Trk::MaterialInteraction Class Reference

#include <MaterialInteraction.h>

Collaboration diagram for Trk::MaterialInteraction:

Static Public Member Functions
static double	dEdl_ionization (double p, const Material &mat, ParticleHypothesis particle, double &sigma, double &kazL)
	dE/dl ionization energy loss per path unit More...
static double	dEdXBetheBloch (const Trk::MaterialProperties &mat, double beta, double gamma, Trk::ParticleHypothesis particle)
	dE/dl ionization energy loss per path unit More...
static double	dE_MPV_ionization (double p, const Trk::Material &mat, Trk::ParticleHypothesis particle, double &sigma, double &kazL, double path)
	Most Propable dE ionization energly loss. More...
static double	dEdl_radiation (double p, const Material &mat, ParticleHypothesis particle, double &sigma)
	dE/dl radiation energy loss per path unit More...
static double	dEdXBetheHeitler (const Trk::MaterialProperties &mat, double initialE, Trk::ParticleHypothesis particle)
static double	sigmaMS (double dInX0, double p, double beta)
	multiple scattering as function of dInX0 More...

Detailed Description

Collection of parametrizations used in the Tracking realm

Author

sarka.nosp@m..tod.nosp@m.orova.nosp@m.@cer.nosp@m.n.ch

Christos Anastopoulos (Athena MT)

Definition at line 24 of file MaterialInteraction.h.

Member Function Documentation

dE_MPV_ionization()

double Trk::MaterialInteraction::dE_MPV_ionization ( double  p, const Trk::Material &  mat, Trk::ParticleHypothesis  particle, double &  sigma, double &  kazL, double  path  )

static

Most Propable dE ionization energly loss.

Most Propable dE ionization energly loss It returns dE in MeV.

For the meaning of sigma, kazL look at comments on std Landau distribution

Definition at line 205 of file MaterialInteraction.cxx.

                                              {
 
  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;
}

dEdl_ionization()

double Trk::MaterialInteraction::dEdl_ionization ( double  p, const Material &  mat, Trk::ParticleHypothesis  particle, double &  sigma, double &  kazL  )

static

dE/dl ionization energy loss per path unit

dE/dl ionization energy loss per path unit It returns de/dl in MeV/mm For the meaning of sigma and kazL look at comments on the ATLAS Landau approximation.

Definition at line 117 of file MaterialInteraction.cxx.

                                 {
 
  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;
}

dEdl_radiation()

double Trk::MaterialInteraction::dEdl_radiation ( double  p, const Material &  mat, Trk::ParticleHypothesis  particle, double &  sigma  )

static

dE/dl radiation energy loss per path unit

Definition at line 229 of file MaterialInteraction.cxx.

                   {
  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();
}

dEdXBetheBloch()

double Trk::MaterialInteraction::dEdXBetheBloch ( const Trk::MaterialProperties &  mat, double  beta, double  gamma, Trk::ParticleHypothesis  particle  )

static

dE/dl ionization energy loss per path unit

Definition at line 165 of file MaterialInteraction.cxx.

                                    {
  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);
}

dEdXBetheHeitler()

double Trk::MaterialInteraction::dEdXBetheHeitler ( const Trk::MaterialProperties &  mat, double  initialE, Trk::ParticleHypothesis  particle  )

static

Definition at line 266 of file MaterialInteraction.cxx.

                                    {
  if (particle == Trk::undefined || particle == Trk::nonInteracting) {
    return 0.;
  }
  double mfrac = (s_me / Trk::ParticleMasses::mass[particle]);
  mfrac *= mfrac;
  return initialE / mat.x0() * mfrac;
}

sigmaMS()

double Trk::MaterialInteraction::sigmaMS ( double  dInX0, double  p, double  beta  )

static

multiple scattering as function of dInX0

Definition at line 278 of file MaterialInteraction.cxx.

                                                                          {
 
  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)));
}

---

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

• MaterialInteraction.h
• MaterialInteraction.cxx