MARLEY (Model of Argon Reaction Low Energy Yields)  v1.1.0 A Monte Carlo event generator for tens-of-MeV neutrino-nucleus interactions in liquid argon
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. More...

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. More...

Public Member Functions inherited from marley::GammaStrengthFunctionModel
GammaStrengthFunctionModel (int Z, int A)

double transmission_coefficient (double Exi, int twoJ, marley::Parity Pi, marley::Level &level_f)
Returns the gamma-ray transmission coefficient (dimensionless) for a transition from a given initial state to a final discrete Level. More...

Public Types inherited from marley::GammaStrengthFunctionModel
enum  TransitionType { electric, magnetic, unphysical }
Electromagnetic transitions in nuclei may be classified by their multipolarity (electric vs. magnetic multipole radiation)

Static Public Member Functions inherited from marley::GammaStrengthFunctionModel
static TransitionType determine_transition_type (int twoJi, marley::Parity Pi, int twoJf, marley::Parity Pf, int &l)
Determines whether a given electromagnetic transition between two nuclear states corresponds to electric or magnetic multipole radiation. More...

static TransitionType determine_transition_type (int twoJi, marley::Parity Pi, marley::Level &level_f, int &l)
Determines whether a given electromagnetic transition between two nuclear states corresponds to electric or magnetic multipole radiation. More...

static TransitionType determine_transition_type (marley::Level &level_i, marley::Level &level_f, int &l)
Determines whether a given electromagnetic transition between two nuclear states corresponds to electric or 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. More...

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.

TransitionParametersUnits 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

## Constructor & Destructor Documentation

 marley::StandardLorentzianModel::StandardLorentzianModel ( int Z, int A )
Note
Be careful! You must initialize the E1 giant resonance parameters before the M1 parameters!

## Member Function Documentation

 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.

 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.

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