marley::KoningDelarocheOpticalModel Class Reference

Nuclear optical model for fragment emission calculations. More...

#include <KoningDelarocheOpticalModel.hh>

Inheritance diagram for marley::KoningDelarocheOpticalModel:

Classes
class	ParamConfig

Public Member Functions
	KoningDelarocheOpticalModel (int Z, int A, const JSON &om_config)
virtual std::complex< double >	optical_model_potential (double r, double fragment_KE_lab, int fragment_pdg, int two_j, int l, int two_s, int target_charge=0) override
	Calculate the optical model potential (including the Coulomb potential)
virtual void	print (std::ostream &out) const override
	Print information about the optical model parameters.
virtual double	total_cross_section (double fragment_KE_lab, int fragment_pdg, int two_s, size_t l_max, int target_charge=0) override
	Compute the energy-averaged total cross section (MeV -2) for a nuclear fragment projectile.
Public Member Functions inherited from marley::CachedOpticalModel
	CachedOpticalModel (int Z, int A)
virtual double	transmission_coefficient (double total_KE_CM, int fragment_pdg, int two_j, int l, int two_s, int target_charge=0) override
	Calculate the transmission coefficient for a nuclear fragment.
Public Member Functions inherited from marley::OpticalModel
	OpticalModel (int Z, int A)
int	A () const
	Get the mass number.
int	Z () const
	Get the atomic number.

Additional Inherited Members
Static Public Member Functions inherited from marley::CachedOpticalModel
static void	set_use_cache (bool use_it)
Protected Attributes inherited from marley::CachedOpticalModel
std::map< TCKey, std::shared_ptr< InterpolatingFunction > >	tc_cache_
	Saved InterpolatingFunction objects corresponding to previously-encountered transmission coefficient requests.
Protected Attributes inherited from marley::OpticalModel
int	A_
int	Z_
Static Protected Attributes inherited from marley::CachedOpticalModel
static constexpr double	MAX_TOTAL_KE_CM = 100.
	Maximum kinetic energy to use when interacting with the cache.
static constexpr double	MIN_TOTAL_KE_CM = 1e-10
	Minimum kinetic energy to use when interacting with the cache.
static bool	USE_CACHE = true
	Boolean switch that allows global enabling/disabling of the cache, which is used by default.

Detailed Description

Nuclear optical model for fragment emission calculations.

This class implements the global optical model potential of A. J. Koning and J. P. Delaroche, Nucl. Phys. A 713 (2003) 231-310. Numerov's method is used to integrate the Schrödinger equation during transmission coefficient and cross section calculations.

Definition at line 41 of file KoningDelarocheOpticalModel.hh.

Constructor & Destructor Documentation

KoningDelarocheOpticalModel()

marley::KoningDelarocheOpticalModel::KoningDelarocheOpticalModel	(	int	Z,
		int	A,
		const JSON &	om_config )

Parameters

Z	Atomic number of the desired nuclide
A	Mass number of the desired nuclide
om_config	JSON object containing the parameter values for the optical model calculation

Definition at line 25 of file KoningDelarocheOpticalModel.cc.

                                       : marley::CachedOpticalModel( Z, A )
{
  // Set the step size (fm) for numerically solving the Schrodinger equation
  // using Numerov's method
  get_from_json( "step_size", om_config, step_size_,
    DEFAULT_NUMEROV_STEP_SIZE_ );
 
  // Calculate the target mass
  const auto& mt = marley::MassTable::Instance();
  target_mass_ = mt.get_atomic_mass( Z, A );
 
  // Parse the JSON input needed to set up the optical model parameters
  marley::KoningDelarocheOpticalModel::ParamConfig om( om_config );
 
  // Initialize the spherical optical model parameters (see
  // https://doi.org/10.1103/PhysRevC.107.014602)
 
  int N = A_ - Z_; // Neutron number
  double alpha = ( N - Z_ ) / static_cast< double >( A_ );
 
  double A_to_the_one_third = std::pow( A_, 1.0/3.0 );
 
  // Neutrons
  v1n = om["v10"] - om["v1A"]*A_ - om["v1alpha"]*alpha; // MeV
  v2n = om["vn20"] - om["vn2A"]*A_; // MeV^(-1)
  v3n = om["vn30"] - om["vn3A"]*A_; // MeV^(-2)
  v4n = om["v40"]; // MeV^(-3)
  w1n = om["wn10"] + om["wn1A"]*A_; // MeV
  w2n = om["w20"] + om["w2A"]*A_; // MeV
  d1n = om["d10"] - om["d1alpha"]*alpha; // MeV
  d2n = om["d20"] + om["d2A"]/( 1. + std::exp(
    ( A_ - om["d2A3"]) / om["d2A2"] )
  ); // MeV^(-1)
  d3n = om["d30"]; // MeV
  vso1n = om["vSO10"] + om["vSO1A"]*A_; // MeV
  vso2n = om["vSO20"]; // MeV^(-1)
  wso1n = om["wSO10"]; // MeV
  wso2n = om["wSO20"]; // MeV
  Efn = -11.2814 + 0.02646*A_; // MeV
  Rvn = om["rV0"]*A_to_the_one_third - om["rVA"]; // fm
  avn = om["aV0"] - om["aVA"]*A_; // fm
  Rdn = om["rD0"]*A_to_the_one_third
    - om["rDA"]*std::pow( A_to_the_one_third, 2 ); // fm
  adn = om["anD0"] - om["anDA"]*A_; // fm
  Rso_n = om["rSO0"]*A_to_the_one_third - om["rSOA"]; // fm
  aso_n = om["aSO0"]; // fm
 
  // Protons
  v1p = om["v10"] - om["v1A"]*A_ + om["v1alpha"]*alpha; // MeV
  v2p = om["vp20"] + om["vp2A"]*A_; // MeV^(-1)
  v3p = om["vp30"] + om["vp3A"]*A_; // MeV^(-2)
  v4p = om["v40"]; // MeV^(-3)
  w1p = om["wp10"] + om["wp1A"]*A_; // MeV
  w2p = om["w20"] + om["w2A"]*A_; // MeV
  d1p = om["d10"] + om["d1alpha"]*alpha; // MeV
  d2p = om["d20"] + om["d2A"]/( 1. + std::exp(
    ( A_ - om["d2A3"]) / om["d2A2"] )
  ); // MeV^(-1)
  d3p = om["d30"]; // MeV
  vso1p = om["vSO10"] + om["vSO1A"]*A_; // MeV
  vso2p = om["vSO20"]; // MeV^(-1)
  wso1p = om["wSO10"]; // MeV
  wso2p = om["wSO20"]; // MeV
  Efp = -8.4075 + 0.01378*A_; // MeV
  Rvp = om["rV0"]*A_to_the_one_third - om["rVA"]; // fm
  avp = om["aV0"] - om["aVA"]*A_; // fm
  Rdp = om["rD0"]*A_to_the_one_third
    - om["rDA"]*std::pow( A_to_the_one_third, 2 ); // fm
  adp = om["apD0"] + om["apDA"]*A_; // fm
  Rso_p = om["rSO0"]*A_to_the_one_third - om["rSOA"]; // fm
  aso_p = om["aSO0"]; // fm
  Rc = om["rC0"]*A_to_the_one_third + om["rCA"]/A_to_the_one_third
    + om["rCA2"]*std::pow( A_to_the_one_third, -4 ); // fm
 
  // Note that Koning and Delaroche approximated (6/5)*e^2 = 1.73 in their
  // original paper, following a book by Wilkinson cited in their bibliography.
  Vcbar_p = 6. * Z_ * marley_utils::e2 / ( 5. * Rc ); // MeV
}

References marley::CachedOpticalModel::CachedOpticalModel(), marley::OpticalModel::A(), marley::MassTable::Instance(), and marley::OpticalModel::Z().

Member Function Documentation

optical_model_potential()

std::complex< double > marley::KoningDelarocheOpticalModel::optical_model_potential ( double r, double fragment_KE_lab, int fragment_pdg, int two_j, int l, int two_s, int target_charge = 0 )

overridevirtual

Calculate the optical model potential (including the Coulomb potential)

Parameters

r	Distance from nuclear center (fm)
fragment_KE_lab	Fragment kinetic energy (MeV) in the lab frame
fragment_pdg	PDG code for the nuclear fragment
two_j	Two times the total angular momentum of the fragment
l	Orbital angular momentum of the fragment
two_s	Two times the spin of the fragment
target_charge	Net charge of the target atom

Returns

Complex-valued optical model potential (MeV)

Todo

TODO: find a better way of doing this!

Implements marley::OpticalModel.

Definition at line 106 of file KoningDelarocheOpticalModel.cc.

{
  update_target_mass( target_charge );
 
  // The calculate_kinematic_variables() function will set the fragment_mass_
  // member variable, but we need that value in advance in order to provide the
  // total CM frame kinetic energy as input. To get around this, retrieve the
  // fragment mass directly from the mass table instead
  const auto& mt = marley::MassTable::Instance();
  double m_fragment = mt.get_particle_mass( fragment_pdg );
 
  double KE_tot_CM = std::max( 0., marley_utils::real_sqrt(
    std::pow(target_mass_ + m_fragment, 2)
    + 2.*target_mass_*fragment_KE_lab) - m_fragment - target_mass_ );
 
  calculate_kinematic_variables( KE_tot_CM, fragment_pdg );
  calculate_om_parameters( fragment_pdg, two_j, l, two_s );
  return omp( r );
}

References marley::MassTable::Instance().

print()

void marley::KoningDelarocheOpticalModel::print ( std::ostream & out ) const

overridevirtual

Print information about the optical model parameters.

Implements marley::OpticalModel.

Definition at line 559 of file KoningDelarocheOpticalModel.cc.

{
  out << "----------------------------------------------------------\n";
  out << "KD optical model for Z = " << Z_ << ", A = " << A_ << '\n';
  out << "----------------------------------------------------------\n";
  out << "Neutron parameters:\n\n";
 
  out << "  v1n = " << v1n << " MeV\n";
  out << "  v2n = " << v2n << " MeV^{-1}\n";
  out << "  v3n = " << v3n << " MeV^{-2}\n";
  out << "  v4n = " << v4n << " MeV^{-3}\n\n";
 
  out << "  w1n = " << w1n << " MeV\n";
  out << "  w2n = " << w2n << " MeV\n\n";
 
  out << "  d1n = " << d1n << " MeV\n";
  out << "  d2n = " << d2n << " MeV^{-1}\n";
  out << "  d3n = " << d3n << " MeV\n\n";
 
  out << "  vso1n = " << vso1n << " MeV\n";
  out << "  vso2n = " << vso2n << " MeV^{-1}\n\n";
 
  out << "  wso1n = " << wso1n << " MeV\n";
  out << "  wso2n = " << wso2n << " MeV\n\n";
 
  out << "  Efn = " << Efn << " MeV\n\n";
 
  out << "  Rvn = " << Rvn << " fm\n";
  out << "  avn = " << avn << " fm\n";
  out << "  Rdn = " << Rdn << " fm\n";
  out << "  adn = " << adn << " fm\n";
  out << "  Rso_n = " << Rso_n << " fm\n";
  out << "  aso_n = " << aso_n << " fm\n";
 
  out << "----------------------------------------------------------\n";
  out << "Proton parameters:\n\n";
 
  out << "  v1p = " << v1p << " MeV\n";
  out << "  v2p = " << v2p << " MeV^{-1}\n";
  out << "  v3p = " << v3p << " MeV^{-2}\n";
  out << "  v4p = " << v4p << " MeV^{-3}\n\n";
 
  out << "  w1p = " << w1p << " MeV\n";
  out << "  w2p = " << w2p << " MeV\n\n";
 
  out << "  d1p = " << d1p << " MeV\n";
  out << "  d2p = " << d2p << " MeV^{-1}\n";
  out << "  d3p = " << d3p << " MeV\n\n";
 
  out << "  vso1p = " << vso1p << " MeV\n";
  out << "  vso2p = " << vso2p << " MeV^{-1}\n\n";
 
  out << "  wso1p = " << wso1p << " MeV\n";
  out << "  wso2p = " << wso2p << " MeV\n\n";
 
  out << "  Efp = " << Efp << " MeV\n\n";
 
  out << "  Rvp = " << Rvp << " fm\n";
  out << "  avp = " << avp << " fm\n";
  out << "  Rdp = " << Rdp << " fm\n";
  out << "  adp = " << adp << " fm\n";
  out << "  Rso_p = " << Rso_p << " fm\n";
  out << "  aso_p = " << aso_p << " fm\n\n";
 
  out << "  Rc = " << Rc << " fm\n";
  out << "  Vcbar_p = " << Vcbar_p << " MeV\n";
  out << "----------------------------------------------------------\n";
  out << "  Step size = " << step_size_ << " fm\n";
  out << "----------------------------------------------------------\n";
}

total_cross_section()

double marley::KoningDelarocheOpticalModel::total_cross_section ( double fragment_KE_lab, int fragment_pdg, int two_s, size_t l_max, int target_charge = 0 )

overridevirtual

Compute the energy-averaged total cross section (MeV ^-2) for a nuclear fragment projectile.

The total cross section given here by the optical model may be directly compared to experiment. Expressions exist for the optical model elastic and reaction (absorption) cross sections, but these are hard to directly compare to the data because the absorption cross section includes the compound elastic channel.

For more details, see appendix A (especially equation A.12) of S. Gardiner, "Nuclear Effects in Neutrino Detection," PhD thesis, University of California, Davis, 2018. Note that we assume in this function that the target nucleus has zero spin (spherical optical model).

Parameters

fragment_KE_lab	Lab-frame kinetic energy of the incident projectile (MeV)
fragment_pdg	Projectile's PDG code
two_s	Two times the spin of the projectile
l_max	The maximum value of the orbital angular momentum quantum number \(\ell\) to include in the sum over S-matrix elements
target_charge	Net charge of the target atom (used to adjust the atomic mass by the appropriate number of electron masses if the target is ionized)

Returns

Energy-averaged total scattering cross section (MeV ^-2)

Todo

TODO: find a better way of doing this!

Implements marley::OpticalModel.

Definition at line 275 of file KoningDelarocheOpticalModel.cc.

{
  update_target_mass( target_charge );
 
  // The calculate_kinematic_variables() function will set the fragment_mass_
  // member variable, but we need that value in advance in order to provide the
  // total CM frame kinetic energy as input. To get around this, retrieve the
  // fragment mass directly from the mass table instead
  const auto& mt = marley::MassTable::Instance();
  double m_fragment = mt.get_particle_mass( fragment_pdg );
 
  double KE_tot_CM = std::max( 0., marley_utils::real_sqrt(
    std::pow(target_mass_ + m_fragment, 2)
    + 2.*target_mass_*fragment_KE_lab) - m_fragment - target_mass_ );
 
  calculate_kinematic_variables( KE_tot_CM, fragment_pdg );
 
  double sum = 0.;
  for ( size_t l = 0; l <= l_max; ++l ) {
    int two_l = 2*l;
    for ( int two_j = std::abs(two_l - two_s);
      two_j <= two_l + two_s; two_j += 2 )
    {
      std::complex< double > S = s_matrix_element( fragment_pdg, two_j,
        l, two_s );
      sum += ( two_j + 1 ) * ( 1. - S.real() );
    }
  }
 
  // Compute the cross section in natural units (MeV^(-2))
  double xs = marley_utils::two_pi * sum / ( (two_s + 1)
    * CM_frame_momentum_squared_ );
  return xs;
}

References marley::MassTable::Instance().

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

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