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25 //
26 //
27 // Author: D.H. Wright
28 // Date: 2 February 2011
29 //
30 // Description: model of muon nuclear interaction in which a gamma from
31 // the virtual photon spectrum interacts in the nucleus as
32 // a real gamma at low energies and as a pi0 at high energies.
33 // Kokoulin's muon cross section and equivalent gamma spectrum
34 // are used.
35 //
36
37 #include "G4MuonVDNuclearModel.hh"
38
39 #include "Randomize.hh"
40 #include "G4Log.hh"
41 #include "G4PhysicalConstants.hh"
42 #include "G4SystemOfUnits.hh"
43 #include "G4CascadeInterface.hh"
44 #include "G4TheoFSGenerator.hh"
45 #include "G4GeneratorPrecompoundInterface.hh"
46 #include "G4PreCompoundModel.hh"
47 #include "G4LundStringFragmentation.hh"
48 #include "G4ExcitedStringDecay.hh"
49 #include "G4FTFModel.hh"
50 #include "G4HadronicInteractionRegistry.hh"
51 #include "G4KokoulinMuonNuclearXS.hh"
52 #include "G4CrossSectionDataSetRegistry.hh"
53 #include "G4ElementData.hh"
54 #include "G4Physics2DVector.hh"
55 #include "G4Pow.hh"
56 #include "G4PhysicsModelCatalog.hh"
57
58 const G4int G4MuonVDNuclearModel::zdat[] = {1, 4, 13, 29, 92};
59 const G4double G4MuonVDNuclearModel::adat[] = {1.01,9.01,26.98,63.55,238.03};
60 const G4double G4MuonVDNuclearModel::tdat[] = {
61 1.e3,2.e3,3.e3,4.e3,5.e3,6.e3,7.e3,8.e3,9.e3,
62 1.e4,2.e4,3.e4,4.e4,5.e4,6.e4,7.e4,8.e4,9.e4,
63 1.e5,2.e5,3.e5,4.e5,5.e5,6.e5,7.e5,8.e5,9.e5,
64 1.e6,2.e6,3.e6,4.e6,5.e6,6.e6,7.e6,8.e6,9.e6,
65 1.e7,2.e7,3.e7,4.e7,5.e7,6.e7,7.e7,8.e7,9.e7,
66 1.e8,2.e8,3.e8,4.e8,5.e8,6.e8,7.e8,8.e8,9.e8,
67 1.e9,2.e9,3.e9,4.e9,5.e9,6.e9,7.e9,8.e9,9.e9,
68 1.e10,2.e10,3.e10,4.e10,5.e10,6.e10,7.e10,8.e10,9.e10,1.e11};
69
70 G4ElementData* G4MuonVDNuclearModel::fElementData = nullptr;
71
72 G4MuonVDNuclearModel::G4MuonVDNuclearModel()
73 : G4HadronicInteraction("G4MuonVDNuclearModel")
74 {
75 muNucXS = (G4KokoulinMuonNuclearXS*)G4CrossSectionDataSetRegistry::Instance()->
76 GetCrossSectionDataSet(G4KokoulinMuonNuclearXS::Default_Name());
77
78 SetMinEnergy(0.0);
79 SetMaxEnergy(1*CLHEP::PeV);
80 CutFixed = 0.2*CLHEP::GeV;
81
82 if (nullptr == fElementData) {
83 fElementData = new G4ElementData(93);
84 MakeSamplingTable();
85 }
86
87 // reuse existing pre-compound model
88 G4GeneratorPrecompoundInterface* precoInterface
89 = new G4GeneratorPrecompoundInterface();
90 G4HadronicInteraction* p =
91 G4HadronicInteractionRegistry::Instance()->FindModel("PRECO");
92 G4VPreCompoundModel* pre = static_cast<G4VPreCompoundModel*>(p);
93 if(nullptr == pre) { pre = new G4PreCompoundModel(); }
94 precoInterface->SetDeExcitation(pre);
95
96 // Build FTFP model
97 ftfp = new G4TheoFSGenerator();
98 ftfp->SetTransport(precoInterface);
99 theFragmentation = new G4LundStringFragmentation();
100 theStringDecay = new G4ExcitedStringDecay(theFragmentation);
101 G4FTFModel* theStringModel = new G4FTFModel;
102 theStringModel->SetFragmentationModel(theStringDecay);
103 ftfp->SetHighEnergyGenerator(theStringModel);
104
105 // Build Bertini cascade
106 bert = new G4CascadeInterface();
107
108 // Creator model ID
109 secID = G4PhysicsModelCatalog::GetModelID( "model_" + GetModelName() );
110 }
111
112 G4MuonVDNuclearModel::~G4MuonVDNuclearModel()
113 {
114 delete theFragmentation;
115 delete theStringDecay;
116 }
117
118 G4HadFinalState*
119 G4MuonVDNuclearModel::ApplyYourself(const G4HadProjectile& aTrack,
120 G4Nucleus& targetNucleus)
121 {
122 theParticleChange.Clear();
123
124 // For very low energy, return initial track
125 G4double epmax = aTrack.GetTotalEnergy() - 0.5*proton_mass_c2;
126 if (epmax <= CutFixed) {
127 theParticleChange.SetStatusChange(isAlive);
128 theParticleChange.SetEnergyChange(aTrack.GetKineticEnergy());
129 theParticleChange.SetMomentumChange(aTrack.Get4Momentum().vect().unit());
130 return &theParticleChange;
131 }
132
133 // Produce recoil muon and transferred photon
134 G4DynamicParticle* transferredPhoton = CalculateEMVertex(aTrack, targetNucleus);
135
136 // Interact the gamma with the nucleus
137 CalculateHadronicVertex(transferredPhoton, targetNucleus);
138 return &theParticleChange;
139 }
140
141 G4DynamicParticle*
142 G4MuonVDNuclearModel::CalculateEMVertex(const G4HadProjectile& aTrack,
143 G4Nucleus& targetNucleus)
144 {
145 // Select sampling table
146 G4double KineticEnergy = aTrack.GetKineticEnergy();
147 G4double TotalEnergy = aTrack.GetTotalEnergy();
148 G4double Mass = G4MuonMinus::MuonMinus()->GetPDGMass();
149 G4Pow* g4calc = G4Pow::GetInstance();
150 G4double lnZ = g4calc->logZ(targetNucleus.GetZ_asInt());
151
152 G4double epmin = CutFixed;
153 G4double epmax = TotalEnergy - 0.5*proton_mass_c2;
154 G4double m0 = CutFixed;
155
156 G4double delmin = 1.e10;
157 G4double del;
158 G4int izz = 0;
159 G4int itt = 0;
160
161 for (G4int iz = 0; iz < nzdat; ++iz) {
162 del = std::abs(lnZ - g4calc->logZ(zdat[iz]));
163 if (del < delmin) {
164 delmin = del;
165 izz = iz;
166 }
167 }
168
169 delmin = 1.e10;
170 for (G4int it = 0; it < ntdat; ++it) {
171 del = std::abs(G4Log(KineticEnergy)-G4Log(tdat[it]) );
172 if (del < delmin) {
173 delmin = del;
174 itt = it;
175 }
176 }
177
178 // Sample the energy transfer according to the probability table
179 G4double r = G4UniformRand();
180
181 G4int iy;
182
183 G4int Z = zdat[izz];
184
185 for(iy = 0; iy<NBIN; ++iy) {
186
187 G4double pvv = fElementData->GetElement2DData(Z)->GetValue(iy, itt);
188 if(pvv >= r) { break; }
189 }
190
191 // Sampling is done uniformly in y in the bin
192 G4double pvx = fElementData->GetElement2DData(Z)->GetX(iy);
193 G4double pvx1 = fElementData->GetElement2DData(Z)->GetX(iy+1);
194 G4double y = pvx + G4UniformRand() * (pvx1 - pvx);
195
196 G4double x = G4Exp(y);
197 G4double ep = epmin*G4Exp(x*G4Log(epmax/epmin) );
198
199 // Sample scattering angle of mu, but first t should be sampled.
200 G4double yy = ep/TotalEnergy;
201 G4double tmin = Mass*Mass*yy*yy/(1.-yy);
202 G4double tmax = 2.*proton_mass_c2*ep;
203 G4double t1;
204 G4double t2;
205 if (m0 < ep) {
206 t1 = m0*m0;
207 t2 = ep*ep;
208 } else {
209 t1 = ep*ep;
210 t2 = m0*m0;
211 }
212
213 G4double w1 = tmax*t1;
214 G4double w2 = tmax+t1;
215 G4double w3 = tmax*(tmin+t1)/(tmin*w2);
216 G4double y1 = 1.-yy;
217 G4double y2 = 0.5*yy*yy;
218 G4double y3 = y1+y2;
219
220 G4double t = 0.0;
221 G4double rej = 0.0;
222
223 // Now sample t
224 G4int ntry = 0;
225 do
226 {
227 ntry += 1;
228 if (ntry > 10000) {
229 G4ExceptionDescription eda;
230 eda << " While count exceeded " << G4endl;
231 G4Exception("G4MuonVDNuclearModel::CalculateEMVertex()", "HAD_RPG_100", JustWarning, eda);
232 break;
233 }
234
235 t = w1/(w2*G4Exp(G4UniformRand()*G4Log(w3))-tmax);
236 rej = (1.-t/tmax)*(y1*(1.-tmin/t)+y2)/(y3*(1.-t/t2));
237 } while (G4UniformRand() > rej) ; /* Loop checking, 01.09.2015, D.Wright */
238
239 // compute angle from t
240 G4double sinth2 =
241 0.5*(t-tmin)/(2.*(TotalEnergy*(TotalEnergy-ep)-Mass*Mass)-tmin);
242 G4double theta = std::acos(1. - 2.*sinth2);
243
244 G4double phi = twopi*G4UniformRand();
245 G4double sinth = std::sin(theta);
246 G4double dirx = sinth*std::cos(phi);
247 G4double diry = sinth*std::sin(phi);
248 G4double dirz = std::cos(theta);
249 G4ThreeVector finalDirection(dirx,diry,dirz);
250 G4ThreeVector ParticleDirection(aTrack.Get4Momentum().vect().unit() );
251 finalDirection.rotateUz(ParticleDirection);
252
253 G4double NewKinEnergy = KineticEnergy - ep;
254 G4double finalMomentum = std::sqrt(NewKinEnergy*(NewKinEnergy+2.*Mass) );
255 G4double Ef = NewKinEnergy + Mass;
256 G4double initMomentum = std::sqrt(KineticEnergy*(TotalEnergy+Mass) );
257
258 // Set energy and direction of scattered primary in theParticleChange
259 theParticleChange.SetStatusChange(isAlive);
260 theParticleChange.SetEnergyChange(NewKinEnergy);
261 theParticleChange.SetMomentumChange(finalDirection);
262
263 // Now create the emitted gamma
264 G4LorentzVector primaryMomentum(initMomentum*ParticleDirection, TotalEnergy);
265 G4LorentzVector fsMomentum(finalMomentum*finalDirection, Ef);
266 G4LorentzVector momentumTransfer = primaryMomentum - fsMomentum;
267
268 G4DynamicParticle* gamma =
269 new G4DynamicParticle(G4Gamma::Gamma(), momentumTransfer);
270
271 return gamma;
272 }
273
274 void
275 G4MuonVDNuclearModel::CalculateHadronicVertex(G4DynamicParticle* incident,
276 G4Nucleus& target)
277 {
278 G4HadFinalState* hfs = 0;
279 G4double gammaE = incident->GetTotalEnergy();
280
281 if (gammaE < 10*GeV) {
282 G4HadProjectile projectile(*incident);
283 hfs = bert->ApplyYourself(projectile, target);
284 } else {
285 // convert incident gamma to a pi0
286 G4double piMass = G4PionZero::PionZero()->GetPDGMass();
287 G4double piKE = incident->GetTotalEnergy() - piMass;
288 G4double piMom = std::sqrt(piKE*(piKE + 2*piMass) );
289 G4ThreeVector piMomentum(incident->GetMomentumDirection() );
290 piMomentum *= piMom;
291 G4DynamicParticle theHadron(G4PionZero::PionZero(), piMomentum);
292 G4HadProjectile projectile(theHadron);
293 hfs = ftfp->ApplyYourself(projectile, target);
294 }
295
296 delete incident;
297
298 // Assign the creator model ID to the secondaries
299 for ( size_t i = 0; i < hfs->GetNumberOfSecondaries(); ++i ) {
300 hfs->GetSecondary( i )->SetCreatorModelID( secID );
301 }
302
303 // Copy secondaries from sub-model to model
304 theParticleChange.AddSecondaries(hfs);
305 }
306
307
308 void G4MuonVDNuclearModel::MakeSamplingTable()
309 {
310 G4int nbin;
311 G4double KineticEnergy;
312 G4double TotalEnergy;
313 G4double Maxep;
314 G4double CrossSection;
315
316 G4double c;
317 G4double y;
318 G4double ymin,ymax;
319 G4double dy,yy;
320 G4double dx,x;
321 G4double ep;
322
323 G4double AtomicNumber;
324 G4double AtomicWeight;
325
326 G4double mumass = G4MuonMinus::MuonMinus()->GetPDGMass();
327
328 for (G4int iz = 0; iz < nzdat; ++iz) {
329 AtomicNumber = zdat[iz];
330 AtomicWeight = adat[iz]*(g/mole);
331
332 G4Physics2DVector* pv = new G4Physics2DVector(NBIN+1,ntdat+1);
333 G4double pvv;
334
335 for (G4int it = 0; it < ntdat; ++it) {
336 KineticEnergy = tdat[it];
337 TotalEnergy = KineticEnergy + mumass;
338 Maxep = TotalEnergy - 0.5*proton_mass_c2;
339
340 CrossSection = 0.0;
341
342 // Calculate the differential cross section
343 // numerical integration in log .........
344 c = G4Log(Maxep/CutFixed);
345 ymin = -5.0;
346 ymax = 0.0;
347 dy = (ymax-ymin)/NBIN;
348
349 nbin=-1;
350
351 y = ymin - 0.5*dy;
352 yy = ymin - dy;
353 for (G4int i = 0; i < NBIN; ++i) {
354 y += dy;
355 x = G4Exp(y);
356 yy += dy;
357 dx = G4Exp(yy+dy)-G4Exp(yy);
358
359 ep = CutFixed*G4Exp(c*x);
360
361 CrossSection +=
362 ep*dx*muNucXS->ComputeDDMicroscopicCrossSection(KineticEnergy,
363 AtomicNumber,
364 AtomicWeight, ep);
365 if (nbin < NBIN) {
366 ++nbin;
367 pv->PutValue(nbin, it, CrossSection);
368 pv->PutX(nbin, y);
369 }
370 }
371 pv->PutX(NBIN, 0.);
372
373 if (CrossSection > 0.0) {
374 for (G4int ib = 0; ib <= nbin; ++ib) {
375 pvv = pv->GetValue(ib, it);
376 pvv = pvv/CrossSection;
377 pv->PutValue(ib, it, pvv);
378 }
379 }
380 } // loop on it
381
382 fElementData->InitialiseForElement(zdat[iz], pv);
383 } // loop on iz
384
385 // G4cout << " Kokoulin XS = "
386 // << muNucXS->ComputeDDMicroscopicCrossSection(1*GeV, 20.0,
387 // 40.0*g/mole, 0.3*GeV)/millibarn
388 // << G4endl;
389 }
390
391 void G4MuonVDNuclearModel::ModelDescription(std::ostream& outFile) const
392 {
393 outFile << "G4MuonVDNuclearModel handles the inelastic scattering\n"
394 << "of mu- and mu+ from nuclei using the equivalent photon\n"
395 << "approximation in which the incoming lepton generates a\n"
396 << "virtual photon at the electromagnetic vertex, and the\n"
397 << "virtual photon is converted to a real photon. At low\n"
398 << "energies, the photon interacts directly with the nucleus\n"
399 << "using the Bertini cascade. At high energies the photon\n"
400 << "is converted to a pi0 which interacts using the FTFP\n"
401 << "model. The muon-nuclear cross sections of R. Kokoulin \n"
402 << "are used to generate the virtual photon spectrum\n";
403 }
404
405