#include <G4MuonicAtomHelper.hh>

Static Public Member Functions
static G4MuonicAtom *	ConstructMuonicAtom (const G4String &name, G4int encoding, G4Ions const *baseion)

static G4double	GetKShellEnergy (G4double A)

static G4double	GetLinApprox (G4int N, const G4double const X, const G4double const Y, G4double Xuser)

static G4double	GetMuonCaptureRate (G4int Z, G4int A)

static G4double	GetMuonDecayRate (G4int Z)

static G4double	GetMuonZeff (G4int Z)

Detailed Description

Definition at line 38 of file G4MuonicAtomHelper.hh.

Member Function Documentation

◆ ConstructMuonicAtom()

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

static

Definition at line 41 of file G4MuonicAtomHelper.cc.

{
  // 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;
 
}

Referenced by G4IonTable::GetMuonicAtom().

◆ GetKShellEnergy()

G4double G4MuonicAtomHelper::GetKShellEnergy ( G4double A )

static

Definition at line 336 of file G4MuonicAtomHelper.cc.

{
  // 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;
}

References GetLinApprox(), and Z.

Referenced by ConstructMuonicAtom(), and G4MuonicAtomDecay::DecayIt().

◆ GetLinApprox()

G4double G4MuonicAtomHelper::GetLinApprox	(	G4int	N,
		const G4double *const	X,
		const G4double *const	Y,
		G4double	Xuser
	)

static

Definition at line 361 of file G4MuonicAtomHelper.cc.

{
  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;
}

References Y().

Referenced by GetKShellEnergy().

◆ GetMuonCaptureRate()

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

static

Definition at line 99 of file G4MuonicAtomHelper.cc.

{
 
  // 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.;
 
  std::size_t nCapRates = sizeof(capRates)/sizeof(capRates[0]);
  for (std::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;
 
}

References A, GetMuonZeff(), G4InuclParticleNames::lambda, microsecond, and Z.

Referenced by ConstructMuonicAtom().

◆ GetMuonDecayRate()

G4double G4MuonicAtomHelper::GetMuonDecayRate ( G4int Z )

static

Definition at line 282 of file G4MuonicAtomHelper.cc.

{
  // 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;
}

References source.hepunit::fine_structure_const, GetMuonZeff(), G4InuclParticleNames::lambda, microsecond, and Z.

Referenced by ConstructMuonicAtom().

◆ GetMuonZeff()

G4double G4MuonicAtomHelper::GetMuonZeff ( G4int Z )

static

Definition at line 254 of file G4MuonicAtomHelper.cc.

{
  // ==  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];
}

References maxZ, and Z.

Referenced by GetMuonCaptureRate(), and GetMuonDecayRate().

The documentation for this class was generated from the following files:

source/particles/management/include/G4MuonicAtomHelper.hh
source/particles/management/src/G4MuonicAtomHelper.cc

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ ConstructMuonicAtom()

◆ GetKShellEnergy()

◆ GetLinApprox()

◆ GetMuonCaptureRate()

◆ GetMuonDecayRate()

◆ GetMuonZeff()