marley::StandardLorentzianModel Class Reference

Implements Brink-Axel strength functions based on the Reference Input Parameter Library's Standard Lorentzian (SLO) Model. More...

#include <StandardLorentzianModel.hh>

Inheritance diagram for marley::StandardLorentzianModel:

Public Member Functions
	StandardLorentzianModel (int Z, int A)
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 Brink-Axel strength functions based on the Reference Input Parameter Library's Standard Lorentzian (SLO) Model.

Under this model, the gamma-ray strength functions are taken to have a Lorentzian shape with an energy-independent width. If \(E_{\text{X}\ell}\), \(\Gamma_{\text{X}\ell}\), and \(\sigma_{\text{X}\ell}\) are respectively the energy, width, and peak cross section of the \(\text{X}\ell\) giant resonance, then the standard Lorentzian model gamma-ray strength function is given by

\[f_{\text{X}\ell}(E_\gamma) = \frac{\sigma_{\text{X}\ell}} {(2\ell+1)\pi^2(\hbar c)^2}\left[\frac{\Gamma_{\text{X}\ell}^2 E_\gamma^{3-2\ell}}{\left(E_\gamma^2 - E_{\text{X}\ell}^2\right)^2 + E_\gamma^2\Gamma_{\text{X}\ell}^2}\right] \]

where \(E_\gamma\) is the gamma-ray energy and the type of transition \(\text{X}\) is either electric \(\text{(E)}\) or magnetic \(\text{(M)}\).

The giant resonance parameters \(E_{\text{X}\ell}\), \(\Gamma_{\text{X}\ell}\), and \(\sigma_{\text{X}\ell}\) used by StandardLorentzianModel are the same as those used by default in the TALYS nuclear reaction code, version 1.6. More details about these parameters are given in the table below.

Transition	Parameters	Units	Source
Electric dipole (E1)	\(E_{\text{E}1} = 31.2A^{-1/3} + 20.6A^{-1/6}\)	MeV	Empirical fit for spherical nuclei from the RIPL-2 handbook, p. 129
	\(\Gamma_{\text{E}1} = 0.026{E_{\text{E}1}}^{1.91}\)	MeV
	\(\displaystyle\sigma_{\text{E}1} = 1.2\left(\frac{120NZ}{\pi A \,\Gamma_{\text{E}1}}\right)\)	mb
Electric quadrupole (E2)	\(E_{\text{E}2} = 63A^{-1/3}\)	MeV	Global fit given by Kopecky in the RIPL-1 handbook, p. 103
	\(\Gamma_{\text{E}2} = 6.11 - 0.012A\)	MeV
	\(\displaystyle\sigma_{\text{E}2} = \frac{0.00014Z^2 E_{\text{E}2}}{A^{1/3}\Gamma_{\text{E}2}}\)	mb
Magnetic dipole (M1)	\(E_{\text{M}1} = 41A^{-1/3}\)	MeV	Global SLO model fit given in the RIPL-2 handbook, p. 132
	\(\Gamma_{\text{M}1} = 4\)	MeV
	\(\displaystyle\sigma_{\text{M}1} = 3\,\pi^2\hbar^2c^2\left[\frac{\left(B_\text{n}^2 - E_{\text{M}1}^2\right)^2 + B_\text{n}^2\, \Gamma_{\text{M}1}^2}{B_\text{n}\,\Gamma_{\text{M}1}^2} \right]\Bigg[\frac{f_{\text{E}1}(B_\text{n})}{0.0588A^{0.878}}\Bigg] \) where \(B_\text{n}\) = 7 MeV and \(f_{\text{E}1}\) is calculated using the E1 parameters above.	mb
Other electric transitions (E3+)	\(E_{\text{E}\ell} = E_{\text{E}2}\)	MeV	Default approximation used by the TALYS nuclear code, version 1.6
	\(\Gamma_{\text{E}\ell} = \Gamma_{\text{E}2}\)	MeV
	\(\displaystyle\sigma_{\text{E}\ell} = (0.0008)^{\ell - 2}\,\sigma_{\text{E}2}\)	mb
Other magnetic transitions (M2+)	\(M_{\text{M}\ell} = M_{\text{M}1}\)	MeV	Default approximation used by the TALYS nuclear code, version 1.6
	\(\Gamma_{\text{M}\ell} = \Gamma_{\text{M}1}\)	MeV
	\(\displaystyle\sigma_{\text{M}\ell} = (0.0008)^{\ell - 1}\,\sigma_{\text{M}1}\)	mb

Definition at line 108 of file StandardLorentzianModel.hh.

Constructor & Destructor Documentation

StandardLorentzianModel()

marley::StandardLorentzianModel::StandardLorentzianModel	(	int	Z,
		int	A )

Note

Be careful! You must initialize the E1 giant resonance parameters before the M1 parameters!

Definition at line 29 of file StandardLorentzianModel.cc.

  : GammaStrengthFunctionModel(Z, A)
{
  // E1 giant resonance parameterization taken from the empirical fit for
  // spherical nuclei given in the
  // <a href="https://www-nds.iaea.org/RIPL-2/handbook/ripl2.pdf">
  // RIPL-2 handbook</a>, p. 129
  // @todo Consider updating E1 parameters to the new SLO fit from RIPL-3 (see
  // equation 174 in the RIPL-3 Nuclear Data Sheets paper, and compare equation
  // 173)
  e_E1_ = 31.2*std::pow(A_, -1.0/3.0) + 20.6*std::pow(A_, -1.0/6.0); // MeV
  gamma_E1_ = 0.026 * std::pow(e_E1_, 1.91); // MeV
  sigma_E1_ = 1.2 * 120 * (A_ - Z_) * Z_/(A_ * marley_utils::pi * gamma_E1_)
    * marley_utils::mb; // mb
 
  // E2 giant resonance parameterization taken from the global fit given by
  // Kopecky in the
  // <a href="https://www-nds.iaea.org/ripl/readme/ripl_handbook.ps">RIPL-1
  // handbook</a>, p. 103
  // RIPL-2 and RIPL-3 do not update this parameterization for the SLO
  e_E2_ = 63*std::pow(A_, -1.0/3.0); // MeV
  gamma_E2_ = 6.11 - 0.012*A_; // MeV
  sigma_E2_ = 0.00014 * std::pow(Z_, 2) * e_E2_
    / (std::pow(A_, 1.0/3.0) * gamma_E2_) * marley_utils::mb; // mb
 
  // M1 parameterization taken from the global SLO model fit given in the
  // <a href="https://www-nds.iaea.org/RIPL-2/handbook/ripl2.pdf">RIPL-2
  // handbook</a>, p. 132
  constexpr double e_gamma_ref = 7.0; // MeV
  double factor_m1 = strength_function(TrType::electric, 1, e_gamma_ref)
    / (0.0588 * std::pow(A_, 0.878));
  gamma_M1_ = 4.0; // MeV
  e_M1_ = 41*std::pow(A_, -1.0/3.0); // MeV
  sigma_M1_ = (std::pow(std::pow(e_gamma_ref, 2) - std::pow(e_M1_, 2), 2)
    + std::pow(e_gamma_ref, 2) * std::pow(gamma_M1_, 2))
    * (3 * std::pow(marley_utils::pi, 2) * factor_m1)
    / (e_gamma_ref * std::pow(gamma_M1_, 2)); // mb
}

References marley::GammaStrengthFunctionModel::GammaStrengthFunctionModel(), marley::GammaStrengthFunctionModel::A_, strength_function(), and marley::GammaStrengthFunctionModel::Z_.

Member Function Documentation

strength_function()

double marley::StandardLorentzianModel::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)

Implements marley::GammaStrengthFunctionModel.

Definition at line 134 of file StandardLorentzianModel.cc.

{
  return std::pow(e_gamma, 3 - 2*l)
    * strength_function_coefficient(type, l, e_gamma);
}

Referenced by StandardLorentzianModel().

transmission_coefficient()

double marley::StandardLorentzianModel::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 141 of file StandardLorentzianModel.cc.

{
  // Eg^4 = (Eg^[2l + 1] * Eg^[3 - 2l]
  return 2. * marley_utils::pi * strength_function_coefficient(type, l, e_gamma)
    * std::pow(e_gamma, 4);
}

---

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

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