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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/xs/ScreeningFunctions.hh
 //---------------------------------------------------------------------------//
 #pragma once
 
 #include "corecel/Macros.hh"
 #include "corecel/Types.hh"
 #include "corecel/math/PolyEvaluator.hh"
 #include "corecel/math/Quantity.hh"
 #include "corecel/math/UnitUtils.hh"
 #include "celeritas/Quantities.hh"
 
 namespace celeritas
 {
 //---------------------------------------------------------------------------//
 /*!
  * Bethe-Heitler-Wheeler-Lamb screening factors for use in atomic showers.
  *
  * These are derived from \citet{bethe-stopping-1934,
  * https://doi.org/10.1098/rspa.1934.0140} (Eq. 31) for the \f$ \phi\f$
  * (elastic) components and \citet{wheeler-electrons-1939,
  * https://doi.org/10.1103/PhysRev.55.858} for the \f$ \psi \f$ (inelastic)
  * components.
  */
 struct BhwlScreeningFactors
 {
     //! Elastic component, to be multiplied into Z^2
     real_type phi1{};
     //! \f$\phi_1 - \phi_2\f$ corrective term for low-energy secondary
     real_type dphi{};
     //! Inelastic component, to be multiplied into Z
     real_type psi1{};
     //! \f$\psi_1 - \psi_2\f$ corrective term for low-energy secondary
     real_type dpsi{};
 };
 
 //---------------------------------------------------------------------------//
 /*!
  * Thomas-Fermi screening functions from Tsai.
  *
  * This calculates atomic screening factors given by  \citet{tsai-1974,
  * https://doi.org/10.1103/RevModPhys.46.815} Eq. 3.30-31, as part of the
  * relativistic bremsstrahlung cross section calculation.
  * This model is valid for \f$ Z \ge 5 \f$.
  *
  * The calculator argument is the fraction \f[
  * \delta = \frac{k}{E(k - E)} \equiv \frac{2\delta_\mathrm{Tsai}}{m_e}
  * \f]
  * where \f$E\f$ is the kinetic plus rest mass energy of the electron
  * and \f$k\f$ is the photon energy. (For Bremsstrahlung, the electron is
  * incident and photon is exiting.)
  *
  * The calculated screening functions are:
  * \f[
    \begin{aligned}
    \varphi_1(\gamma) &= 20.863 - 2 \ln \left( 1 + (0.55846\gamma)^2 \right)
      - 4 \left( 1 - 0.6 \exp(-0.9\gamma) - 0.4 \exp(-1.5\gamma) \right), \\
    \varphi_2(\gamma) = \varphi_1(\gamma)
      - \frac{2}{3} \left( 1 + 6.5\gamma + 6\gamma^2 \right)^{-1}, \\
    \psi_1(\epsilon) &= 28.340 - 2 \ln \left( 1 + (3.621\epsilon)^2 \right)
      - 4 \left( 1 - 0.7 \exp(-8\epsilon) - 0.3 \exp(-29.2\epsilon) \right),
    \psi_2(\epsilon) &= \psi_1(\epsilon)
      - \frac{2}{3} \left( 1 + 40\epsilon + 400\epsilon^2 \right)^{-1}.
    \end{aligned}
  * \f]
  *
  * Here,
  * \f[
    \begin{aligned}
    \gamma &= \frac{100 m_e k}{E (k - E) Z^{1/3}} \\
    \epsilon &= \frac{100 m_e k}{E (k - E) Z^{2/3}}
    \end{aligned}
  * \f]
  * from which we extract input factors precalculated in
  * \c celeritas::RelativisticBremModel:
  * \f[
  * f_\gamma = \frac{100 m_e}{Z^{1/3}}
  * \f]
  * and
  * \f[
  * f_\epsilon = \frac{100 m_e}{Z^{2/3}}
  * \f]
  *
  * \sa RBDiffXsCalculator
  */
 class TsaiScreeningCalculator
 {
   public:
     //!@{
     //! \name Type aliases
     using result_type = BhwlScreeningFactors;
     using Mass = units::MevMass;
     using InvEnergy = RealQuantity<UnitInverse<units::Mev>>;
     //!@}
 
   public:
     // Construct with defaults
     CELER_FUNCTION inline TsaiScreeningCalculator(Mass gamma_factor,
                                                   Mass epsilon_factor);
 
     // Calculate screening function from energy transfer
     CELER_FUNCTION inline result_type operator()(InvEnergy delta) const;
 
   private:
     real_type f_gamma_;
     real_type f_epsilon_;
 };
 
 //---------------------------------------------------------------------------//
 // INLINE DEFINITIONS
 //---------------------------------------------------------------------------//
 /*!
  * Construct with gamma and epsilon factors.
  */
 CELER_FUNCTION
 TsaiScreeningCalculator::TsaiScreeningCalculator(Mass gamma_factor,
                                                  Mass epsilon_factor)
     : f_gamma_{gamma_factor.value()}, f_epsilon_{epsilon_factor.value()}
 {
     CELER_EXPECT(epsilon_factor > zero_quantity());
     CELER_EXPECT(gamma_factor > epsilon_factor);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate screening function from energy transfer.
  */
 CELER_FUNCTION auto TsaiScreeningCalculator::operator()(InvEnergy delta) const
     -> result_type
 {
     real_type gam = delta.value() * f_gamma_;
     real_type eps = delta.value() * f_epsilon_;
 
     using PolyQuad = PolyEvaluator<real_type, 2>;
     using R = real_type;
     result_type func;
 
     func.phi1 = R(20.863 - 4) - 2 * std::log(1 + ipow<2>(R(0.55846) * gam))
                 + R(-4 * -0.6) * std::exp(R(-0.9) * gam)
                 + R(-4 * -0.4) * std::exp(R(-1.5) * gam);
     func.dphi = (R{2} / R{3}) / PolyQuad{1, 6.5, 6}(gam);
 
     func.psi1 = R(28.340 - 4) - 2 * std::log(1 + ipow<2>(R(3.621) * eps))
                 + R(-4 * -0.7) * std::exp(R(-8) * eps)
                 + R(-4 * -0.3) * std::exp(R(-29.2) * eps);
     func.dpsi = (R{2} / R{3}) / PolyQuad{1, 40, 400}(eps);
 
     return func;
 }
 
 //---------------------------------------------------------------------------//
 }  // namespace celeritas

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