4double G4eplusTo3GammaOKVIModel::ComputeFS(G4double fr1,
158 G4double fr2, G4double fr3, G4double kinEnergy)
159 {
160 G4double ekin = std::max(eV,kinEnergy);
161 G4double tau = ekin/electron_mass_c2;
162 G4double gam = tau + 1.0;
163
164 G4double fsum = fr1*fr1*(ComputeF(fr1,fr2,fr3,ekin) +
165 ComputeF(fr3,fr1,fr2,ekin) +
166 ComputeF(fr2,fr3,fr1,ekin));
167
168 G4double dcross = fsum/((3*fr1*fr1*(gam+1.)));
169
170 return dcross;
171 }
172
173 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
174
175 G4double
176 G4eplusTo3GammaOKVIModel::ComputeCrossSectionPerElectron(G4double kinEnergy)
177 {
178 // Calculates the cross section per electron of annihilation into 3 photons
179 // from the Heilter formula.
180
181 G4double ekin = std::max(CLHEP::eV, kinEnergy);
182 G4double tau = ekin/CLHEP::electron_mass_c2;
183 G4double gam = tau + 1.0;
184 G4double gamma2 = gam*gam;
185 G4double bg2 = tau * (tau+2.0);
186 G4double bg = sqrt(bg2);
187
188 G4double rho = (gamma2+4*gam+1.)*G4Log(gam+bg)/(gamma2-1.)
189 - (gam+3.)/(sqrt(gam*gam - 1.));
190
191 G4double cross = alpha_rcl2*(4.2 - (2.*G4Log(fDelta)+1.)*rho*rho)/(gam+1.);
192 return cross;
193 }
194
195 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
196
197 G4double G4eplusTo3GammaOKVIModel::ComputeCrossSectionPerAtom(
198 const G4ParticleDefinition*,
199 G4double kineticEnergy, G4double Z,
200 G4double, G4double, G4double)
201 {
202 G4double cross = Z*ComputeCrossSectionPerElectron(kineticEnergy);
203 return cross;
204 }
205
206 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
207
208 G4double G4eplusTo3GammaOKVIModel::CrossSectionPerVolume(
209 const G4Material* material,
210 const G4ParticleDefinition*,
211 G4double kineticEnergy,
212 G4double, G4double)
213 {
214 // Calculates the cross section per volume of annihilation into two photons
215
216 G4double eDensity = material->GetElectronDensity();
217 G4double cross = eDensity*ComputeCrossSectionPerElectron(kineticEnergy);
218 return cross;
219 }
220
221 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
222
223 // Polarisation of gamma according to M.H.L.Pryce and J.C.Ward,
224 // Nature 4065 (1947) 435.
225
226 void
227 G4eplusTo3GammaOKVIModel::SampleSecondaries(vector<G4DynamicParticle*>* vdp,
228 const G4MaterialCutsCouple*,
229 const G4DynamicParticle* dp,
230 G4double, G4double)
231 {
232 // let us perform sampling in C.M.S. reference frame of e- at rest and e+ on fly
233 G4double posiKinEnergy = dp->GetKineticEnergy();
234 G4LorentzVector lv(dp->GetMomentum(),
235 posiKinEnergy + 2*CLHEP::electron_mass_c2);
236 G4double eGammaCMS = 0.5 * lv.mag();
237
238 // the limit value fDelta is defined by a class, which call this method
239 // thickness of border defined by C.M.S. energy
240 G4double border =
241 1.0 - std::min(std::max(CLHEP::electron_mass_c2/eGammaCMS, fDelta), 0.1);
242
243 CLHEP::HepRandomEngine* rndmEngine = G4Random::getTheEngine();
244
245 G4ThreeVector posiDirection = dp->GetMomentumDirection();
246
247 // (A.A.) LIMITS FOR 1st GAMMA
248 G4double xmin = 0.01;
249 G4double xmax = 0.667; // CHANGE to 3/2
250
251 G4double d1, d0, x1, x2, dmax, x2min;
252
253 // (A.A.) sampling of x1 x2 x3 (whole cycle of rejection)
254 do {
255 x1 = 1./((1./xmin) - ((1./xmin)-(1./xmax))*rndmEngine->flat());
256 dmax = ComputeFS(eGammaCMS, x1, 1.-x1, border);
257 x2min = 1. - x1;
258 x2 = 1 - rndmEngine->flat()*(1. - x2min);
259 d1 = dmax*rndmEngine->flat();
260 d0 = ComputeFS(eGammaCMS, x1, x2, 2.-x1-x2);
261 }
262 while(d0 < d1);
263
264 G4double x3 = 2 - x1 - x2;
265 //
266 // angles between Gammas
267 //
268 G4double psi13 = 2*std::asin(std::sqrt(std::abs((x1+x3-1.)/(x1*x3))));
269 G4double psi12 = 2*std::asin(std::sqrt(std::abs((x1+x2-1.)/(x1*x2))));
270 //
271 // kinematic of the created pair
272 //
273 G4double phot1Energy = x1*eGammaCMS;
274 G4double phot2Energy = x2*eGammaCMS;
275 G4double phot3Energy = x3*eGammaCMS;
276
277 // DIRECTIONS
278
279 // The azimuthal angles of q1 and q3 with respect to some plane
280 // through the beam axis are generated at random.
281
282 G4ThreeVector phot1Direction(0, 0, 1);
283 G4ThreeVector phot2Direction(0, std::sin(psi12), std::cos(psi12));
284 G4ThreeVector phot3Direction(0, std::sin(psi13), std::cos(psi13));
285
286 G4LorentzVector lv1(phot1Energy*phot1Direction, phot1Energy);
287 G4LorentzVector lv2(phot2Energy*phot2Direction, phot2Energy);
288 G4LorentzVector lv3(phot3Energy*phot3Direction, phot3Energy);
289
290 auto boostV = lv.boostVector();
291 lv1.boost(boostV);
292 lv2.boost(boostV);
293 lv3.boost(boostV);
294
295 auto aGamma1 = new G4DynamicParticle (theGamma, lv1.vect());
296 auto aGamma2 = new G4DynamicParticle (theGamma, lv2.vect());
297 auto aGamma3 = new G4DynamicParticle (theGamma, lv3.vect());
298
299 //!!! POLARIZATION - not yet implemented
300
301 vdp->push_back(aGamma1);
302 vdp->push_back(aGamma2);
303 vdp->push_back(aGamma3);
304 }
305
306 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
307