marley::WeisskopfSingleParticleModel Class Reference

Implements the Weisskopf single-particle estimates of the gamma-ray strength functions. More...

#include <WeisskopfSingleParticleModel.hh>

Inheritance diagram for marley::WeisskopfSingleParticleModel:

Public Member Functions
	WeisskopfSingleParticleModel (int Z, int A, double D0=1.)
virtual double	strength_function (TransitionType type, int l, double e_gamma) override
	Returns the gamma-ray strength function (MeV –2 \(\ell\)–1) for the requested gamma energy and multipolarity.
virtual double	transmission_coefficient (TransitionType type, int l, double e_gamma) override
	Returns the gamma-ray transmission coefficient (dimensionless) for the requested gamma energy and multipolarity.
Public Member Functions inherited from marley::GammaStrengthFunctionModel
	GammaStrengthFunctionModel (int Z, int A)

Additional Inherited Members
Public Types inherited from marley::GammaStrengthFunctionModel
enum class	TransitionType { electric , magnetic , unphysical }
	Electromagnetic transitions in nuclei may be classified by their multipolarity (electric vs. magnetic multipole radiation) More...
Static Protected Member Functions inherited from marley::GammaStrengthFunctionModel
static void	check_multipolarity (int l)
	Check that l > 0 and throw a marley::Error if it is not.
Protected Attributes inherited from marley::GammaStrengthFunctionModel
int	A_
	Mass number.
int	Z_
	Atomic number.

Detailed Description

Implements the Weisskopf single-particle estimates of the gamma-ray strength functions.

Under this model, the electric ( \(f_{\text{E}\ell}\)) and magnetic ( \(f_{\text{M}\ell}\)) gamma-ray strength functions are independent of the gamma energy and are given by

\[ f_{\text{E}\ell} = \frac{2\alpha\Lambda}{\text{D}_0} \left(\frac{R}{\hbar c}\right)^{\!2\ell} \]

and

\[ f_{\text{M}\ell} = 10\left(\frac{\hbar c} {R\,m_\text{p}}\right)^{\!2} f_{\text{E}\ell}, \]

where \(\alpha\) is the fine-structure constant, \(\text{D}_0\) is the level spacing parameter (MeV), \(R = (1.2\text{ fm})A^{1/3}\) is the approximate nuclear radius, \(m_\text{p}\) is the proton mass (MeV), and \(\Lambda\) is a function of the multipolarity \(\ell\) given by

\[ \Lambda \equiv \left(\frac{3}{\ell + 3}\right)^{\!2} \left(\frac{\ell + 1}{\ell\left[(2\ell + 1)!!\right]^2} \right).\]

These estimates are typically only good to an order of magnitude, so using a more sophisticated model, e.g., the StandardLorentzianModel, is strongly recommended.

Definition at line 46 of file WeisskopfSingleParticleModel.hh.

Constructor & Destructor Documentation

WeisskopfSingleParticleModel()

marley::WeisskopfSingleParticleModel::WeisskopfSingleParticleModel	(	int	Z,
		int	A,
		double	D0 = 1. )

Parameters

Z	Atomic number of the desired nuclide
A	Mass number of the desired nuclide
D0	Level spacing parameter (MeV)

Definition at line 25 of file WeisskopfSingleParticleModel.cc.

                    : marley::GammaStrengthFunctionModel(Z, A), D0_(D0)
{
  if (D0_ <= 0.) throw marley::Error("Invalid"
    " level spacing parameter " + std::to_string(D0_)
    + " MeV passed to the constructor of"
    " marley::WeisskopfGammaStrengthFunctionModel.");
}

References marley::GammaStrengthFunctionModel::GammaStrengthFunctionModel().

Member Function Documentation

strength_function()

double marley::WeisskopfSingleParticleModel::strength_function ( TransitionType type, int l, double e_gamma )

overridevirtual

Returns the gamma-ray strength function (MeV ^{–2 \(\ell\)–1}) for the requested gamma energy and multipolarity.

Parameters

type	Electric or magnetic transition
l	Multipolarity of the transition
e_gamma	Gamma-ray energy (MeV)

Note

As described above, the Weisskopf estimates of the gamma-ray strength functions are independent of the gamma energy, and so the parameter e_gamma is ignored by this function.

Implements marley::GammaStrengthFunctionModel.

Definition at line 43 of file WeisskopfSingleParticleModel.cc.

{
  check_multipolarity(l);
 
  // Compute double factorial of 2l + 1
  int dfact = 1;
  for (int n = 2*l + 1; n > 0; n -= 2) dfact *= n;
 
  // Multipolarity factor (dimensionless)
  double lambda = (l + 1.) / (l * std::pow(dfact, 2))
    * std::pow(3.0 / (l + 3.), 2);
 
  // Estimated nuclear radius (fm)
  double R = marley_utils::r0 * std::pow(A_, 1.0/3.0);
 
  // Electric transition strength function (MeV^[-2l-1])
  double el_sf = 2 * marley_utils::alpha * lambda
    * std::pow(R / marley_utils::hbar_c, 2*l) / D0_;
 
  if (type == TrType::electric) {
    return el_sf;
  }
 
  else if (type == TrType::magnetic) {
    static const double mp = marley::MassTable::Instance().get_particle_mass(
      marley_utils::PROTON);
    return 10. * el_sf * std::pow(marley_utils::hbar_c / (mp * R), 2);
  }
 
  else if (type == TrType::unphysical) {
    MARLEY_LOG( WARN, "physics.deexcitation" )
      << "Unphysical EM transition encountered in"
      << " WeisskopfSingleParticleModel::strength_function()."
      << " The strength function will be set to zero.";
    return 0.;
  }
 
  // @todo Improve error message
  else throw marley::Error( "Invalid transition type"
    " given for Weisskopf gamma-ray strength function calculation" );
}

References marley::GammaStrengthFunctionModel::A_, marley::GammaStrengthFunctionModel::check_multipolarity(), marley::MassTable::get_particle_mass(), and marley::MassTable::Instance().

Referenced by transmission_coefficient().

transmission_coefficient()

double marley::WeisskopfSingleParticleModel::transmission_coefficient ( TransitionType type, int l, double e_gamma )

overridevirtual

Returns the gamma-ray transmission coefficient (dimensionless) for the requested gamma energy and multipolarity.

The gamma-ray transmission coefficient and strength function are related via \(\text{T}_{\text{X}\ell}(\text{E}_\gamma) = 2\pi f_{\text{X}\ell}(\text{E}_\gamma)\text{E}_\gamma^{(2\ell + 1)},\) where X is the type of transition (electric or magnetic), \(\ell\) is the multipolarity, \(\text{T}_{\text{X}\ell}\) is the transmission coefficient, \(f_{\text{X}\ell}\) is the strength function, and \(\text{E}_\gamma\) is the gamma-ray energy.

Parameters

type	Electric or magnetic transition
l	Multipolarity of the transition
e_gamma	Gamma-ray energy (MeV)

Implements marley::GammaStrengthFunctionModel.

Definition at line 86 of file WeisskopfSingleParticleModel.cc.

{
  return 2. * marley_utils::pi * strength_function(type, l, e_gamma)
    * std::pow(e_gamma, 2*l + 1);
}

References strength_function().

---

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

• /home/sjg/Desktop/marley/include/marley/WeisskopfSingleParticleModel.hh
• /home/sjg/Desktop/marley/src/WeisskopfSingleParticleModel.cc