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1 // 2 // ******************************************************************** 3 // * License and Disclaimer * 4 // * * 5 // * The Geant4 software is copyright of the Copyright Holders of * 6 // * the Geant4 Collaboration. It is provided under the terms and * 7 // * conditions of the Geant4 Software License, included in the file * 8 // * LICENSE and available at http://cern.ch/geant4/license . These * 9 // * include a list of copyright holders. * 10 // * * 11 // * Neither the authors of this software system, nor their employing * 12 // * institutes,nor the agencies providing financial support for this * 13 // * work make any representation or warranty, express or implied, * 14 // * regarding this software system or assume any liability for its * 15 // * use. Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitation of liability. * 17 // * * 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************************************** 25 // 26 // 27 //----------------------------------------------------------------------------- 28 // 29 // GEANT4 Class header file 30 // 31 // File name: G4MuonMinusBoundDecay 32 // 33 // Author: V.Ivanchenko (Vladimir.Ivantchenko@cern.ch) 34 // 35 // Creation date: 24 April 2012 on base of G4MuMinusCaptureAtRest 36 // 37 // Modified: 38 // 04/23/2013 K.Genser Fixed a constant in computation of lambda 39 // as suggested by J P Miller/Y Oksuzian; 40 // Optimized and corrected lambda calculation/lookup 41 // 04/30/2013 K.Genser Improved GetMuonCaptureRate extended data and lookup 42 // to take both Z & A into account 43 // Improved GetMuonDecayRate by using Zeff instead of Z 44 // Extracted Zeff into GetMuonZeff 45 // 10/08/2018 K.Genser Improved accuracy of the bound decay rate 46 // 47 //---------------------------------------------------------------------- 48 49 #include "G4MuonMinusBoundDecay.hh" 50 #include "Randomize.hh" 51 #include "G4RandomDirection.hh" 52 #include "G4PhysicalConstants.hh" 53 #include "G4SystemOfUnits.hh" 54 #include "G4ThreeVector.hh" 55 #include "G4NistManager.hh" 56 #include "G4NucleiProperties.hh" 57 #include "G4IonTable.hh" 58 #include "G4MuonMinus.hh" 59 #include "G4Electron.hh" 60 #include "G4NeutrinoMu.hh" 61 #include "G4AntiNeutrinoE.hh" 62 #include "G4Log.hh" 63 64 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 65 66 G4MuonMinusBoundDecay::G4MuonMinusBoundDecay() 67 : G4HadronicInteraction("muMinusBoundDeacy") 68 { 69 fMuMass = G4MuonMinus::MuonMinus()->GetPDGMass(); 70 } 71 72 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 73 74 G4MuonMinusBoundDecay::~G4MuonMinusBoundDecay() 75 {} 76 77 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 78 79 G4HadFinalState* 80 G4MuonMinusBoundDecay::ApplyYourself(const G4HadProjectile& projectile, 81 G4Nucleus& targetNucleus) 82 { 83 result.Clear(); 84 G4int Z = targetNucleus.GetZ_asInt(); 85 G4int A = targetNucleus.GetA_asInt(); 86 87 // Decide on Decay or Capture, and doit. 88 G4double lambdac = GetMuonCaptureRate(Z, A); 89 G4double lambdad = GetMuonDecayRate(Z, A, fMuMass, 90 targetNucleus.AtomicMass(A,Z)); 91 G4double lambda = lambdac + lambdad; 92 93 // === sample capture time and change time of projectile 94 // === this is needed for the case when bound decay is not happen 95 // === but muon is capruted by the nucleus with some delay 96 97 G4HadProjectile* p = const_cast<G4HadProjectile*>(&projectile); 98 G4double time = p->GetGlobalTime() - G4Log(G4UniformRand())/lambda; 99 p->SetGlobalTime(time); 100 101 //G4cout << "lambda= " << lambda << " lambdac= " << lambdac 102 //<< " t= " << time << G4endl; 103 104 // cascade 105 if( G4UniformRand()*lambda < lambdac) { 106 result.SetStatusChange(isAlive); 107 108 } else { 109 110 // Simulation on Decay of mu- on a K-shell of the muonic atom 111 result.SetStatusChange(stopAndKill); 112 G4double xmax = 1 + electron_mass_c2*electron_mass_c2/(fMuMass*fMuMass); 113 G4double xmin = 2.0*electron_mass_c2/fMuMass; 114 G4double KEnergy = projectile.GetBoundEnergy(); 115 116 /* 117 G4cout << "G4MuonMinusBoundDecay::ApplyYourself" 118 << " XMAX= " << xmax << " Ebound= " << KEnergy<< G4endl; 119 */ 120 G4double pmu = std::sqrt(KEnergy*(KEnergy + 2.0*fMuMass)); 121 G4double emu = KEnergy + fMuMass; 122 G4ThreeVector dir = G4RandomDirection(); 123 G4LorentzVector MU(pmu*dir, emu); 124 G4ThreeVector bst = MU.boostVector(); 125 126 G4double Eelect, Pelect, x, ecm; 127 G4LorentzVector EL, NN; 128 // Calculate electron energy 129 // these do/while loops are safe 130 do { 131 do { 132 x = xmin + (xmax-xmin)*G4UniformRand(); 133 } while (G4UniformRand() > (3.0 - 2.0*x)*x*x ); 134 Eelect = x*fMuMass*0.5; 135 Pelect = 0.0; 136 if(Eelect > electron_mass_c2) { 137 Pelect = std::sqrt(Eelect*Eelect - electron_mass_c2*electron_mass_c2); 138 } else { 139 Pelect = 0.0; 140 Eelect = electron_mass_c2; 141 } 142 dir = G4RandomDirection(); 143 EL = G4LorentzVector(Pelect*dir,Eelect); 144 EL.boost(bst); 145 Eelect = EL.e() - electron_mass_c2 - 2.0*KEnergy; 146 // 147 // Calculate rest frame parameters of 2 neutrinos 148 // 149 NN = MU - EL; 150 ecm = NN.mag2(); 151 // Loop checking, 06-Aug-2015, Vladimir Ivanchenko 152 } while (Eelect < 0.0 || ecm < 0.0); 153 154 // 155 // Create electron 156 // 157 G4DynamicParticle* dp = new G4DynamicParticle(G4Electron::Electron(), 158 EL.vect().unit(), 159 Eelect); 160 161 AddNewParticle(dp, time); 162 // 163 // Create Neutrinos 164 // 165 ecm = 0.5*std::sqrt(ecm); 166 bst = NN.boostVector(); 167 G4ThreeVector p1 = ecm * G4RandomDirection(); 168 G4LorentzVector N1 = G4LorentzVector(p1,ecm); 169 N1.boost(bst); 170 dp = new G4DynamicParticle(G4AntiNeutrinoE::AntiNeutrinoE(), N1); 171 AddNewParticle(dp, time); 172 NN -= N1; 173 dp = new G4DynamicParticle(G4NeutrinoMu::NeutrinoMu(), NN); 174 AddNewParticle(dp, time); 175 } 176 return &result; 177 } 178 179 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 180 181 G4double G4MuonMinusBoundDecay::GetMuonCaptureRate(G4int Z, G4int A) 182 { 183 184 // Initialize data 185 186 // Mu- capture data from 187 // T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212 188 // weighted average of the two most precise measurements 189 190 // Data for Hydrogen from Phys. Rev. Lett. 99(2007)032002 191 // Data for Helium from D.F. Measday Phys. Rep. 354(2001)243 192 193 struct capRate { 194 G4int Z; 195 G4int A; 196 G4double cRate; 197 G4double cRErr; 198 }; 199 200 // this struct has to be sorted by Z when initialized as we exit the 201 // loop once Z is above the stored value; cRErr are not used now but 202 // are included for completeness and future use 203 204 static const capRate capRates [] = { 205 { 1, 1, 0.000725, 0.000017 }, 206 { 2, 3, 0.002149, 0.00017 }, 207 { 2, 4, 0.000356, 0.000026 }, 208 { 3, 6, 0.004647, 0.00012 }, 209 { 3, 7, 0.002229, 0.00012 }, 210 { 4, 9, 0.006107, 0.00019 }, 211 { 5, 10, 0.02757 , 0.00063 }, 212 { 5, 11, 0.02188 , 0.00064 }, 213 { 6, 12, 0.03807 , 0.00031 }, 214 { 6, 13, 0.03474 , 0.00034 }, 215 { 7, 14, 0.06885 , 0.00057 }, 216 { 8, 16, 0.10242 , 0.00059 }, 217 { 8, 18, 0.0880 , 0.0015 }, 218 { 9, 19, 0.22905 , 0.00099 }, 219 { 10, 20, 0.2288 , 0.0045 }, 220 { 11, 23, 0.3773 , 0.0014 }, 221 { 12, 24, 0.4823 , 0.0013 }, 222 { 13, 27, 0.6985 , 0.0012 }, 223 { 14, 28, 0.8656 , 0.0015 }, 224 { 15, 31, 1.1681 , 0.0026 }, 225 { 16, 32, 1.3510 , 0.0029 }, 226 { 17, 35, 1.800 , 0.050 }, 227 { 17, 37, 1.250 , 0.050 }, 228 { 18, 40, 1.2727 , 0.0650 }, 229 { 19, 39, 1.8492 , 0.0050 }, 230 { 20, 40, 2.5359 , 0.0070 }, 231 { 21, 45, 2.711 , 0.025 }, 232 { 22, 48, 2.5908 , 0.0115 }, 233 { 23, 51, 3.073 , 0.022 }, 234 { 24, 50, 3.825 , 0.050 }, 235 { 24, 52, 3.465 , 0.026 }, 236 { 24, 53, 3.297 , 0.045 }, 237 { 24, 54, 3.057 , 0.042 }, 238 { 25, 55, 3.900 , 0.030 }, 239 { 26, 56, 4.408 , 0.022 }, 240 { 27, 59, 4.945 , 0.025 }, 241 { 28, 58, 6.11 , 0.10 }, 242 { 28, 60, 5.56 , 0.10 }, 243 { 28, 62, 4.72 , 0.10 }, 244 { 29, 63, 5.691 , 0.030 }, 245 { 30, 66, 5.806 , 0.031 }, 246 { 31, 69, 5.700 , 0.060 }, 247 { 32, 72, 5.561 , 0.031 }, 248 { 33, 75, 6.094 , 0.037 }, 249 { 34, 80, 5.687 , 0.030 }, 250 { 35, 79, 7.223 , 0.28 }, 251 { 35, 81, 7.547 , 0.48 }, 252 { 37, 85, 6.89 , 0.14 }, 253 { 38, 88, 6.93 , 0.12 }, 254 { 39, 89, 7.89 , 0.11 }, 255 { 40, 91, 8.620 , 0.053 }, 256 { 41, 93, 10.38 , 0.11 }, 257 { 42, 96, 9.298 , 0.063 }, 258 { 45, 103, 10.010 , 0.045 }, 259 { 46, 106, 10.000 , 0.070 }, 260 { 47, 107, 10.869 , 0.095 }, 261 { 48, 112, 10.624 , 0.094 }, 262 { 49, 115, 11.38 , 0.11 }, 263 { 50, 119, 10.60 , 0.11 }, 264 { 51, 121, 10.40 , 0.12 }, 265 { 52, 128, 9.174 , 0.074 }, 266 { 53, 127, 11.276 , 0.098 }, 267 { 55, 133, 10.98 , 0.25 }, 268 { 56, 138, 10.112 , 0.085 }, 269 { 57, 139, 10.71 , 0.10 }, 270 { 58, 140, 11.501 , 0.087 }, 271 { 59, 141, 13.45 , 0.13 }, 272 { 60, 144, 12.35 , 0.13 }, 273 { 62, 150, 12.22 , 0.17 }, 274 { 64, 157, 12.00 , 0.13 }, 275 { 65, 159, 12.73 , 0.13 }, 276 { 66, 163, 12.29 , 0.18 }, 277 { 67, 165, 12.95 , 0.13 }, 278 { 68, 167, 13.04 , 0.27 }, 279 { 72, 178, 13.03 , 0.21 }, 280 { 73, 181, 12.86 , 0.13 }, 281 { 74, 184, 12.76 , 0.16 }, 282 { 79, 197, 13.35 , 0.10 }, 283 { 80, 201, 12.74 , 0.18 }, 284 { 81, 205, 13.85 , 0.17 }, 285 { 82, 207, 13.295 , 0.071 }, 286 { 83, 209, 13.238 , 0.065 }, 287 { 90, 232, 12.555 , 0.049 }, 288 { 92, 238, 12.592 , 0.035 }, 289 { 92, 233, 14.27 , 0.15 }, 290 { 92, 235, 13.470 , 0.085 }, 291 { 92, 236, 13.90 , 0.40 }, 292 { 93, 237, 13.58 , 0.18 }, 293 { 94, 239, 13.90 , 0.20 }, 294 { 94, 242, 12.86 , 0.19 } 295 }; 296 297 G4double lambda = -1.; 298 299 size_t nCapRates = sizeof(capRates)/sizeof(capRates[0]); 300 for (size_t j = 0; j < nCapRates; ++j) { 301 if( capRates[j].Z == Z && capRates[j].A == A ) { 302 lambda = capRates[j].cRate / microsecond; 303 break; 304 } 305 // make sure the data is sorted for the next statement to work correctly 306 if (capRates[j].Z > Z) {break;} 307 } 308 309 if (lambda < 0.) { 310 311 // == Mu capture lifetime (Goulard and Primakoff PRC10(1974)2034. 312 313 static const G4double b0a = -0.03; 314 static const G4double b0b = -0.25; 315 static const G4double b0c = 3.24; 316 static const G4double t1 = 875.e-9; // -10-> -9 suggested by user 317 G4double r1 = GetMuonZeff(Z); 318 G4double zeff2 = r1 * r1; 319 320 // ^-4 -> ^-5 suggested by user 321 G4double xmu = zeff2 * 2.663e-5; 322 G4double a2ze = 0.5 *G4double(A) / G4double(Z); 323 G4double r2 = 1.0 - xmu; 324 lambda = t1 * zeff2 * zeff2 * (r2 * r2) * (1.0 - (1.0 - xmu) * .75704) * 325 (a2ze * b0a + 1.0 - (a2ze - 1.0) * b0b - 326 G4double(2 * (A - Z) + std::abs(a2ze - 1.) ) * b0c / G4double(A * 4) ); 327 328 } 329 330 return lambda; 331 332 } 333 334 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 335 336 337 G4double G4MuonMinusBoundDecay::GetMuonZeff(G4int ZZ) 338 { 339 340 // == Effective charges from 341 // "Total Nuclear Capture Rates for Negative Muons" 342 // T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212 343 // and if not present from 344 // Ford and Wills Nucl Phys 35(1962)295 or interpolated 345 346 static const G4int maxZ = 100; 347 static const G4double zeff[] = 348 { 0., 349 1.00, 1.98, 2.94, 3.89, 4.81, 5.72, 6.61, 7.49, 8.32, 9.14, 350 9.95,10.69,11.48,12.22,12.90,13.64,14.24,14.89,15.53,16.15, 351 16.77,17.38,18.04,18.49,19.06,19.59,20.13,20.66,21.12,21.61, 352 22.02,22.43,22.84,23.24,23.65,24.06,24.47,24.85,25.23,25.61, 353 25.99,26.37,26.69,27.00,27.32,27.63,27.95,28.20,28.42,28.64, 354 28.79,29.03,29.27,29.51,29.75,29.99,30.22,30.36,30.53,30.69, 355 30.85,31.01,31.18,31.34,31.48,31.62,31.76,31.90,32.05,32.19, 356 32.33,32.47,32.61,32.76,32.94,33.11,33.29,33.46,33.64,33.81, 357 34.21,34.18,34.00,34.10,34.21,34.31,34.42,34.52,34.63,34.73, 358 34.84,34.94,35.05,35.16,35.25,35.36,35.46,35.57,35.67,35.78 }; 359 360 G4int Z = std::max(std::min(ZZ, maxZ), 1); 361 return zeff[Z]; 362 } 363 364 G4double G4MuonMinusBoundDecay::GetMuonDecayRate(G4int Z) 365 { 366 G4int A = G4lrint(G4NistManager::Instance()->GetAtomicMassAmu(Z)); 367 return GetMuonDecayRate(Z, A, G4MuonMinus::MuonMinus()->GetPDGMass(), 368 G4NucleiProperties::GetNuclearMass(A,Z)); 369 } 370 371 G4double G4MuonMinusBoundDecay::GetMuonDecayRate(G4int Z, G4int A, 372 G4double muMass, 373 G4double nuclMass) 374 { 375 // Decay time correction based on 376 // H. C. Von Baeyer and D. Leiter, Phys. Rev. A 19, 1371 (1979). 377 // replacing N.C.Mukhopadhyay Phys. Rep. 30 (1977) 1. 378 // for Z < 14 inspired by report 2049 379 // Lambda(bound)/Lambda(free) = 1-(0.5+0.06*Mu_Mass/NuclMass)(Z*alpha)^2 380 381 // PDG 2012 muon lifetime value is 2.1969811(22) 1e-6s 382 // which when inverted gives 0.45517005 1e+6/s 383 384 // we pass known alraedy in ApplyYourself muon and nucleus masses to 385 // avoid refetching/recalculations 386 387 struct decRate { 388 G4int Z; 389 G4int A; 390 G4double dRate; 391 G4double dRErr; 392 }; 393 394 // this struct has to be sorted by Z when initialized as we exit the 395 // loop once Z is above the stored value 396 397 static const decRate decRates [] = { 398 { 0, 0, 0.45517005, 0.00000046 } // free muon 399 }; 400 401 G4double lambda = -1.; 402 if (Z == 0 && A == 0) {lambda = decRates[0].dRate/microsecond;} // free muon 403 404 // size_t nDecRates = sizeof(decRates)/sizeof(decRates[0]); 405 // for (size_t j = 0; j < nDecRates; ++j) { 406 // if( decRates[j].Z == Z && decRates[j].A == A ) { 407 // lambda = decRates[j].cRate / microsecond; 408 // break; 409 // } 410 // // make sure the data is sorted for the next statement to work correctly 411 // if (decRates[j].Z > Z) {break;} 412 // } 413 414 // we'll use the above code once we have the data 415 // if we had one value we would just assign it 416 // if (Z == 1 && A == 1) {lambda = decRates[1].dRate/microsecond;} 417 418 if (lambda < 0.) { 419 const G4double freeMuonDecayRate = 0.45517005 / microsecond; 420 lambda = 1.0; 421 G4double x = Z*fine_structure_const; 422 if (Z<14) { 423 // using the Phys. Rev. formula 424 lambda -= x * x * (0.5 + 0.06 * muMass/nuclMass); 425 } else { 426 // based on a fit to the data ref. in Phys.Rev. C35 (1987) 2212 427 lambda -= x * x * (0.868699 - x * 0.708985); 428 } 429 lambda *= freeMuonDecayRate; 430 } 431 return lambda; 432 } 433 434 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 435 436 void G4MuonMinusBoundDecay::ModelDescription(std::ostream& outFile) const 437 { 438 outFile << " Sample probabilities of mu- nuclear capture of decay" 439 << " from K-shell orbit.\n" 440 << " Time of projectile is changed taking into account life time" 441 << " of muonic atom.\n" 442 << " If decay is sampled primary state become stopAndKill," 443 << " else - isAlive.\n" 444 << " Mainly based on:\n" 445 << " H.C. Von Baeyer and D.Leiter, Phys. Rev. A 19, 1371 (1979)\n" 446 << " T.Suzuki, D.F.Measday, J.P.Roalsvig Phys.Rev. C35 (1987) 2212\n" 447 << " with an emprical fit to the Huff factors for Z >= 14\n" 448 << " from the above review\n"; 449 } 450 451 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... 452