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 //------------------------------- -*- C++ -*- -------------------------------//
 // Copyright Celeritas contributors: see top-level COPYRIGHT file for details
 // SPDX-License-Identifier: (Apache-2.0 OR MIT)
 //---------------------------------------------------------------------------//
 //! \file celeritas/em/interactor/detail/SBPositronXsCorrector.hh
 //---------------------------------------------------------------------------//
 #pragma once
 
 #include <cmath>
 
 #include "corecel/Types.hh"
 #include "corecel/math/NumericLimits.hh"
 #include "celeritas/Constants.hh"
 #include "celeritas/Quantities.hh"
 #include "celeritas/mat/ElementView.hh"
 
 namespace celeritas
 {
 namespace detail
 {
 //---------------------------------------------------------------------------//
 /*!
  * Scale SB differential cross sections for positrons.
  *
  * This correction factor is the ratio of the positron to electron cross
  * sections. It appears in the bowels of \c
  * G4SeltzerBergerModel::SampleEnergyTransfer in Geant4 and scales the SB cross
  * section by a factor
  * \f[
    \frac{\sigma^+}{\sigma^-}
        = \exp( 2 \pi \alpha Z [ \beta^{-1}(E - k_c) - \beta^{-1}(E - k) ] )
  * \f]
  * where the inverse positron speed is : \f[
   \beta^{-1}(E) = \frac{c}{v} = \sqrt{1 - \left( \frac{m_e c^2}{E + m_e c^2}
   \right)^2}
   \,,
  * \f]
  * \f$ \alpha \f$ is the fine structure constant, \f$E\f$ is the
  * incident positron kinetic energy, \f$k_c\f$ is the gamma
  * production cutoff energy, and \f$ k \f$ is the provisionally sampled
  * energy of the emitted photon.
  *
  * \f$ \frac{\sigma^+}{\sigma^-} = 1 \f$ at the low end of the spectrum (where
  * \f$ k / E = 0 \f$) and is 0 at the tip of the spectrum where \f$ k / E \to 1
  * \f$.
  *
  * The correction factor is described in:
  *
  *   Kim, Longhuan, R. H. Pratt, S. M. Seltzer, and M. J. Berger. “Ratio of
  *   Positron to Electron Bremsstrahlung Energy Loss: An Approximate Scaling
  *   Law.” Physical Review A 33, no. 5 (May 1, 1986): 3002–9.
  *   https://doi.org/10.1103/PhysRevA.33.3002.
  */
 class SBPositronXsCorrector
 {
   public:
     //!@{
     using Energy = units::MevEnergy;
     using Mass = units::MevMass;
     using Xs = RealQuantity<SBElementTableData::XsUnits>;
     //!@}
 
   public:
     // Construct with positron data
     inline CELER_FUNCTION SBPositronXsCorrector(Mass positron_mass,
                                                 ElementView const& el,
                                                 Energy min_gamma_energy,
                                                 Energy inc_energy);
 
     // Calculate cross section scaling factor for the given exiting energy
     inline CELER_FUNCTION real_type operator()(Energy energy) const;
 
   private:
     //// DATA ////
 
     real_type const positron_mass_;
     real_type const alpha_z_;
     real_type const inc_energy_;
     real_type const cutoff_invbeta_;
 
     //// HELPER FUNCTIONS ////
 
     inline CELER_FUNCTION real_type calc_invbeta(real_type gamma_energy) const;
 };
 
 //---------------------------------------------------------------------------//
 // INLINE DEFINITIONS
 //---------------------------------------------------------------------------//
 /*!
  * Construct with positron data and energy range.
  */
 CELER_FUNCTION
 SBPositronXsCorrector::SBPositronXsCorrector(Mass positron_mass,
                                              ElementView const& el,
                                              Energy min_gamma_energy,
                                              Energy inc_energy)
     : positron_mass_{positron_mass.value()}
     , alpha_z_{2 * constants::pi * celeritas::constants::alpha_fine_structure
                * el.atomic_number().unchecked_get()}
     , inc_energy_(inc_energy.value())
     , cutoff_invbeta_{this->calc_invbeta(min_gamma_energy.value())}
 {
     CELER_EXPECT(inc_energy > min_gamma_energy);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate scaling factor for the given exiting gamma energy.
  *
  * Eq. 21 in Kim et al.
  */
 CELER_FUNCTION real_type SBPositronXsCorrector::operator()(Energy energy) const
 {
     CELER_EXPECT(energy > zero_quantity());
     CELER_EXPECT(energy.value() < inc_energy_);
     real_type delta = cutoff_invbeta_ - this->calc_invbeta(energy.value());
 
     // Avoid positive delta values due to floating point inaccuracies
     // See https://github.com/celeritas-project/celeritas/issues/617
     CELER_ASSERT(delta < 100 * numeric_limits<real_type>::epsilon());
     real_type result = std::exp(alpha_z_ * celeritas::min(delta, real_type{0}));
     CELER_ENSURE(result <= 1);
     return result;
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate the inverse of the relativistic positron speed.
  *
  * The input here is the exiting gamma energy, so the positron energy is the
  * remainder from the incident energy. The relativistic speed \f$ \beta \f$
  * is:
  * \f[
   \beta^{-1}(K)
    = \frac{K + m c^2}{\sqrt{K (K + 2 m c^2)}}
    = \frac{K + mc^2}{\sqrt{K^2 + 2 K mc^2 + (mc^2)^2 - (mc^2)^2}}
    = \frac{K + mc^2}{\sqrt{(K + mc^2)^2 - mc^2}}
    = 1/\sqrt{1 - \left( \frac{mc^2}{K + mc^2} \right)^2}
    = 1 / \beta(K)
  * \f]
  */
 CELER_FUNCTION real_type
 SBPositronXsCorrector::calc_invbeta(real_type gamma_energy) const
 {
     CELER_EXPECT(gamma_energy > 0 && gamma_energy < inc_energy_);
     //! \todo Use local-data ParticleTrackView
     // Positron has all the energy except what it gave to the gamma
     real_type energy = inc_energy_ - gamma_energy;
     return (energy + positron_mass_)
            / std::sqrt(energy * (energy + 2 * positron_mass_));
 }
 
 //---------------------------------------------------------------------------//
 }  // namespace detail
 }  // namespace celeritas

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