#include <G4MuonMinusBoundDecay.hh>

Inheritance diagram for G4MuonMinusBoundDecay:

Public Member Functions
	G4MuonMinusBoundDecay ()

	~G4MuonMinusBoundDecay ()

G4HadFinalState *	ApplyYourself (const G4HadProjectile &aTrack, G4Nucleus &targetNucleus)

void	ModelDescription (std::ostream &outFile) const

Public Member Functions inherited from G4HadronicInteraction
	G4HadronicInteraction (const G4String &modelName="HadronicModel")

virtual	~G4HadronicInteraction ()

virtual G4HadFinalState *	ApplyYourself (const G4HadProjectile &aTrack, G4Nucleus &targetNucleus)

virtual G4double	SampleInvariantT (const G4ParticleDefinition *p, G4double plab, G4int Z, G4int A)

virtual G4bool	IsApplicable (const G4HadProjectile &aTrack, G4Nucleus &targetNucleus)

G4double	GetMinEnergy () const

G4double	GetMinEnergy (const G4Material aMaterial, const G4Element anElement) const

void	SetMinEnergy (G4double anEnergy)

void	SetMinEnergy (G4double anEnergy, const G4Element *anElement)

void	SetMinEnergy (G4double anEnergy, const G4Material *aMaterial)

G4double	GetMaxEnergy () const

G4double	GetMaxEnergy (const G4Material aMaterial, const G4Element anElement) const

void	SetMaxEnergy (const G4double anEnergy)

void	SetMaxEnergy (G4double anEnergy, const G4Element *anElement)

void	SetMaxEnergy (G4double anEnergy, const G4Material *aMaterial)

G4int	GetVerboseLevel () const

void	SetVerboseLevel (G4int value)

const G4String &	GetModelName () const

void	DeActivateFor (const G4Material *aMaterial)

void	ActivateFor (const G4Material *aMaterial)

void	DeActivateFor (const G4Element *anElement)

void	ActivateFor (const G4Element *anElement)

G4bool	IsBlocked (const G4Material *aMaterial) const

G4bool	IsBlocked (const G4Element *anElement) const

void	SetRecoilEnergyThreshold (G4double val)

G4double	GetRecoilEnergyThreshold () const

virtual const std::pair< G4double, G4double >	GetFatalEnergyCheckLevels () const

virtual std::pair< G4double, G4double >	GetEnergyMomentumCheckLevels () const

void	SetEnergyMomentumCheckLevels (G4double relativeLevel, G4double absoluteLevel)

virtual void	ModelDescription (std::ostream &outFile) const

virtual void	BuildPhysicsTable (const G4ParticleDefinition &)

virtual void	InitialiseModel ()

	G4HadronicInteraction (const G4HadronicInteraction &right)=delete

const G4HadronicInteraction &	operator= (const G4HadronicInteraction &right)=delete

G4bool	operator== (const G4HadronicInteraction &right) const =delete

G4bool	operator!= (const G4HadronicInteraction &right) const =delete

Static Public Member Functions
static G4double	GetMuonCaptureRate (G4int Z, G4int A)

static G4double	GetMuonDecayRate (G4int Z, G4int A, G4double muMass, G4double nuclMass)

static G4double	GetMuonDecayRate (G4int Z)

static G4double	GetMuonZeff (G4int Z)

Additional Inherited Members
Protected Member Functions inherited from G4HadronicInteraction
void	SetModelName (const G4String &nam)

G4bool	IsBlocked () const

void	Block ()

Protected Attributes inherited from G4HadronicInteraction
G4HadFinalState	theParticleChange

G4int	verboseLevel

G4double	theMinEnergy

G4double	theMaxEnergy

G4bool	isBlocked

Detailed Description

Definition at line 71 of file G4MuonMinusBoundDecay.hh.

Constructor & Destructor Documentation

◆ G4MuonMinusBoundDecay()

G4MuonMinusBoundDecay::G4MuonMinusBoundDecay ( )

Definition at line 66 of file G4MuonMinusBoundDecay.cc.

  : G4HadronicInteraction("muMinusBoundDeacy")
{
  fMuMass = G4MuonMinus::MuonMinus()->GetPDGMass(); 
}

◆ ~G4MuonMinusBoundDecay()

G4MuonMinusBoundDecay::~G4MuonMinusBoundDecay ( )

Definition at line 74 of file G4MuonMinusBoundDecay.cc.

75{}

Member Function Documentation

◆ ApplyYourself()

G4HadFinalState * G4MuonMinusBoundDecay::ApplyYourself	(	const G4HadProjectile &	aTrack,
		G4Nucleus &	targetNucleus
	)

virtual

Reimplemented from G4HadronicInteraction.

Definition at line 80 of file G4MuonMinusBoundDecay.cc.

{
  result.Clear();
  G4int Z = targetNucleus.GetZ_asInt(); 
  G4int A = targetNucleus.GetA_asInt(); 
 
  // Decide on Decay or Capture, and doit.
  G4double lambdac  = GetMuonCaptureRate(Z, A);
  G4double lambdad  = GetMuonDecayRate(Z, A, fMuMass, 
                                       targetNucleus.AtomicMass(A,Z));
  G4double lambda   = lambdac + lambdad;
 
  // ===  sample capture  time and change time of projectile
  // ===  this is needed for the case when bound decay is not happen
  // ===  but muon is capruted by the nucleus with some delay
 
  G4HadProjectile* p = const_cast<G4HadProjectile*>(&projectile);
  G4double time = p->GetGlobalTime() - G4Log(G4UniformRand())/lambda;
  p->SetGlobalTime(time);
    
  //G4cout << "lambda= " << lambda << " lambdac= " << lambdac 
  //<< " t= " << time << G4endl;
 
  // cascade
  if( G4UniformRand()*lambda < lambdac) {
    result.SetStatusChange(isAlive);
 
  } else {
 
    // Simulation on Decay of mu- on a K-shell of the muonic atom
    result.SetStatusChange(stopAndKill);
    G4double xmax = 1 + electron_mass_c2*electron_mass_c2/(fMuMass*fMuMass);
    G4double xmin = 2.0*electron_mass_c2/fMuMass;
    G4double KEnergy = projectile.GetBoundEnergy();
 
    /*
      G4cout << "G4MuonMinusBoundDecay::ApplyYourself" 
      << " XMAX= " << xmax << " Ebound= " << KEnergy<< G4endl;
    */
    G4double pmu = std::sqrt(KEnergy*(KEnergy + 2.0*fMuMass));
    G4double emu = KEnergy + fMuMass;
    G4ThreeVector dir = G4RandomDirection();
    G4LorentzVector MU(pmu*dir, emu);
    G4ThreeVector bst = MU.boostVector();
 
    G4double Eelect, Pelect, x, ecm;
    G4LorentzVector EL, NN;
    // Calculate electron energy
    // these do/while loops are safe
    do {
      do {
        x = xmin + (xmax-xmin)*G4UniformRand();
      } while (G4UniformRand() > (3.0 - 2.0*x)*x*x );
      Eelect = x*fMuMass*0.5;
      Pelect = 0.0;
      if(Eelect > electron_mass_c2) { 
        Pelect = std::sqrt(Eelect*Eelect - electron_mass_c2*electron_mass_c2);
      } else {
        Pelect = 0.0;
        Eelect = electron_mass_c2;
      }
      dir = G4RandomDirection();
      EL = G4LorentzVector(Pelect*dir,Eelect);
      EL.boost(bst);
      Eelect = EL.e() - electron_mass_c2 - 2.0*KEnergy;
      //
      // Calculate rest frame parameters of 2 neutrinos
      //
      NN = MU - EL;
      ecm = NN.mag2();
      // Loop checking, 06-Aug-2015, Vladimir Ivanchenko
    } while (Eelect < 0.0 || ecm < 0.0);
 
    //
    // Create electron
    //
    G4DynamicParticle* dp = new G4DynamicParticle(G4Electron::Electron(),
                                                  EL.vect().unit(),
                                                  Eelect);
 
    AddNewParticle(dp, time);
    //
    // Create Neutrinos
    //
    ecm = 0.5*std::sqrt(ecm);
    bst = NN.boostVector();
    G4ThreeVector p1 = ecm * G4RandomDirection();
    G4LorentzVector N1 = G4LorentzVector(p1,ecm);
    N1.boost(bst);
    dp = new G4DynamicParticle(G4AntiNeutrinoE::AntiNeutrinoE(), N1);
    AddNewParticle(dp, time);
    NN -= N1;
    dp = new G4DynamicParticle(G4NeutrinoMu::NeutrinoMu(), NN);
    AddNewParticle(dp, time);
  }
  return &result;
}

◆ GetMuonCaptureRate()

G4double G4MuonMinusBoundDecay::GetMuonCaptureRate	(	G4int	Z,
		G4int	A
	)

static

Definition at line 181 of file G4MuonMinusBoundDecay.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
 
  static const 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.
 
    static const G4double b0a = -0.03;
    static const G4double b0b = -0.25;
    static const G4double b0c =  3.24;
    static const 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;
 
}

Referenced by ApplyYourself().

◆ GetMuonDecayRate() [1/2]

G4double G4MuonMinusBoundDecay::GetMuonDecayRate ( G4int Z )

static

Definition at line 364 of file G4MuonMinusBoundDecay.cc.

{
  G4int A = G4lrint(G4NistManager::Instance()->GetAtomicMassAmu(Z));
  return GetMuonDecayRate(Z, A, G4MuonMinus::MuonMinus()->GetPDGMass(),
                          G4NucleiProperties::GetNuclearMass(A,Z));
}

◆ GetMuonDecayRate() [2/2]

G4double G4MuonMinusBoundDecay::GetMuonDecayRate	(	G4int	Z,
		G4int	A,
		G4double	muMass,
		G4double	nuclMass
	)

static

Definition at line 371 of file G4MuonMinusBoundDecay.cc.

{
  // Decay time correction based on 
  // H. C. Von Baeyer and D. Leiter, Phys. Rev. A 19, 1371 (1979).
  // replacing N.C.Mukhopadhyay Phys. Rep. 30 (1977) 1.
  // for Z < 14 inspired by report 2049
  // Lambda(bound)/Lambda(free) = 1-(0.5+0.06*Mu_Mass/NuclMass)(Z*alpha)^2
 
  // PDG 2012 muon lifetime value is 2.1969811(22) 1e-6s
  // which when inverted gives       0.45517005    1e+6/s
 
  // we pass known alraedy in ApplyYourself muon and nucleus masses to
  // avoid refetching/recalculations
 
  struct decRate {
    G4int         Z;
    G4int         A;
    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
 
  static const decRate decRates [] = {
    {  0,  0, 0.45517005, 0.00000046 } // free muon
  };
 
  G4double lambda = -1.;
  if (Z == 0 && A == 0) {lambda =  decRates[0].dRate/microsecond;}  // free muon
 
  // size_t nDecRates = sizeof(decRates)/sizeof(decRates[0]);
  // for (size_t j = 0; j < nDecRates; ++j) {
  //   if( decRates[j].Z == Z && decRates[j].A == A ) {
  //     lambda = decRates[j].cRate / microsecond;
  //     break;
  //   }
  //   // make sure the data is sorted for the next statement to work correctly
  //   if (decRates[j].Z > Z) {break;}
  // }
 
  // we'll use the above code once we have the data
  // if we had one value we would just assign it
  // if (Z == 1 && A == 1) {lambda =  decRates[1].dRate/microsecond;}
 
  if (lambda < 0.) {
    const G4double freeMuonDecayRate =  0.45517005 / microsecond;
    lambda = 1.0;
    G4double x = Z*fine_structure_const;
    if (Z<14) {
      // using the Phys. Rev. formula
      lambda -= x * x * (0.5 + 0.06 * muMass/nuclMass);
    } else {
      // based on a fit to the data ref. in Phys.Rev. C35 (1987) 2212
      lambda -=  x * x * (0.868699 - x * 0.708985);
    }
    lambda *= freeMuonDecayRate;
  }
  return lambda;
}

Referenced by ApplyYourself(), and GetMuonDecayRate().

◆ GetMuonZeff()

G4double G4MuonMinusBoundDecay::GetMuonZeff ( G4int Z )

static

Definition at line 337 of file G4MuonMinusBoundDecay.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
 
  static const G4int maxZ = 100;
  static const G4double zeff[] = 
    {  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 };
 
  G4int Z = std::max(std::min(ZZ, maxZ), 1);
  return zeff[Z];
}

Referenced by GetMuonCaptureRate().

◆ ModelDescription()

void G4MuonMinusBoundDecay::ModelDescription ( std::ostream & outFile ) const

virtual

Reimplemented from G4HadronicInteraction.

Definition at line 436 of file G4MuonMinusBoundDecay.cc.

{
  outFile << " Sample probabilities of mu- nuclear capture of decay"
          << "  from K-shell orbit.\n"
          << " Time of projectile is changed taking into account life time"
          << "  of muonic atom.\n"
          << " If decay is sampled primary state become stopAndKill,"
          << "  else - isAlive.\n"
          << " Mainly based on:\n"
          << "  H.C. Von Baeyer and D.Leiter, Phys. Rev. A 19, 1371 (1979)\n"
          << "  T.Suzuki, D.F.Measday, J.P.Roalsvig Phys.Rev. C35 (1987) 2212\n"
          << " with an emprical fit to the Huff factors for Z >= 14\n"
          << " from the above review\n";
}

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

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ G4MuonMinusBoundDecay()

◆ ~G4MuonMinusBoundDecay()

Member Function Documentation

◆ ApplyYourself()

◆ GetMuonCaptureRate()

◆ GetMuonDecayRate() [1/2]

◆ GetMuonDecayRate() [2/2]

◆ GetMuonZeff()

◆ ModelDescription()