#include <G4VEmissionProbability.hh>

Inheritance diagram for G4VEmissionProbability:

Public Member Functions
virtual G4double	ComputeProbability (G4double anEnergy, G4double CB)

virtual G4double	EmissionProbability (const G4Fragment &fragment, G4double anEnergy)

	G4VEmissionProbability (G4int Z, G4int A)

G4int	GetA (void) const

G4double	GetProbability () const

G4double	GetRecoilExcitation () const

G4int	GetZ (void) const

void	Initialise ()

void	ResetProbability ()

G4double	SampleEnergy ()

void	SetDecayKinematics (G4int Z, G4int A, G4double rmass, G4double fmass)

void	SetEvapExcitation (G4double exc)

virtual	~G4VEmissionProbability ()

Protected Member Functions
G4double	IntegrateProbability (G4double elow, G4double ehigh, G4double CB)

void	ResetIntegrator (size_t nbin, G4double de, G4double eps)

Protected Attributes
G4int	OPTxs

G4double	pEvapMass

G4Pow *	pG4pow

G4double	pMass

G4NuclearLevelData *	pNuclearLevelData

G4double	pProbability

G4double	pResMass

G4int	pVerbose

G4int	resA

G4int	resZ

G4int	theA

G4int	theZ

Private Member Functions
G4double	FindRecoilExcitation (G4double e)

	G4VEmissionProbability (const G4VEmissionProbability &right)

G4bool	operator!= (const G4VEmissionProbability &right) const

const G4VEmissionProbability &	operator= (const G4VEmissionProbability &right)

G4bool	operator== (const G4VEmissionProbability &right) const

Private Attributes
G4double	accuracy

G4double	eCoulomb

G4double	elimit

G4double	emax

G4double	emin

G4double	fExc

G4double	fExcRes

G4bool	fFD

size_t	length

size_t	nbin

G4double	probmax

Detailed Description

Definition at line 47 of file G4VEmissionProbability.hh.

Constructor & Destructor Documentation

◆ G4VEmissionProbability() [1/2]

G4VEmissionProbability::G4VEmissionProbability	(	G4int	Z,
		G4int	A
	)

explicit

Definition at line 39 of file G4VEmissionProbability.cc.

  : OPTxs(3),pVerbose(1),theZ(Z),theA(A),resZ(0),resA(0),
    pMass(0.0),pEvapMass(0.0),pResMass(0.0),fExc(0.0),fExcRes(0.0),
    elimit(CLHEP::MeV),accuracy(0.02),fFD(false)
{
  pNuclearLevelData = G4NuclearLevelData::GetInstance(); 
  pG4pow = G4Pow::GetInstance();
  if(A > 0) { pEvapMass = G4NucleiProperties::GetNuclearMass(theA, theZ); }
  // G4cout << "G4VEvaporationProbability: Z= " << theZ << " A= " << theA 
  // << " M(GeV)= " << pEvapMass/1000. << G4endl;
  length = nbin = 0;
  emin = emax = eCoulomb = pProbability = probmax = 0.0;
}

References A, eCoulomb, emax, emin, G4Pow::GetInstance(), G4NuclearLevelData::GetInstance(), G4NucleiProperties::GetNuclearMass(), length, nbin, pEvapMass, pG4pow, pNuclearLevelData, pProbability, probmax, theA, and theZ.

◆ ~G4VEmissionProbability()

G4VEmissionProbability::~G4VEmissionProbability ( )

virtual

Definition at line 53 of file G4VEmissionProbability.cc.

54{}

◆ G4VEmissionProbability() [2/2]

G4VEmissionProbability::G4VEmissionProbability ( const G4VEmissionProbability & right )

private

Member Function Documentation

◆ ComputeProbability()

G4double G4VEmissionProbability::ComputeProbability	(	G4double	anEnergy,
		G4double	CB
	)

virtual

Reimplemented in G4GEMProbabilityVI, and G4EvaporationProbability.

Definition at line 76 of file G4VEmissionProbability.cc.

{
  return 0.0;
}

Referenced by IntegrateProbability(), and SampleEnergy().

◆ EmissionProbability()

G4double G4VEmissionProbability::EmissionProbability	(	const G4Fragment &	fragment,
		G4double	anEnergy
	)

virtual

Reimplemented in G4FissionProbability, and G4GEMProbability.

Definition at line 71 of file G4VEmissionProbability.cc.

{
  return 0.0;
}

Referenced by G4CompetitiveFission::GetEmissionProbability().

◆ FindRecoilExcitation()

G4double G4VEmissionProbability::FindRecoilExcitation ( G4double e )

private

Definition at line 187 of file G4VEmissionProbability.cc.

{
  fExcRes = 0.0;
  G4double mass = pEvapMass + fExc;
  // abnormal case - should never happens
  if(pMass < mass + pResMass) { return 0.0; }
    
  G4double m02   = pMass*pMass;
  G4double m12   = mass*mass;
  G4double m22   = pResMass*pResMass;
  G4double mres  = std::sqrt(m02 + m12 - 2.*pMass*(mass + e));
 
  fExcRes = mres - pResMass;
  const G4double tolerance = 0.1*CLHEP::keV;
 
  if(pVerbose > 1) {
    G4cout << "### G4VEmissionProbability::FindRecoilExcitation for resZ= " 
           << resZ << " resA= " << resA 
           << " evaporated Z= " << theZ << " A= " << theA
       << " Ekin= " << e << " Eexc= " << fExcRes << G4endl;
  }
 
  // residual nucleus is in the ground state
  if(fExcRes < tolerance) {
    fExcRes = 0.0;
    //G4cout<<"Ground state Ekin= "<< 0.5*(m02 + m12 - m22)/pMass - mass<<G4endl;
    return std::max(0.5*(m02 + m12 - m22)/pMass - mass,0.0);
  }
  // select final state excitation
  auto lManager = pNuclearLevelData->GetLevelManager(resZ, resA);
  if(!lManager) { return e; }
 
  //G4cout<<"ExcMax= "<< lManager->MaxLevelEnergy()<<" CB= "<<eCoulomb<<G4endl;
  // levels are not known
  if(fExcRes > lManager->MaxLevelEnergy() + tolerance) { return e; }
 
  // find level
  auto idx = lManager->NearestLevelIndex(fExcRes);
  //G4cout << "idx= " << idx << " Exc= " << fExcRes 
  //     << " Elevel= " << lManager->LevelEnergy(idx) << G4endl;
  for(; idx > 0; --idx) {
    fExcRes = lManager->LevelEnergy(idx);
    // excited level
    if(pMass > mass + pResMass + fExcRes && lManager->FloatingLevel(idx) == 0) { 
      G4double massR = pResMass + fExcRes;
      G4double mr2 = massR*massR;
      //G4cout << "Result idx= " << idx << " Eexc= " << fExcRes
      //     << " Ekin= " << 0.5*(m02 + m12 - mr2)/pMass - mass << G4endl;
      return std::max(0.5*(m02 + m12 - mr2)/pMass - mass,0.0);
    }
  }
  // ground level
  fExcRes = 0.0;
  //G4cout << "Ground state Ekin= " << 0.5*(m02 + m12 - m22)/pMass - mass << G4endl;
  return std::max(0.5*(m02 + m12 - m22)/pMass - mass,0.0);
}

References fExc, fExcRes, G4cout, G4endl, G4NuclearLevelData::GetLevelManager(), CLHEP::keV, G4INCL::Math::max(), G4LevelManager::NearestLevelIndex(), pEvapMass, pMass, pNuclearLevelData, pResMass, pVerbose, resA, resZ, theA, and theZ.

Referenced by SampleEnergy().

◆ GetA()

G4int G4VEmissionProbability::GetA ( void ) const

inline

Definition at line 63 of file G4VEmissionProbability.hh.

63{ return theA; }

References theA.

◆ GetProbability()

G4double G4VEmissionProbability::GetProbability ( ) const

inline

Definition at line 75 of file G4VEmissionProbability.hh.

75{ return pProbability; };

References pProbability.

◆ GetRecoilExcitation()

G4double G4VEmissionProbability::GetRecoilExcitation ( ) const

inline

Definition at line 71 of file G4VEmissionProbability.hh.

71{ return fExcRes; };

References fExcRes.

◆ GetZ()

G4int G4VEmissionProbability::GetZ ( void ) const

inline

Definition at line 61 of file G4VEmissionProbability.hh.

61{ return theZ; }

References theZ.

Referenced by G4TritonEvaporationProbability::CalcAlphaParam(), G4AlphaEvaporationProbability::CalcAlphaParam(), G4DeuteronEvaporationProbability::CalcAlphaParam(), G4He3EvaporationProbability::CalcAlphaParam(), and G4ProtonEvaporationProbability::CalcAlphaParam().

◆ Initialise()

void G4VEmissionProbability::Initialise ( )

Definition at line 56 of file G4VEmissionProbability.cc.

{
  G4DeexPrecoParameters* param = pNuclearLevelData->GetParameters();
  OPTxs = param->GetDeexModelType();
  pVerbose = param->GetVerbose();
  fFD = param->GetDiscreteExcitationFlag();
}

References fFD, G4DeexPrecoParameters::GetDeexModelType(), G4DeexPrecoParameters::GetDiscreteExcitationFlag(), G4NuclearLevelData::GetParameters(), G4DeexPrecoParameters::GetVerbose(), OPTxs, pNuclearLevelData, and pVerbose.

Referenced by G4EvaporationChannel::Initialise().

◆ IntegrateProbability()

G4double G4VEmissionProbability::IntegrateProbability	(	G4double	elow,
		G4double	ehigh,
		G4double	CB
	)

protected

Definition at line 81 of file G4VEmissionProbability.cc.

{
  pProbability = 0.0;
  if(elow >= ehigh) { return pProbability; }
 
  emin = elow;
  emax = ehigh;
  eCoulomb = cb;
 
  G4double edelta = elimit;
  nbin = (size_t)((emax - emin)/edelta) + 1;
  const G4double edeltamin = 0.2*CLHEP::MeV;
  const G4double edeltamax = 2*CLHEP::MeV;
  if(nbin < 4) { 
    nbin = 4;
    edelta = (emax - emin)/(G4double)nbin;
  } else if(nbin > length) {
    nbin = length;
  }
 
  G4double x(emin), del, y; 
  G4double edelmicro= edelta*0.02;
  probmax = ComputeProbability(x + edelmicro, eCoulomb);
  G4double problast = probmax;
  if(pVerbose > 2) {
    G4cout << "### G4VEmissionProbability::IntegrateProbability: " 
       << " Emax= " << emax << " QB= " << cb << " nbin= " << nbin 
       << G4endl;
    G4cout << "    0.  E= " << emin << "  prob= " << probmax << G4endl;
  }
  for(size_t i=1; i<=nbin; ++i) {
    x += edelta;
    if(x > emax) { 
      edelta += (emax - x);
      x = emax; 
    }
    G4bool endpoint = (std::abs(x - emax) < edelmicro) ? true : false;
    G4double xx = endpoint ? x - edelmicro : x;
    y = ComputeProbability(xx, eCoulomb);
    if(pVerbose > 2) { 
      G4cout << "    " << i << ".  E= " << x << "  prob= " << y 
         << " Edel= " << edelta << G4endl;
    } 
    probmax = std::max(probmax, y);
    del = (y + problast)*edelta*0.5;
    pProbability += del;
    // end of the loop
    if(del < accuracy*pProbability || endpoint) { break; }
    problast = y;
 
    // smart step definition
    if(del != pProbability && del > 0.8*pProbability && 
       0.7*edelta > edeltamin) { 
      edelta *= 0.7;
    } else if(del < 0.1*pProbability && 1.5*edelta < edeltamax) { 
      edelta *= 1.5;
    }
  }
 
  if(pVerbose > 1) { 
    G4cout << " Probability= " << pProbability << " probmax= " 
           << probmax << G4endl; 
  }
  return pProbability;
}

References accuracy, ComputeProbability(), eCoulomb, elimit, emax, emin, G4cout, G4endl, length, G4INCL::Math::max(), CLHEP::MeV, nbin, pProbability, probmax, and pVerbose.

Referenced by G4GEMProbabilityVI::ComputeTotalProbability(), and G4EvaporationProbability::TotalProbability().

◆ operator!=()

G4bool G4VEmissionProbability::operator!= ( const G4VEmissionProbability & right ) const

private

◆ operator=()

const G4VEmissionProbability & G4VEmissionProbability::operator= ( const G4VEmissionProbability & right )

private

◆ operator==()

G4bool G4VEmissionProbability::operator== ( const G4VEmissionProbability & right ) const

private

◆ ResetIntegrator()

void G4VEmissionProbability::ResetIntegrator	(	size_t	nbin,
		G4double	de,
		G4double	eps
	)

protected

Definition at line 64 of file G4VEmissionProbability.cc.

{
  if(nbins > 0) { length = nbins; }
  if(de > 0.0)  { elimit = de; }
  if(eps > 0.0) { accuracy = eps; }
}

References accuracy, elimit, eps, and length.

Referenced by G4EvaporationProbability::G4EvaporationProbability(), and G4GEMProbabilityVI::G4GEMProbabilityVI().

◆ ResetProbability()

void G4VEmissionProbability::ResetProbability ( )

inline

Definition at line 77 of file G4VEmissionProbability.hh.

77{ pProbability = 0.0; };

References pProbability.

Referenced by G4EvaporationChannel::GetEmissionProbability(), and G4GEMChannelVI::GetEmissionProbability().

◆ SampleEnergy()

G4double G4VEmissionProbability::SampleEnergy ( )

Definition at line 149 of file G4VEmissionProbability.cc.

{
  static const G4double fact = 1.05;
  probmax *= fact;
 
  if(pVerbose > 1) {
    G4cout << "### G4VEmissionProbability::SampleEnergy: " 
       << " Emin= " << emin << " Emax= " << emax 
       << " probmax= " << probmax << G4endl;
  }
 
  CLHEP::HepRandomEngine* rndm = G4Random::getTheEngine();
  const G4int nmax = 100;
  G4double del = emax - emin;
  G4double ekin, g;
  G4int n = 0;
  do {
    ekin = del*rndm->flat() + emin; 
    ++n;
    g = ComputeProbability(ekin, eCoulomb);
    if(pVerbose > 2) {
      G4cout << "    " << n
         << ". prob= " << g << " probmax= " << probmax
         << " Ekin= " << ekin << G4endl;
    }
    if((g > probmax || n > nmax) && pVerbose > 1) {
      G4cout << "### G4VEmissionProbability::SampleEnergy for Z= " << theZ 
             << " A= " << theA 
             << "\n    Warning n= " << n
         << " prob/probmax= " << g/probmax 
         << " prob= " << g << " probmax= " << probmax 
         << "\n    Ekin= " << ekin << " Emin= " << emin
         << " Emax= " << emax << G4endl;
    }
  } while(probmax*rndm->flat() > g && n < nmax);
  return (fFD) ? FindRecoilExcitation(ekin) : ekin;
}

References ComputeProbability(), eCoulomb, emax, emin, fFD, FindRecoilExcitation(), CLHEP::HepRandomEngine::flat(), g, G4cout, G4endl, CLHEP::detail::n, probmax, pVerbose, theA, and theZ.

Referenced by G4EvaporationChannel::EmittedFragment(), G4GEMProbabilityVI::SampleEvaporationFragment(), and G4EvaporationProbability::SampleKineticEnergy().

◆ SetDecayKinematics()

void G4VEmissionProbability::SetDecayKinematics	(	G4int	Z,
		G4int	A,
		G4double	rmass,
		G4double	fmass
	)

inline

Definition at line 131 of file G4VEmissionProbability.hh.

{
  resZ = Z;
  resA = A;
  pMass = fmass;
  pResMass = rmass;
}

References A, pMass, pResMass, resA, resZ, and Z.

Referenced by G4EvaporationChannel::GetEmissionProbability(), and G4GEMChannelVI::GetEmissionProbability().

◆ SetEvapExcitation()

void G4VEmissionProbability::SetEvapExcitation ( G4double exc )

inline

Definition at line 73 of file G4VEmissionProbability.hh.

73{ fExc = exc; };

References fExc.

Field Documentation

◆ accuracy

G4double G4VEmissionProbability::accuracy

private

Definition at line 124 of file G4VEmissionProbability.hh.

Referenced by IntegrateProbability(), and ResetIntegrator().

◆ eCoulomb

G4double G4VEmissionProbability::eCoulomb

private

Definition at line 123 of file G4VEmissionProbability.hh.

Referenced by G4VEmissionProbability(), IntegrateProbability(), and SampleEnergy().

◆ elimit

G4double G4VEmissionProbability::elimit

private

Definition at line 122 of file G4VEmissionProbability.hh.

Referenced by IntegrateProbability(), and ResetIntegrator().

◆ emax

G4double G4VEmissionProbability::emax

private

Definition at line 121 of file G4VEmissionProbability.hh.

Referenced by G4VEmissionProbability(), IntegrateProbability(), and SampleEnergy().

◆ emin

G4double G4VEmissionProbability::emin

private

Definition at line 120 of file G4VEmissionProbability.hh.

Referenced by G4VEmissionProbability(), IntegrateProbability(), and SampleEnergy().

◆ fExc

G4double G4VEmissionProbability::fExc

private

Definition at line 117 of file G4VEmissionProbability.hh.

Referenced by FindRecoilExcitation(), and SetEvapExcitation().

◆ fExcRes

G4double G4VEmissionProbability::fExcRes

private

Definition at line 118 of file G4VEmissionProbability.hh.

Referenced by FindRecoilExcitation(), and GetRecoilExcitation().

◆ fFD

G4bool G4VEmissionProbability::fFD

private

Definition at line 127 of file G4VEmissionProbability.hh.

Referenced by Initialise(), and SampleEnergy().

◆ length

size_t G4VEmissionProbability::length

private

Definition at line 114 of file G4VEmissionProbability.hh.

Referenced by G4VEmissionProbability(), IntegrateProbability(), and ResetIntegrator().

◆ nbin

size_t G4VEmissionProbability::nbin

private

Definition at line 115 of file G4VEmissionProbability.hh.

Referenced by G4VEmissionProbability(), and IntegrateProbability().

◆ OPTxs

G4int G4VEmissionProbability::OPTxs

protected

Definition at line 89 of file G4VEmissionProbability.hh.

Referenced by G4EvaporationProbability::CrossSection(), Initialise(), G4EvaporationProbability::SampleKineticEnergy(), and G4EvaporationProbability::TotalProbability().

◆ pEvapMass

G4double G4VEmissionProbability::pEvapMass

protected

Definition at line 97 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeProbability(), G4EvaporationProbability::ComputeProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), FindRecoilExcitation(), G4EvaporationProbability::G4EvaporationProbability(), G4GEMProbabilityVI::G4GEMProbabilityVI(), G4VEmissionProbability(), G4GEMProbabilityVI::ProbabilityDistributionFunction(), G4GEMProbabilityVI::SampleEvaporationFragment(), and G4EvaporationProbability::TotalProbability().

◆ pG4pow

G4Pow* G4VEmissionProbability::pG4pow

protected

Definition at line 102 of file G4VEmissionProbability.hh.

Referenced by G4NeutronEvaporationProbability::CalcAlphaParam(), G4NeutronEvaporationProbability::CalcBetaParam(), G4GEMProbabilityVI::ComputeTotalProbability(), G4GEMProbabilityVI::G4GEMProbabilityVI(), G4VEmissionProbability(), and G4EvaporationProbability::TotalProbability().

◆ pMass

G4double G4VEmissionProbability::pMass

protected

Definition at line 96 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeProbability(), G4EvaporationProbability::ComputeProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), FindRecoilExcitation(), G4GEMProbabilityVI::ProbabilityDistributionFunction(), and SetDecayKinematics().

◆ pNuclearLevelData

G4NuclearLevelData* G4VEmissionProbability::pNuclearLevelData

protected

Definition at line 101 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeProbability(), G4EvaporationProbability::ComputeProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), FindRecoilExcitation(), G4VEmissionProbability(), Initialise(), and G4EvaporationProbability::TotalProbability().

◆ pProbability

G4double G4VEmissionProbability::pProbability

protected

Definition at line 99 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeTotalProbability(), G4VEmissionProbability(), GetProbability(), IntegrateProbability(), ResetProbability(), and G4EvaporationProbability::TotalProbability().

◆ pResMass

G4double G4VEmissionProbability::pResMass

protected

Definition at line 98 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeProbability(), G4EvaporationProbability::ComputeProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), FindRecoilExcitation(), G4GEMProbabilityVI::ProbabilityDistributionFunction(), and SetDecayKinematics().

◆ probmax

G4double G4VEmissionProbability::probmax

private

Definition at line 125 of file G4VEmissionProbability.hh.

Referenced by G4VEmissionProbability(), IntegrateProbability(), and SampleEnergy().

◆ pVerbose

G4int G4VEmissionProbability::pVerbose

protected

Definition at line 90 of file G4VEmissionProbability.hh.

Referenced by FindRecoilExcitation(), Initialise(), IntegrateProbability(), and SampleEnergy().

◆ resA

G4int G4VEmissionProbability::resA

protected

Definition at line 94 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeProbability(), G4EvaporationProbability::ComputeProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), G4EvaporationProbability::CrossSection(), FindRecoilExcitation(), G4GEMProbabilityVI::ProbabilityDistributionFunction(), SetDecayKinematics(), and G4EvaporationProbability::TotalProbability().

◆ resZ

G4int G4VEmissionProbability::resZ

protected

Definition at line 93 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbabilityVI::ComputeProbability(), G4EvaporationProbability::ComputeProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), FindRecoilExcitation(), SetDecayKinematics(), and G4EvaporationProbability::TotalProbability().

◆ theA

G4int G4VEmissionProbability::theA

protected

Definition at line 92 of file G4VEmissionProbability.hh.

◆ theZ

G4int G4VEmissionProbability::theZ

protected

Definition at line 91 of file G4VEmissionProbability.hh.

Referenced by G4GEMProbability::CalcAlphaParam(), G4GEMProbability::CalcBetaParam(), G4GEMProbability::CalcProbability(), G4GEMProbabilityVI::ComputeTotalProbability(), G4EvaporationProbability::CrossSection(), G4GEMProbability::Dump(), FindRecoilExcitation(), G4EvaporationProbability::G4EvaporationProbability(), G4VEmissionProbability(), G4GEMProbability::GetCoulombBarrier(), GetZ(), G4GEMProbabilityVI::ProbabilityDistributionFunction(), SampleEnergy(), G4GEMProbabilityVI::SampleEvaporationFragment(), and G4EvaporationProbability::SampleKineticEnergy().

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

source/processes/hadronic/models/de_excitation/management/include/G4VEmissionProbability.hh
source/processes/hadronic/models/de_excitation/management/src/G4VEmissionProbability.cc

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ G4VEmissionProbability() [1/2]

◆ ~G4VEmissionProbability()

◆ G4VEmissionProbability() [2/2]

Member Function Documentation

◆ ComputeProbability()

◆ EmissionProbability()

◆ FindRecoilExcitation()

◆ GetA()

◆ GetProbability()

◆ GetRecoilExcitation()

◆ GetZ()

◆ Initialise()

◆ IntegrateProbability()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ ResetIntegrator()

◆ ResetProbability()

◆ SampleEnergy()

◆ SetDecayKinematics()

◆ SetEvapExcitation()

Field Documentation

◆ accuracy

◆ eCoulomb

◆ elimit

◆ emax

◆ emin

◆ fExc

◆ fExcRes

◆ fFD

◆ length

◆ nbin

◆ OPTxs

◆ pEvapMass

◆ pG4pow

◆ pMass

◆ pNuclearLevelData

◆ pProbability

◆ pResMass

◆ probmax

◆ pVerbose

◆ resA

◆ resZ

◆ theA

◆ theZ