MaterialInteraction.cxx

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/*
  Copyright (C) 2002-2023 CERN for the benefit of the ATLAS collaboration
*/
 
// MaterialInteraction.cxx, (c) ATLAS Detector software
#include "TrkExUtils/MaterialInteraction.h"
 
#include <cmath>
#include "CxxUtils/inline_hints.h"
 
namespace {
 
constexpr double s_me = Trk::ParticleMasses::mass[Trk::electron];
 
//The following were repeated in the code.
//Now moved to helpers, lets keep the same
//semantics as before for all builds.
 
// mean excitation energy --> I
ATH_ALWAYS_INLINE
double
MeanExcitationEnergy(const Trk::Material& mat) {
  // 16 eV * Z**0.9 - bring to MeV
  return 16.e-6 * std::pow(mat.averageZ(), 0.9);
}
 
ATH_ALWAYS_INLINE
double
DensityEffect(const double zOverAtimesRho, const double eta,
              const double gamma, const double I) {
 
  // density effect. Done for gamma > 10  ( p > 1GeV for muons)
  // see ATLASRECTS-3144 and ATLASRECTS-7586
  // for possible issues
  if (gamma > 10.) {
    // PDG 2022 Table 34.1
    double eplasma = 28.816e-6 * std::sqrt(1000. * zOverAtimesRho);
    // PDG 2022 Eq. 34.6
    //2. * std::log(eplasma / I) + std::log(eta2) - 1.
    //applying logarithmic identities becomes
    // 2*(log(eplasma/I) + log(eta))  = 2*log(eplasma*eta/I)
    return 2. * std::log(eplasma*eta / I) - 1.;
  }
  return 0;
}
 
ATH_ALWAYS_INLINE
double
KAZ(const double zOverAtimesRho) {
  // K/A*Z = 0.5 * 30.7075MeV/(g/mm2) * Z/A * rho[g/mm3]
  return 0.5 * 30.7075 * zOverAtimesRho;
}
 
ATH_ALWAYS_INLINE
double
LandauMPV(const double kazL, const double eta2, const double I,
          const double beta, const double delta) {
  // PDG 2022 Eq 34.12
  // then apply logarithmic identity
  // log(2. * s_me * eta2 / I) + log(kazL / I) = log(2. * s_me* eta2 * kazL/(I*I))
  return -kazL * (std::log(2. * s_me * eta2*kazL/(I*I)) + 0.2 -
                  (beta * beta) - delta);
}
 
}  // namespace
 
double Trk::MaterialInteraction::dEdl_ionization(
    double p, const Trk::Material& mat, Trk::ParticleHypothesis particle,
    double& sigma, double& kazL) {
 
  sigma = 0.;
  kazL = 0.;
  if (mat.averageZ() < 1) {
    return 0.;
  }
  const double m = Trk::ParticleMasses::mass[particle];
  const double mfrac = s_me / m;
  const double E = std::sqrt(p * p + m * m);
  const double beta = p / E;
  const double gamma = E / m;
  const double I = MeanExcitationEnergy(mat);
  const double zOverAtimesRho = mat.zOverAtimesRho();
  double kaz = KAZ(zOverAtimesRho);
  double Ionization = 0.;
 
  if (particle == Trk::electron) {
    // for electrons use slightly different BetheBloch adaption
    // see Stampfer, et al, "Track Fitting With Energy Loss", Comp. Pyhs. Comm.
    // 79 (1994), 157-164
    Ionization = -kaz * (2. * log(2. * s_me / I) + 3. * log(gamma) - 1.95);
    //  sigmaL --> FWHM of Landau
    sigma = 4 * kaz;
  } else {
    const double eta = beta * gamma;
    const double eta2 = eta*eta;
    const double delta = DensityEffect(zOverAtimesRho, eta, gamma, I);
    // tmax - cut off energy
    const double tMax =
        2. * eta2 * s_me / (1. + 2. * gamma * mfrac + mfrac * mfrac);
    // divide by beta^2 for non-electrons
    kaz /= beta * beta;
    // PDG 2022 Eq 34.5
    Ionization = -kaz * (std::log(2. * s_me * eta2 * tMax / (I * I)) -
                         2. * (beta * beta) - delta);
    // The MPV is path lenght dependent, here we set pathlenght = 1 (mm)
    // so kazL = kaz
    const double MPV = LandauMPV(kaz, eta2, I, beta, delta);
    constexpr double factor = (1. / 3.59524);
    sigma = -(Ionization - MPV) * factor;
    kazL = kaz * factor;
  }
  return Ionization;
}
 
double Trk::MaterialInteraction::dEdXBetheBloch(
    const Trk::MaterialProperties& mat, double beta, double gamma,
    Trk::ParticleHypothesis particle) {
  if (particle == Trk::undefined || particle == Trk::nonInteracting) {
    return 0.;
  }
 
  if (mat.averageZ() == 0. || mat.zOverAtimesRho() == 0.) {
    return 0.;
  }
  const double iPot = 16.e-6 * std::pow(mat.averageZ(), 0.9);
  const double m = Trk::ParticleMasses::mass[particle];
  const double zOverAtimesRho = mat.zOverAtimesRho();
  double kaz = KAZ(mat.zOverAtimesRho());
 
  if (particle != Trk::electron) {
    const double eta = beta * gamma;
    const double eta2 = eta*eta;
    double delta = DensityEffect(zOverAtimesRho, eta, gamma, iPot);
    // mass fraction
    double mfrac = s_me / m;
    // tmax - cut off energy
    double tMax = 2. * eta2 * s_me / (1. + 2. * gamma * mfrac + mfrac * mfrac);
    // divide by beta^2 for non-electrons
    kaz /= beta * beta;
    // return PDG 2022 Eq 34.5
    return kaz * (std::log(2. * s_me * eta2 * tMax / (iPot * iPot)) -
                  2. * (beta * beta) - delta);
  }
  // for electrons use slightly different BetheBloch adaption
  // see Stampfer, et al, "Track Fitting With Energy Loss", Comp. Pyhs. Comm. 79
  // (1994), 157-164
  return kaz * (2. * std::log(2. * s_me / iPot) + 3. * std::log(gamma) - 1.95);
}
 
double Trk::MaterialInteraction::dE_MPV_ionization(
    double p, const Trk::Material& mat, Trk::ParticleHypothesis particle,
    double& sigma, double& kazL, double path) {
 
  const double m = Trk::ParticleMasses::mass[particle];
  const double E = std::sqrt(p * p + m * m);
  const double beta = p / E;
  const double gamma = E / m;
  const double I = MeanExcitationEnergy(mat);
  const double zOverAtimesRho = mat.zOverAtimesRho();
  double kaz = KAZ(zOverAtimesRho);
  const double eta = beta * gamma;
  const double eta2 = eta*eta;
  const double delta = DensityEffect(zOverAtimesRho, eta, gamma, I);
  // divide by beta^2 for non-electrons
  kaz /= beta * beta;
  kazL = kaz * path;
  const double MPV = LandauMPV(kazL, eta2, I, beta, delta);
  sigma = 0.424 * 4. * kazL;  // 0.424 FWHM to sigma
 
  return MPV;
}
 
double Trk::MaterialInteraction::dEdl_radiation(
    double p, const Trk::Material& mat, Trk::ParticleHypothesis particle,
    double& sigma) {
  sigma = 0.;
  if (mat.x0() == 0.)
    return 0.;
 
  // preparation of kinetic constants
  const double m = Trk::ParticleMasses::mass[particle];
  const double mfrac = s_me / m;
  const double E = sqrt(p * p + m * m);
 
  // Bremsstrahlung - Bethe-Heitler
  double Radiation = -E * mfrac * mfrac;
  // sigma the rms of steep exponential
  sigma = -Radiation;
 
  // Add e+e- pair production and photonuclear effect for muons at energies
  // above 8 GeV
  // Radiation gives mean Eloss including the long tail from 'catastrophic'
  // Eloss sigma the rms of steep exponential
  // For the parametrization see section 2.3 of Ref [4]
  if ((particle == Trk::muon) && (E > 8000.)) {
    if (E < 1.e6) {
      Radiation += 0.5345 - 6.803e-5 * E - 2.278e-11 * E * E +
                   9.899e-18 * E * E * E;  // E below 1 TeV
      sigma += (0.1828 - 3.966e-3 * std::sqrt(E) + 2.151e-5 * E);  // idem
    } else {
      Radiation += 2.986 - 9.253e-5 * E;           // E above 1 TeV
      sigma += 17.73 + 2.409e-5 * (E - 1000000.);  // idem
    }
  }
  sigma = sigma / mat.x0();
 
  return Radiation / mat.x0();
}
 
double Trk::MaterialInteraction::dEdXBetheHeitler(
    const Trk::MaterialProperties& mat, double initialE,
    Trk::ParticleHypothesis particle) {
  if (particle == Trk::undefined || particle == Trk::nonInteracting) {
    return 0.;
  }
  double mfrac = (s_me / Trk::ParticleMasses::mass[particle]);
  mfrac *= mfrac;
  return initialE / mat.x0() * mfrac;
}
 
double Trk::MaterialInteraction::sigmaMS(double dInX0, double p, double beta) {
 
  if (dInX0 == 0. || p == 0. || beta == 0.) {
    return 0.;
  }
  // Improved (See [5] Lynch & Dahl) Highland formula
  // projected sigma_s PDG 2022 34.16
  return 13.6 * std::sqrt(dInX0) / (beta * p) *
         (1. + 0.038 * std::log(dInX0 / (beta * beta)));
}