G4MuonicAtomHelper.cc

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//
// $Id: G4MuonicAtomHelper.cc 96797 2016-05-09 10:13:42Z gcosmo $
//
//
// --------------------------------------------------------------
//  GEANT 4 class implementation file
//
//  History:
//      July 2016, K.Lynch - first implementation
//      June 2017, K.L.Genser - major revision; 
//                 also copied functions from G4MuonMinusBoundDecay & 
//                 old G4MuMinusCaptureCascade; used constexpr
// ---------------------------------------------------------------

#include "G4MuonicAtomHelper.hh"
#include "G4DecayTable.hh"
#include "G4PhaseSpaceDecayChannel.hh"
#include "G4ParticleTable.hh"
#include "G4SystemOfUnits.hh"
#include "G4PhysicalConstants.hh"
#include "Randomize.hh"

G4MuonicAtom*
G4MuonicAtomHelper::ConstructMuonicAtom(G4String name, G4int encoding, G4Ions const* baseion){

  // what should static charge be?  for G4Ions, it is Z ... should it
  // be Z-1 here (since there will always be a muon attached), or Z?
  const G4double charge = baseion->GetPDGCharge();

  static const G4String pType("MuonicAtom"); // put in an include? in an enum?

  G4bool   stable = false;
  // Get the lifetime
  G4int Z = baseion->GetAtomicNumber();
  G4int A = baseion->GetAtomicMass();
  G4double lambdac = GetMuonCaptureRate(Z, A);
  G4double lambdad = GetMuonDecayRate(Z);
  G4double lifetime = 1./(lambdac+lambdad);
  G4bool   shortlived = false;

  const G4double mass =
    (G4ParticleTable::GetParticleTable()->FindParticle("mu-"))->GetPDGMass() +
    baseion->GetPDGMass() - GetKShellEnergy(G4double(Z)); //fixme check

  G4DecayTable* decayTable = new G4DecayTable();
  auto muatom = new G4MuonicAtom(name, mass, 0.0, charge,
         baseion->GetPDGiSpin(),
         baseion->GetPDGiParity(),
         baseion->GetPDGiConjugation(),
         baseion->GetPDGiIsospin(),
         baseion->GetPDGiIsospin3(),
         baseion->GetPDGiGParity(),
         pType,
         baseion->GetLeptonNumber(),
         baseion->GetBaryonNumber(),
         encoding,
         stable,
         lifetime,
                                 decayTable,
         shortlived,
         baseion->GetParticleSubType(),
                                 baseion);

  muatom->SetPDGMagneticMoment(baseion->GetPDGMagneticMoment());

  // by this time both G4MuonicAtom and baseion should exist

  // if we choose DIO this will be the channel we'll use, so we put
  // br=1. to force it in that case

  decayTable->Insert(new G4PhaseSpaceDecayChannel(name, 1., 4,
                                                  "e-","anti_nu_e","nu_mu",
                                                  baseion->GetParticleName()));

  muatom->SetDIOLifeTime(1./lambdad);
  muatom->SetNCLifeTime(1./lambdac);
  return muatom;

}

G4double G4MuonicAtomHelper::GetMuonCaptureRate(G4int Z, G4int A)
{

  // Initialize data

  // Mu- capture data from
  // T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212
  // weighted average of the two most precise measurements

  // Data for Hydrogen from Phys. Rev. Lett. 99(2007)032002
  // Data for Helium from D.F. Measday Phys. Rep. 354(2001)243

  struct capRate {
    G4int        Z;
    G4int        A;
    G4double cRate;
    G4double cRErr;
  };

  // this struct has to be sorted by Z when initialized as we exit the
  // loop once Z is above the stored value; cRErr are not used now but
  // are included for completeness and future use

  constexpr capRate capRates [] = {
    {  1,   1,  0.000725, 0.000017 },
    {  2,   3,  0.002149, 0.00017 },
    {  2,   4,  0.000356, 0.000026 },
    {  3,   6,  0.004647, 0.00012 },
    {  3,   7,  0.002229, 0.00012 },
    {  4,   9,  0.006107, 0.00019 },
    {  5,  10,  0.02757 , 0.00063 },
    {  5,  11,  0.02188 , 0.00064 },
    {  6,  12,  0.03807 , 0.00031 },
    {  6,  13,  0.03474 , 0.00034 },
    {  7,  14,  0.06885 , 0.00057 },
    {  8,  16,  0.10242 , 0.00059 },
    {  8,  18,  0.0880  , 0.0015  },
    {  9,  19,  0.22905 , 0.00099 },
    { 10,  20,  0.2288  , 0.0045 },
    { 11,  23,  0.3773  , 0.0014 },
    { 12,  24,  0.4823  , 0.0013 },
    { 13,  27,  0.6985  , 0.0012 },
    { 14,  28,  0.8656  , 0.0015 },
    { 15,  31,  1.1681  , 0.0026 },
    { 16,  32,  1.3510  , 0.0029 },
    { 17,  35,  1.800   , 0.050 },
    { 17,  37,  1.250   , 0.050 },
    { 18,  40,  1.2727  , 0.0650 },
    { 19,  39,  1.8492  , 0.0050 },
    { 20,  40,  2.5359  , 0.0070 },
    { 21,  45,  2.711   , 0.025 },
    { 22,  48,  2.5908  , 0.0115 },
    { 23,  51,  3.073   , 0.022 },
    { 24,  50,  3.825   , 0.050 },
    { 24,  52,  3.465   , 0.026 },
    { 24,  53,  3.297   , 0.045 },
    { 24,  54,  3.057   , 0.042 },
    { 25,  55,  3.900   , 0.030 },
    { 26,  56,  4.408   , 0.022 },
    { 27,  59,  4.945   , 0.025 },
    { 28,  58,  6.11    , 0.10 },
    { 28,  60,  5.56    , 0.10 },
    { 28,  62,  4.72    , 0.10 },
    { 29,  63,  5.691   , 0.030 },
    { 30,  66,  5.806   , 0.031 },
    { 31,  69,  5.700   , 0.060 },
    { 32,  72,  5.561   , 0.031 },
    { 33,  75,  6.094   , 0.037 },
    { 34,  80,  5.687   , 0.030 },
    { 35,  79,  7.223   , 0.28 },
    { 35,  81,  7.547   , 0.48 },
    { 37,  85,  6.89    , 0.14 },
    { 38,  88,  6.93    , 0.12 },
    { 39,  89,  7.89    , 0.11 },
    { 40,  91,  8.620   , 0.053 },
    { 41,  93, 10.38    , 0.11 },
    { 42,  96,  9.298   , 0.063 },
    { 45, 103, 10.010   , 0.045 },
    { 46, 106, 10.000   , 0.070 },
    { 47, 107, 10.869   , 0.095 },
    { 48, 112, 10.624   , 0.094 },
    { 49, 115, 11.38    , 0.11 },
    { 50, 119, 10.60    , 0.11 },
    { 51, 121, 10.40    , 0.12 },
    { 52, 128,  9.174   , 0.074 },
    { 53, 127, 11.276   , 0.098 },
    { 55, 133, 10.98    , 0.25 },
    { 56, 138, 10.112   , 0.085 },
    { 57, 139, 10.71    , 0.10 },
    { 58, 140, 11.501   , 0.087 },
    { 59, 141, 13.45    , 0.13 },
    { 60, 144, 12.35    , 0.13 },
    { 62, 150, 12.22    , 0.17 },
    { 64, 157, 12.00    , 0.13 },
    { 65, 159, 12.73    , 0.13 },
    { 66, 163, 12.29    , 0.18 },
    { 67, 165, 12.95    , 0.13 },
    { 68, 167, 13.04    , 0.27 },
    { 72, 178, 13.03    , 0.21 },
    { 73, 181, 12.86    , 0.13 },
    { 74, 184, 12.76    , 0.16 },
    { 79, 197, 13.35    , 0.10 },
    { 80, 201, 12.74    , 0.18 },
    { 81, 205, 13.85    , 0.17 },
    { 82, 207, 13.295   , 0.071 },
    { 83, 209, 13.238   , 0.065 },
    { 90, 232, 12.555   , 0.049 },
    { 92, 238, 12.592   , 0.035 },
    { 92, 233, 14.27    , 0.15 },
    { 92, 235, 13.470   , 0.085 },
    { 92, 236, 13.90    , 0.40 },
    { 93, 237, 13.58    , 0.18 },
    { 94, 239, 13.90    , 0.20 },
    { 94, 242, 12.86    , 0.19 }
  };

  G4double lambda = -1.;

  size_t nCapRates = sizeof(capRates)/sizeof(capRates[0]);
  for (size_t j = 0; j < nCapRates; ++j) {
    if( capRates[j].Z == Z && capRates[j].A == A ) {
      lambda = capRates[j].cRate / microsecond;
      break;
    }
    // make sure the data is sorted for the next statement to work correctly
    if (capRates[j].Z > Z) {break;}
  }

  if (lambda < 0.) {

    // ==  Mu capture lifetime (Goulard and Primakoff PRC10(1974)2034.

    constexpr G4double b0a = -0.03;
    constexpr G4double b0b = -0.25;
    constexpr G4double b0c =  3.24;
    constexpr G4double t1 = 875.e-9; // -10-> -9  suggested by user
    G4double r1 = GetMuonZeff(Z);
    G4double zeff2 = r1 * r1;

    // ^-4 -> ^-5 suggested by user
    G4double xmu = zeff2 * 2.663e-5;
    G4double a2ze = 0.5 *G4double(A) / G4double(Z);
    G4double r2 = 1.0 - xmu;
    lambda = t1 * zeff2 * zeff2 * (r2 * r2) * (1.0 - (1.0 - xmu) * .75704) *
      (a2ze * b0a + 1.0 - (a2ze - 1.0) * b0b -
       G4double(2 * (A - Z)  + std::abs(a2ze - 1.) ) * b0c / G4double(A * 4) );

  }

  return lambda;

}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....


G4double G4MuonicAtomHelper::GetMuonZeff(G4int Z)
{

  // ==  Effective charges from
  // "Total Nuclear Capture Rates for Negative Muons"
  // T. Suzuki, D. F. Measday, J.P. Roalsvig Phys.Rev. C35 (1987) 2212
  // and if not present from
  // Ford and Wills Nucl Phys 35(1962)295 or interpolated


  constexpr size_t maxZ = 100;
  constexpr G4double zeff[maxZ+1] =
    {  0.,
       1.00, 1.98, 2.94, 3.89, 4.81, 5.72, 6.61, 7.49, 8.32, 9.14,
       9.95,10.69,11.48,12.22,12.90,13.64,14.24,14.89,15.53,16.15,
       16.77,17.38,18.04,18.49,19.06,19.59,20.13,20.66,21.12,21.61,
       22.02,22.43,22.84,23.24,23.65,24.06,24.47,24.85,25.23,25.61,
       25.99,26.37,26.69,27.00,27.32,27.63,27.95,28.20,28.42,28.64,
       28.79,29.03,29.27,29.51,29.75,29.99,30.22,30.36,30.53,30.69,
       30.85,31.01,31.18,31.34,31.48,31.62,31.76,31.90,32.05,32.19,
       32.33,32.47,32.61,32.76,32.94,33.11,33.29,33.46,33.64,33.81,
       34.21,34.18,34.00,34.10,34.21,34.31,34.42,34.52,34.63,34.73,
       34.84,34.94,35.05,35.16,35.25,35.36,35.46,35.57,35.67,35.78 };

  if (Z<0) {Z=0;}
  if (Z>G4int(maxZ)) {Z=maxZ;}

  return zeff[Z];

}


G4double G4MuonicAtomHelper::GetMuonDecayRate(G4int Z)
{
  // Decay time on K-shell
  // N.C.Mukhopadhyay Phys. Rep. 30 (1977) 1.

  // this is the "small Z" approximation formula (2.9)
  // Lambda(bound)/Lambda(free) = 1-beta(Z*alpha)**2 with beta~=2.5
  // we assume that Z is Zeff

  // PDG 2012 muon lifetime value is 2.1969811(22) 10e-6s
  // which when inverted gives       0.45517005    10e+6/s

  struct decRate {
    G4int         Z;
    G4double  dRate;
    G4double  dRErr;
  };

  // this struct has to be sorted by Z when initialized as we exit the
  // loop once Z is above the stored value

  constexpr decRate decRates [] = {
    {  1,  0.4558514, 0.0000151 }
  };

  G4double lambda = -1.;

  // size_t nDecRates = sizeof(decRates)/sizeof(decRates[0]);
  // for (size_t j = 0; j < nDecRates; ++j) {
  //   if( decRates[j].Z == Z ) {
  //     lambda = decRates[j].dRate / microsecond;
  //     break;
  //   }
  //   // make sure the data is sorted for the next statement to work
  //   if (decRates[j].Z > Z) {break;}
  // }

  // we'll use the above code once we have more data
  // since we only have one value we just assign it
  if (Z == 1) {lambda =  decRates[0].dRate/microsecond;}

  if (lambda < 0.) {
    constexpr G4double freeMuonDecayRate =  0.45517005 / microsecond;
    lambda = 1.0;
    G4double x = GetMuonZeff(Z)*fine_structure_const;
    lambda -= 2.5 * x * x;
    lambda *= freeMuonDecayRate;
  }

  return lambda;

}

// From  V.Ivanchenko's G4MuMinusCaptureCascade
G4double G4MuonicAtomHelper::GetKShellEnergy(G4double Z) {
  // Calculate the Energy of K Mesoatom Level for this Element using
  // the Energy of Hydrogen Atom taken into account finite size of the
  // nucleus (V.Ivanchenko)
  constexpr G4int ListK = 28;
  constexpr G4double ListZK[ListK] = {
      1., 2.,  4.,  6.,  8., 11., 14., 17., 18., 21., 24.,
     26., 29., 32., 38., 40., 41., 44., 49., 53., 55.,
     60., 65., 70., 75., 81., 85., 92.};
  constexpr G4double ListKEnergy[ListK] = {
     0.00275, 0.011, 0.043, 0.098, 0.173, 0.326,
     0.524, 0.765, 0.853, 1.146, 1.472,
     1.708, 2.081, 2.475, 3.323, 3.627,
     3.779, 4.237, 5.016, 5.647, 5.966,
     6.793, 7.602, 8.421, 9.249, 10.222,
    10.923,11.984};

  // Energy with finite size corrections
  G4double KEnergy = GetLinApprox(ListK,ListZK,ListKEnergy,Z);

  return KEnergy;
}

// From  V.Ivanchenko's G4MuMinusCaptureCascade
G4double G4MuonicAtomHelper::GetLinApprox(G4int N,
                                          const G4double* const X,
                                          const G4double* const Y,
                                          G4double Xuser) {
  G4double Yuser;
  if(Xuser <= X[0])        Yuser = Y[0];
  else if(Xuser >= X[N-1]) Yuser = Y[N-1];
  else {
    G4int i;
    for (i=1; i<N; i++){
      if(Xuser <= X[i]) break;
    }

    if(Xuser == X[i]) Yuser = Y[i];
    else Yuser = Y[i-1] + (Y[i] - Y[i-1])*(Xuser - X[i-1])/(X[i] - X[i-1]);
  }
  return Yuser;
}