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G4MuonMinusBoundDecay.cc
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26 // $Id: G4MuonMinusBoundDecay.cc 69960 2013-05-21 09:26:16Z gcosmo $
27 //
28 //-----------------------------------------------------------------------------
29 //
30 // GEANT4 Class header file
31 //
32 // File name: G4MuonMinusBoundDecay
33 //
34 // Author: V.Ivanchenko (Vladimir.Ivantchenko@cern.ch)
35 //
36 // Creation date: 24 April 2012 on base of G4MuMinusCaptureAtRest
37 //
38 // Modified:
39 // 04/23/2013 K.Genser Fixed a constant in computation of lambda
40 // as suggested by J P Miller/Y Oksuzian;
41 // Optimized and corrected lambda calculation/lookup
42 // 04/30/2013 K.Genser Improved GetMuonCaptureRate
43 // extended data and lookup to take both Z & A into account
44 // Improved GetMuonDecayRate by using Zeff instead of Z
45 // Extracted Zeff into GetMuonZeff
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 "G4MuonMinus.hh"
56 #include "G4Electron.hh"
57 #include "G4NeutrinoMu.hh"
58 #include "G4AntiNeutrinoE.hh"
59 
60 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
61 
62 G4MuonMinusBoundDecay::G4MuonMinusBoundDecay()
63  : G4HadronicInteraction("muMinusBoundDeacy")
64 {
65  fMuMass = G4MuonMinus::MuonMinus()->GetPDGMass();
66 }
67 
68 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
69 
70 G4MuonMinusBoundDecay::~G4MuonMinusBoundDecay()
71 {}
72 
73 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
74 
75 G4HadFinalState*
76 G4MuonMinusBoundDecay::ApplyYourself(const G4HadProjectile& projectile,
77  G4Nucleus& targetNucleus)
78 {
79  result.Clear();
80  G4int Z = targetNucleus.GetZ_asInt();
81  G4int A = targetNucleus.GetA_asInt();
82 
83  // Decide on Decay or Capture, and doit.
84  G4double lambdac = GetMuonCaptureRate(Z, A);
85  G4double lambdad = GetMuonDecayRate(Z);
86  G4double lambda = lambdac + lambdad;
87 
88  // === sample capture time and change time of projectile
89 
90  G4double time = -std::log(G4UniformRand()) / lambda;
91  G4HadProjectile* p = const_cast<G4HadProjectile*>(&projectile);
92  p->SetGlobalTime(time);
93 
94  //G4cout << "lambda= " << lambda << " lambdac= " << lambdac
95  //<< " t= " << time << G4endl;
96 
97  // cascade
98  if( G4UniformRand()*lambda < lambdac) {
99  result.SetStatusChange(isAlive);
100 
101  } else {
102 
103  // Simulation on Decay of mu- on a K-shell of the muonic atom
104  result.SetStatusChange(stopAndKill);
105  G4double xmax = 1 + electron_mass_c2*electron_mass_c2/(fMuMass*fMuMass);
106  G4double xmin = 2.0*electron_mass_c2/fMuMass;
107  G4double KEnergy = projectile.GetBoundEnergy();
108 
109  /*
110  G4cout << "G4MuonMinusBoundDecay::ApplyYourself"
111  << " XMAX= " << xmax << " Ebound= " << KEnergy<< G4endl;
112  */
113  G4double pmu = std::sqrt(KEnergy*(KEnergy + 2.0*fMuMass));
114  G4double emu = KEnergy + fMuMass;
115  G4ThreeVector dir = G4RandomDirection();
116  G4LorentzVector MU(pmu*dir, emu);
117  G4ThreeVector bst = MU.boostVector();
118 
119  G4double Eelect, Pelect, x, ecm;
120  G4LorentzVector EL, NN;
121  // Calculate electron energy
122  do {
123  do {
124  x = xmin + (xmax-xmin)*G4UniformRand();
125  } while (G4UniformRand() > (3.0 - 2.0*x)*x*x );
126  Eelect = x*fMuMass*0.5;
127  Pelect = 0.0;
128  if(Eelect > electron_mass_c2) {
129  Pelect = std::sqrt(Eelect*Eelect - electron_mass_c2*electron_mass_c2);
130  } else {
131  Pelect = 0.0;
132  Eelect = electron_mass_c2;
133  }
134  dir = G4RandomDirection();
135  EL = G4LorentzVector(Pelect*dir,Eelect);
136  EL.boost(bst);
137  Eelect = EL.e() - electron_mass_c2 - 2.0*KEnergy;
138  //
139  // Calculate rest frame parameters of 2 neutrinos
140  //
141  NN = MU - EL;
142  ecm = NN.mag2();
143  } while (Eelect < 0.0 || ecm < 0.0);
144 
145  //
146  // Create electron
147  //
148  G4DynamicParticle* dp = new G4DynamicParticle(G4Electron::Electron(),
149  EL.vect().unit(),
150  Eelect);
151 
152  AddNewParticle(dp, time);
153  //
154  // Create Neutrinos
155  //
156  ecm = 0.5*std::sqrt(ecm);
157  bst = NN.boostVector();
158  G4ThreeVector p1 = ecm * G4RandomDirection();
159  G4LorentzVector N1 = G4LorentzVector(p1,ecm);
160  N1.boost(bst);
161  dp = new G4DynamicParticle(G4AntiNeutrinoE::AntiNeutrinoE(), N1);
162  AddNewParticle(dp, time);
163  NN -= N1;
164  dp = new G4DynamicParticle(G4NeutrinoMu::NeutrinoMu(), NN);
165  AddNewParticle(dp, time);
166  }
167  return &result;
168 }
169 
170 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
171 
172 G4double G4MuonMinusBoundDecay::GetMuonCaptureRate(G4int Z, G4int A)
173 {
174 
175  // Initialize data
176 
177  // Mu- capture data from
178  // T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212
179  // weighted average of the two most precise measurements
180 
181  // Data for Hydrogen from Phys. Rev. Lett. 99(2007)032002
182  // Data for Helium from D.F. Measday Phys. Rep. 354(2001)243
183 
184  struct capRate {
185  G4int Z;
186  G4int A;
187  G4double cRate;
188  G4double cRErr;
189  };
190 
191  // this struct has to be sorted by Z when initialized as we exit the
192  // loop once Z is above the stored value; cRErr are not used now but
193  // are included for completeness and future use
194 
195  const capRate capRates [] = {
196  { 1, 1, 0.000725, 0.000017 },
197  { 2, 3, 0.002149, 0.00017 },
198  { 2, 4, 0.000356, 0.000026 },
199  { 3, 6, 0.004647, 0.00012 },
200  { 3, 7, 0.002229, 0.00012 },
201  { 4, 9, 0.006107, 0.00019 },
202  { 5, 10, 0.02757 , 0.00063 },
203  { 5, 11, 0.02188 , 0.00064 },
204  { 6, 12, 0.03807 , 0.00031 },
205  { 6, 13, 0.03474 , 0.00034 },
206  { 7, 14, 0.06885 , 0.00057 },
207  { 8, 16, 0.10242 , 0.00059 },
208  { 8, 18, 0.0880 , 0.0015 },
209  { 9, 19, 0.22905 , 0.00099 },
210  { 10, 20, 0.2288 , 0.0045 },
211  { 11, 23, 0.3773 , 0.0014 },
212  { 12, 24, 0.4823 , 0.0013 },
213  { 13, 27, 0.6985 , 0.0012 },
214  { 14, 28, 0.8656 , 0.0015 },
215  { 15, 31, 1.1681 , 0.0026 },
216  { 16, 32, 1.3510 , 0.0029 },
217  { 17, 35, 1.800 , 0.050 },
218  { 17, 37, 1.250 , 0.050 },
219  { 18, 40, 1.2727 , 0.0650 },
220  { 19, 39, 1.8492 , 0.0050 },
221  { 20, 40, 2.5359 , 0.0070 },
222  { 21, 45, 2.711 , 0.025 },
223  { 22, 48, 2.5908 , 0.0115 },
224  { 23, 51, 3.073 , 0.022 },
225  { 24, 50, 3.825 , 0.050 },
226  { 24, 52, 3.465 , 0.026 },
227  { 24, 53, 3.297 , 0.045 },
228  { 24, 54, 3.057 , 0.042 },
229  { 25, 55, 3.900 , 0.030 },
230  { 26, 56, 4.408 , 0.022 },
231  { 27, 59, 4.945 , 0.025 },
232  { 28, 58, 6.11 , 0.10 },
233  { 28, 60, 5.56 , 0.10 },
234  { 28, 62, 4.72 , 0.10 },
235  { 29, 63, 5.691 , 0.030 },
236  { 30, 66, 5.806 , 0.031 },
237  { 31, 69, 5.700 , 0.060 },
238  { 32, 72, 5.561 , 0.031 },
239  { 33, 75, 6.094 , 0.037 },
240  { 34, 80, 5.687 , 0.030 },
241  { 35, 79, 7.223 , 0.28 },
242  { 35, 81, 7.547 , 0.48 },
243  { 37, 85, 6.89 , 0.14 },
244  { 38, 88, 6.93 , 0.12 },
245  { 39, 89, 7.89 , 0.11 },
246  { 40, 91, 8.620 , 0.053 },
247  { 41, 93, 10.38 , 0.11 },
248  { 42, 96, 9.298 , 0.063 },
249  { 45, 103, 10.010 , 0.045 },
250  { 46, 106, 10.000 , 0.070 },
251  { 47, 107, 10.869 , 0.095 },
252  { 48, 112, 10.624 , 0.094 },
253  { 49, 115, 11.38 , 0.11 },
254  { 50, 119, 10.60 , 0.11 },
255  { 51, 121, 10.40 , 0.12 },
256  { 52, 128, 9.174 , 0.074 },
257  { 53, 127, 11.276 , 0.098 },
258  { 55, 133, 10.98 , 0.25 },
259  { 56, 138, 10.112 , 0.085 },
260  { 57, 139, 10.71 , 0.10 },
261  { 58, 140, 11.501 , 0.087 },
262  { 59, 141, 13.45 , 0.13 },
263  { 60, 144, 12.35 , 0.13 },
264  { 62, 150, 12.22 , 0.17 },
265  { 64, 157, 12.00 , 0.13 },
266  { 65, 159, 12.73 , 0.13 },
267  { 66, 163, 12.29 , 0.18 },
268  { 67, 165, 12.95 , 0.13 },
269  { 68, 167, 13.04 , 0.27 },
270  { 72, 178, 13.03 , 0.21 },
271  { 73, 181, 12.86 , 0.13 },
272  { 74, 184, 12.76 , 0.16 },
273  { 79, 197, 13.35 , 0.10 },
274  { 80, 201, 12.74 , 0.18 },
275  { 81, 205, 13.85 , 0.17 },
276  { 82, 207, 13.295 , 0.071 },
277  { 83, 209, 13.238 , 0.065 },
278  { 90, 232, 12.555 , 0.049 },
279  { 92, 238, 12.592 , 0.035 },
280  { 92, 233, 14.27 , 0.15 },
281  { 92, 235, 13.470 , 0.085 },
282  { 92, 236, 13.90 , 0.40 },
283  { 93, 237, 13.58 , 0.18 },
284  { 94, 239, 13.90 , 0.20 },
285  { 94, 242, 12.86 , 0.19 }
286  };
287 
288  G4double lambda = -1.;
289 
290  size_t nCapRates = sizeof(capRates)/sizeof(capRates[0]);
291  for (size_t j = 0; j < nCapRates; ++j) {
292  if( capRates[j].Z == Z && capRates[j].A == A ) {
293  lambda = capRates[j].cRate / microsecond;
294  break;
295  }
296  // make sure the data is sorted for the next statement to work correctly
297  if (capRates[j].Z > Z) {break;}
298  }
299 
300  if (lambda < 0.) {
301 
302  // == Mu capture lifetime (Goulard and Primakoff PRC10(1974)2034.
303 
304  const G4double b0a = -0.03;
305  const G4double b0b = -0.25;
306  const G4double b0c = 3.24;
307  const G4double t1 = 875.e-9; // -10-> -9 suggested by user
308  G4double r1 = GetMuonZeff(Z);
309  G4double zeff2 = r1 * r1;
310 
311  // ^-4 -> ^-5 suggested by user
312  G4double xmu = zeff2 * 2.663e-5;
313  G4double a2ze = 0.5 *G4double(A) / G4double(Z);
314  G4double r2 = 1.0 - xmu;
315  lambda = t1 * zeff2 * zeff2 * (r2 * r2) * (1.0 - (1.0 - xmu) * .75704) *
316  (a2ze * b0a + 1.0 - (a2ze - 1.0) * b0b -
317  G4double(2 * (A - Z) + std::fabs(a2ze - 1.) ) * b0c / G4double(A * 4) );
318 
319  }
320 
321  return lambda;
322 
323 }
324 
325 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
326 
327 
328 G4double G4MuonMinusBoundDecay::GetMuonZeff(G4int Z)
329 {
330 
331  // == Effective charges from
332  // "Total Nuclear Capture Rates for Negative Muons"
333  // T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212
334  // and if not present from
335  // Ford and Wills Nucl Phys 35(1962)295 or interpolated
336 
337 
338  const size_t maxZ = 100;
339  const G4double zeff[maxZ+1] =
340  { 0.,
341  1.00, 1.98, 2.94, 3.89, 4.81, 5.72, 6.61, 7.49, 8.32, 9.14,
342  9.95,10.69,11.48,12.22,12.90,13.64,14.24,14.89,15.53,16.15,
343  16.77,17.38,18.04,18.49,19.06,19.59,20.13,20.66,21.12,21.61,
344  22.02,22.43,22.84,23.24,23.65,24.06,24.47,24.85,25.23,25.61,
345  25.99,26.37,26.69,27.00,27.32,27.63,27.95,28.20,28.42,28.64,
346  28.79,29.03,29.27,29.51,29.75,29.99,30.22,30.36,30.53,30.69,
347  30.85,31.01,31.18,31.34,31.48,31.62,31.76,31.90,32.05,32.19,
348  32.33,32.47,32.61,32.76,32.94,33.11,33.29,33.46,33.64,33.81,
349  34.21,34.18,34.00,34.10,34.21,34.31,34.42,34.52,34.63,34.73,
350  34.84,34.94,35.05,35.16,35.25,35.36,35.46,35.57,35.67,35.78 };
351 
352  if (Z<0) {Z=0;}
353  if (Z>G4int(maxZ)) {Z=maxZ;}
354 
355  return zeff[Z];
356 
357 }
358 
359 
360 G4double G4MuonMinusBoundDecay::GetMuonDecayRate(G4int Z)
361 {
362  // Decay time on K-shell
363  // N.C.Mukhopadhyay Phys. Rep. 30 (1977) 1.
364 
365  // this is the "small Z" approximation formula (2.9)
366  // Lambda(bound)/Lambda(free) = 1-beta(Z*alpha)**2 with beta~=2.5
367  // we assume that Z is Zeff
368 
369  // PDG 2012 muon lifetime value is 2.1969811(22) 10e-6s
370  // which when inverted gives 0.45517005 10e+6/s
371 
372  struct decRate {
373  G4int Z;
374  G4double dRate;
375  G4double dRErr;
376  };
377 
378  // this struct has to be sorted by Z when initialized as we exit the
379  // loop once Z is above the stored value
380 
381  const decRate decRates [] = {
382  { 1, 0.4558514, 0.0000151 }
383  };
384 
385  G4double lambda = -1.;
386 
387  // size_t nDecRates = sizeof(decRates)/sizeof(decRates[0]);
388  // for (size_t j = 0; j < nDecRates; ++j) {
389  // if( decRates[j].Z == Z ) {
390  // lambda = decRates[j].dRate / microsecond;
391  // break;
392  // }
393  // // make sure the data is sorted for the next statement to work
394  // if (decRates[j].Z > Z) {break;}
395  // }
396 
397  // we'll use the above code once we have more data
398  // since we only have one value we just assign it
399  if (Z == 1) {lambda = decRates[0].dRate/microsecond;}
400 
401  if (lambda < 0.) {
402  const G4double freeMuonDecayRate = 0.45517005 / microsecond;
403  lambda = 1.0;
404  G4double x = GetMuonZeff(Z)*fine_structure_const;
405  lambda -= 2.5 * x * x;
406  lambda *= freeMuonDecayRate;
407  }
408 
409  return lambda;
410 
411 }
412 
413 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
414 
415 void G4MuonMinusBoundDecay::ModelDescription(std::ostream& outFile) const
416 {
417  outFile << "Sample probabilities of mu- nuclear capture of decay"
418  << " from K-shell orbit.\n"
419  << " Time of projectile is changed taking into account life time"
420  << " of muonic atom.\n"
421  << " If decay is sampled primary state become stopAndKill,"
422  << " else - isAlive.\n"
423  << " Based of reviews:\n"
424  << " N.C.Mukhopadhyay Phy. Rep. 30 (1977) 1.\n"
425  << " T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212\n";
426 
427 }
428 
429 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
430 
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