CbmLitMaterialEffectsImp.cxx

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#include "propagation/CbmLitMaterialEffectsImp.h"
 
#include "base/CbmLitDefaultSettings.h"
#include "data/CbmLitTrackParam.h"
#include "propagation/CbmLitMaterialInfo.h"
 
#include "TDatabasePDG.h"
#include "TParticlePDG.h"
 
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <iostream>
 
CbmLitMaterialEffectsImp::CbmLitMaterialEffectsImp()
  : fMass(0.105), fDownstream(true), fIsElectron(false), fIsMuon(true) {}
 
CbmLitMaterialEffectsImp::~CbmLitMaterialEffectsImp() {}
 
LitStatus CbmLitMaterialEffectsImp::Update(CbmLitTrackParam* par,
                                           const CbmLitMaterialInfo* mat,
                                           int pdg,
                                           bool downstream) {
  if (mat->GetLength() * mat->GetRho() < 1e-10) { return kLITSUCCESS; }
 
  fDownstream            = downstream;
  TDatabasePDG* db       = TDatabasePDG::Instance();
  TParticlePDG* particle = db->GetParticle(pdg);
  assert(particle != NULL);
  fMass       = particle->Mass();
  fIsElectron = (std::abs(pdg) == 11) ? true : false;
  fIsMuon     = (std::abs(pdg) == 13) ? true : false;
 
  AddEnergyLoss(par, mat);
 
  //   AddThinScatter(par, mat);
  AddThickScatter(par, mat);
 
  return kLITSUCCESS;
}
 
void CbmLitMaterialEffectsImp::AddEnergyLoss(
  CbmLitTrackParam* par,
  const CbmLitMaterialInfo* mat) const {
  if (fIsElectron) {
    litfloat radLength = mat->GetLength() / mat->GetRL();
    litfloat t;
 
    if (!fDownstream) {
      t = radLength;
    } else {
      t = -radLength;
    }
 
    litfloat qp = par->GetQp();
    qp *= std::exp(-t);
    par->SetQp(qp);
 
    litfloat cov = par->GetCovariance(18);
    cov += CalcSigmaSqQpElectron(par, mat);
    par->SetCovariance(18, cov);
  } else {
    litfloat Eloss = EnergyLoss(par, mat);
    par->SetQp(CalcQpAfterEloss(par->GetQp(), Eloss));
 
    litfloat cov = par->GetCovariance(18);
    cov += CalcSigmaSqQp(par, mat);
    par->SetCovariance(18, cov);
  }
}
 
void CbmLitMaterialEffectsImp::AddThickScatter(
  CbmLitTrackParam* par,
  const CbmLitMaterialInfo* mat) const {
  if (mat->GetLength() < 1e-10) { return; }
 
  litfloat tx        = par->GetTx();
  litfloat ty        = par->GetTy();
  litfloat thickness = mat->GetLength();  //cm
  litfloat thetaSq   = CalcThetaSq(par, mat);
 
  litfloat t = 1 + tx * tx + ty * ty;
 
  litfloat Q33 = (1 + tx * tx) * t * thetaSq;
  litfloat Q44 = (1 + ty * ty) * t * thetaSq;
  litfloat Q34 = tx * ty * t * thetaSq;
 
  litfloat T23 = (thickness * thickness) / 3.0;
  litfloat T2  = thickness / 2.0;
 
  litfloat D = (fDownstream) ? 1. : -1.;
 
  std::vector<litfloat> C = par->GetCovMatrix();
 
  C[0] += Q33 * T23;
  C[1] += Q34 * T23;
  C[2] += Q33 * D * T2;
  C[3] += Q34 * D * T2;
 
  C[6] += Q44 * T23;
  C[7] += Q34 * D * T2;
  C[8] += Q44 * D * T2;
 
  C[11] += Q33;
  C[12] += Q34;
 
  C[15] += Q44;
 
  par->SetCovMatrix(C);
}
 
void CbmLitMaterialEffectsImp::AddThinScatter(
  CbmLitTrackParam* par,
  const CbmLitMaterialInfo* mat) const {
  if (mat->GetLength() < 1e-10) { return; }
  litfloat tx      = par->GetTx();
  litfloat ty      = par->GetTy();
  litfloat thetaSq = CalcThetaSq(par, mat);
 
  litfloat t = 1 + tx * tx + ty * ty;
 
  litfloat Q33 = (1 + tx * tx) * t * thetaSq;
  litfloat Q44 = (1 + ty * ty) * t * thetaSq;
  litfloat Q34 = tx * ty * t * thetaSq;
 
  std::vector<litfloat> C = par->GetCovMatrix();
  C[11] += Q33;
  C[15] += Q44;
  C[12] += Q34;
  par->SetCovMatrix(C);
}
 
litfloat
CbmLitMaterialEffectsImp::CalcThetaSq(const CbmLitTrackParam* par,
                                      const CbmLitMaterialInfo* mat) const {
  litfloat p    = std::abs(1. / par->GetQp());  //GeV
  litfloat E    = std::sqrt(fMass * fMass + p * p);
  litfloat beta = p / E;
  litfloat x    = mat->GetLength();  //cm
  litfloat X0   = mat->GetRL();      //cm
  litfloat bcp  = beta * p;
  litfloat z    = 1.;
 
  litfloat theta = 0.0136 * (1. / bcp) * z * std::sqrt(x / X0)
                   * (1. + 0.038 * std::log(x / X0));
  return theta * theta;
}
 
litfloat
CbmLitMaterialEffectsImp::EnergyLoss(const CbmLitTrackParam* par,
                                     const CbmLitMaterialInfo* mat) const {
  litfloat length = mat->GetRho() * mat->GetLength();
  return dEdx(par, mat) * length;
  //return MPVEnergyLoss(par, mat);
}
 
litfloat CbmLitMaterialEffectsImp::dEdx(const CbmLitTrackParam* par,
                                        const CbmLitMaterialInfo* mat) const {
  litfloat dedx = BetheBloch(par, mat);
  // dedx += BetheHeitler(par, mat);
  // if (fIsMuon) dedx += PairProduction(par, mat);
  return dedx;
}
 
litfloat
CbmLitMaterialEffectsImp::BetheBloch(const CbmLitTrackParam* par,
                                     const CbmLitMaterialInfo* mat) const {
  litfloat K = 0.000307075;  // GeV * g^-1 * cm^2
  litfloat z = (par->GetQp() > 0.) ? 1 : -1.;
  litfloat Z = mat->GetZ();
  litfloat A = mat->GetA();
 
  litfloat M       = fMass;
  litfloat p       = std::abs(1. / par->GetQp());  //GeV
  litfloat E       = std::sqrt(M * M + p * p);
  litfloat beta    = p / E;
  litfloat betaSq  = beta * beta;
  litfloat gamma   = E / M;
  litfloat gammaSq = gamma * gamma;
 
  litfloat I = CalcI(Z) * 1e-9;  // GeV
 
  litfloat me    = 0.000511;  // GeV
  litfloat ratio = me / M;
  litfloat Tmax =
    (2 * me * betaSq * gammaSq) / (1 + 2 * gamma * ratio + ratio * ratio);
 
  // density correction
  litfloat dc = 0.;
  if (p > 0.5) {  // for particles above 1 Gev
    litfloat rho = mat->GetRho();
    litfloat hwp = 28.816 * std::sqrt(rho * Z / A) * 1e-9;  // GeV
    dc           = std::log(hwp / I) + std::log(beta * gamma) - 0.5;
  }
 
  return K * z * z * (Z / A) * (1. / betaSq)
         * (0.5 * std::log(2 * me * betaSq * gammaSq * Tmax / (I * I)) - betaSq
            - dc);
}
 
litfloat CbmLitMaterialEffectsImp::BetheBlochElectron(
  const CbmLitTrackParam* par,
  const CbmLitMaterialInfo* mat) const {
  litfloat K = 0.000307075;  // GeV * g^-1 * cm^2
  //myf z = (par->GetQp() > 0.) ? 1 : -1.;
  litfloat Z = mat->GetZ();
  litfloat A = mat->GetA();
 
  litfloat me    = 0.000511;                     // GeV;
  litfloat p     = std::abs(1. / par->GetQp());  //GeV
  litfloat E     = std::sqrt(me * me + p * p);
  litfloat gamma = E / me;
 
  litfloat I = CalcI(Z) * 1e-9;  // GeV
 
  if (par->GetQp() > 0) {  // electrons
    return K * (Z / A) * (std::log(2 * me / I) + 1.5 * std::log(gamma) - 0.975);
  } else {  //positrons
    return K * (Z / A) * (std::log(2 * me / I) + 2. * std::log(gamma) - 1.);
  }
}
 
litfloat CbmLitMaterialEffectsImp::CalcQpAfterEloss(litfloat qp,
                                                    litfloat eloss) const {
  litfloat massSq = fMass * fMass;
  litfloat p      = std::abs(1. / qp);
  litfloat E      = std::sqrt(p * p + massSq);
  litfloat q      = (qp > 0) ? 1. : -1.;
  if (!fDownstream) { eloss *= -1.0; }  // TODO check this
  litfloat Enew = E - eloss;
  litfloat pnew = (Enew > fMass) ? std::sqrt(Enew * Enew - massSq) : 0.;
  if (pnew != 0) {
    return q / pnew;
  } else {
    return 1e5;
  }
 
  //if (!fDownstream) eloss *= -1.0;
  //if (p > 0.) p -= eloss;
  //else p += eloss;
  //return 1./p;
}
 
litfloat
CbmLitMaterialEffectsImp::CalcSigmaSqQp(const CbmLitTrackParam* par,
                                        const CbmLitMaterialInfo* mat) const {
  litfloat P     = std::abs(1. / par->GetQp());  // GeV
  litfloat XMASS = fMass;                        // GeV
  litfloat E     = std::sqrt(P * P + XMASS * XMASS);
  litfloat Z     = mat->GetZ();
  litfloat A     = mat->GetA();
  litfloat RHO   = mat->GetRho();
  litfloat STEP  = mat->GetLength();
  litfloat EMASS = 0.511 * 1e-3;  // GeV
 
  litfloat BETA  = P / E;
  litfloat GAMMA = E / XMASS;
 
  // Calculate xi factor (KeV).
  litfloat XI = (153.5 * Z * STEP * RHO) / (A * BETA * BETA);
 
  // Maximum energy transfer to atomic electron (KeV).
  litfloat ETA   = BETA * GAMMA;
  litfloat ETASQ = ETA * ETA;
  litfloat RATIO = EMASS / XMASS;
  litfloat F1    = 2. * EMASS * ETASQ;
  litfloat F2    = 1. + 2. * RATIO * GAMMA + RATIO * RATIO;
  litfloat EMAX  = 1e6 * F1 / F2;
 
  litfloat DEDX2 = XI * EMAX * (1. - (BETA * BETA / 2.)) * 1e-12;
 
  litfloat SDEDX = (E * E * DEDX2) / std::pow(P, 6);
 
  return std::abs(SDEDX);
}
 
litfloat CbmLitMaterialEffectsImp::CalcSigmaSqQpElectron(
  const CbmLitTrackParam* par,
  const CbmLitMaterialInfo* mat) const {
  litfloat x  = mat->GetLength();  //cm
  litfloat X0 = mat->GetRL();      //cm
  return par->GetQp() * par->GetQp()
         * (std::exp(-x / X0 * std::log(3.0) / std::log(2.0))
            - std::exp(-2.0 * x / X0));
}
 
litfloat CbmLitMaterialEffectsImp::CalcI(litfloat Z) const {
  // mean excitation energy in eV
  if (Z > 16.) {
    return 10 * Z;
  } else {
    return 16 * std::pow(Z, 0.9);
  }
}
 
litfloat
CbmLitMaterialEffectsImp::BetheHeitler(const CbmLitTrackParam* par,
                                       const CbmLitMaterialInfo* mat) const {
  litfloat M     = fMass;                        //GeV
  litfloat p     = std::abs(1. / par->GetQp());  // GeV
  litfloat rho   = mat->GetRho();
  litfloat X0    = mat->GetRL();
  litfloat me    = 0.000511;  // GeV
  litfloat E     = std::sqrt(M * M + p * p);
  litfloat ratio = me / M;
 
  return (E * ratio * ratio) / (X0 * rho);
}
 
litfloat
CbmLitMaterialEffectsImp::PairProduction(const CbmLitTrackParam* par,
                                         const CbmLitMaterialInfo* mat) const {
  litfloat p   = std::abs(1. / par->GetQp());  // GeV
  litfloat M   = fMass;                        //GeV
  litfloat rho = mat->GetRho();
  litfloat X0  = mat->GetRL();
  litfloat E   = std::sqrt(M * M + p * p);
 
  return 7e-5 * E / (X0 * rho);
}
 
litfloat CbmLitMaterialEffectsImp::BetheBlochSimple(
  const CbmLitMaterialInfo* mat) const {
  return lit::CbmLitDefaultSettings::ENERGY_LOSS_CONST * mat->GetZ()
         / mat->GetA();
}
 
litfloat
CbmLitMaterialEffectsImp::MPVEnergyLoss(const CbmLitTrackParam* par,
                                        const CbmLitMaterialInfo* mat) const {
  litfloat M = fMass * 1e3;                        //MeV
  litfloat p = std::abs(1. / par->GetQp()) * 1e3;  // MeV
 
  //   myf rho = mat->GetRho();
  litfloat Z = mat->GetZ();
  litfloat A = mat->GetA();
  litfloat x = mat->GetRho() * mat->GetLength();
 
  litfloat I = CalcI(Z) * 1e-6;  // MeV
 
  litfloat K = 0.307075;  // MeV g^-1 cm^2
  litfloat j = 0.200;
 
  litfloat E       = std::sqrt(M * M + p * p);
  litfloat beta    = p / E;
  litfloat betaSq  = beta * beta;
  litfloat gamma   = E / M;
  litfloat gammaSq = gamma * gamma;
 
  litfloat ksi = (K / 2.) * (Z / A) * (x / betaSq);  // MeV
 
  //   myf hwp = 28.816 * std::sqrt(rho*Z/A) * 1e-6 ; // MeV
  //   myf dc = std::log(hwp/I) + std::log(beta*gamma) - 0.5;
  //   dc *= 2;
  litfloat dc = 0.;
 
  litfloat eloss = ksi
                   * (std::log(2 * M * betaSq * gammaSq / I) + std::log(ksi / I)
                      + j - betaSq - dc);
 
  return eloss * 1e-3;  //GeV
}