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/// \file MuCrossSections.cc
/// \brief Implementation of the MuCrossSections class

#include "MuCrossSections.hh"

#include "G4DataVector.hh"
#include "G4Exp.hh"
#include "G4Log.hh"
#include "G4Material.hh"
#include "G4MuonMinus.hh"
#include "G4NistManager.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

using namespace std;

MuCrossSections::MuCrossSections()
{
  fNist = G4NistManager::Instance();
  fMuonMass = G4MuonMinus::MuonMinus()->GetPDGMass();
  fMueRatio = fMuonMass / CLHEP::electron_mass_c2;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CR_Macroscopic(const G4String& process, const G4Material* material,
                                         G4double tkin, G4double ep)
// return the macroscopic cross section (1/L) in GEANT4 internal units
{
  const G4ElementVector* theElementVector = material->GetElementVector();
  const G4double* NbOfAtomsPerVolume = material->GetVecNbOfAtomsPerVolume();

  G4double SIGMA = 0.;
  G4int nelm = material->GetNumberOfElements();
  for (G4int i = 0; i < nelm; ++i) {
    const G4Element* element = (*theElementVector)[i];
    SIGMA += NbOfAtomsPerVolume[i] * CR_PerAtom(process, element, tkin, ep);
  }
  return SIGMA;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CR_PerAtom(const G4String& process, const G4Element* element,
                                     G4double tkin, G4double ep)
{
  G4double z = element->GetZ();
  G4double a = element->GetA();
  G4double sigma = 0.;
  if (process == "muBrems")
    sigma = CRB_Mephi(z, a / (g / mole), tkin / GeV, ep / GeV) * (cm2 / (g * GeV)) * a / Avogadro;

  else if (process == "muIoni")
    sigma = CRK_Mephi(z, a / (g / mole), tkin / GeV, ep / GeV) * (cm2 / (g * GeV)) * a / Avogadro;

  // else if (process == "muNucl")
  else if (process == "muonNuclear")
    sigma = CRN_Mephi(z, a / (g / mole), tkin / GeV, ep / GeV) * (cm2 / (g * GeV)) * a / Avogadro;

  else if (process == "muPairProd")
    sigma = CRP_Mephi(z, a / (g / mole), tkin / GeV, ep / GeV) * (cm2 / (g * GeV)) * a / Avogadro;

  else if (process == "muToMuonPairProd")
    sigma = CRM_Mephi(z, tkin, ep);

  return sigma;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CRB_Mephi(G4double z, G4double a, G4double tkin, G4double ep)

//***********************************************************************
//***        crb_g4_1.inc        in comparison with crb_.inc, following
//***        changes are introduced (September 24th, 1998):
//***                1) function crb_g4 (Z,A,Tkin,EP), Tkin is kinetic energy
//***                2) special case of hidrogen (Z<1.5; b,b1,Dn_star)
//***                Numerical comparison: 5 decimal digits coincide.
//***
//***        Cross section for bremsstrahlung by fast muon
//***        By R.P.Kokoulin, September 1998
//***        Formulae from Kelner,Kokoulin,Petrukhin 1995, Preprint MEPhI
//***        (7,18,19,20,21,25,26); Dn (18) is modified to incorporate
//***        Bugaev's inelatic nuclear correction (28) for Z > 1.
//***********************************************************************
{
  //    G4double Z,A,Tkin,EP;
  G4double crb_g4;
  G4double e, v, delta, rab0, z_13, dn, b, b1, dn_star, rab1, fn, epmax1, fe, rab2;
  //
  G4double ame = 0.51099907e-3;  // GeV
  G4double lamu = 0.105658389;  // GeV
  G4double re = 2.81794092e-13;  // cm
  G4double avno = 6.022137e23;
  G4double alpha = 1. / 137.036;
  G4double rmass = lamu / ame;  // "207"
  G4double coeff = 16. / 3. * alpha * avno * (re / rmass) * (re / rmass);  // cm^2
  G4double sqrte = 1.64872127;  // sqrt(2.71828...)
  G4double btf = 183.;
  G4double btf1 = 1429.;
  G4double bh = 202.4;
  G4double bh1 = 446.;
  //***
  if (ep >= tkin) {
    return 0.;
  }
  e = tkin + lamu;
  v = ep / e;
  delta = lamu * lamu * v / (2. * (e - ep));  // qmin
  rab0 = delta * sqrte;
  G4int Z = G4lrint(z);
  z_13 = 1. / fNist->GetZ13(z);  //
  //***       nuclear size and excitation, screening parameters
  dn = 1.54 * fNist->GetA27(Z);
  if (z <= 1.5)  // special case for hydrogen
  {
    b = bh;
    b1 = bh1;
    dn_star = dn;
  }
  else {
    b = btf;
    b1 = btf1;
    dn_star = pow(dn, (1. - 1. / z));  // with Bugaev's correction
  }
  //***                nucleus contribution logarithm
  rab1 = b * z_13;
  fn = G4Log(rab1 / (dn_star * (ame + rab0 * rab1)) * (lamu + delta * (dn_star * sqrte - 2.)));
  if (fn < 0.) fn = 0.;
  //***                electron contribution logarithm
  epmax1 = e / (1. + lamu * rmass / (2. * e));
  if (ep >= epmax1) {
    fe = 0.;
  }
  else {
    rab2 = b1 * z_13 * z_13;
    fe = G4Log(rab2 * lamu / ((1. + delta * rmass / (ame * sqrte)) * (ame + rab0 * rab2)));
    if (fe < 0.) fe = 0.;
  }
  crb_g4 = coeff * (1. - v * (1. - 0.75 * v)) * z * (z * fn + fe) / (a * ep);
  return crb_g4;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CRK_Mephi(G4double z, G4double a, G4double tkin, G4double ep)
//***********************************************************************
//***        Cross section for knock-on electron production by fast muons
//***        (including bremsstrahlung e-diagrams and rad. correction).
//***        Units: cm^2/(g*GeV); Tkin, ep - GeV.
//***        By R.P.Kokoulin, October 1998
//***        Formulae from Kelner,Kokoulin,Petrukhin, Phys.Atom.Nuclei, 1997
//***        (a bit simplified Kelner's version of Eq.30 - with 2 logarithms).
//***
{
  //    G4double Z,A,Tkin,EP;
  G4double crk_g4;
  G4double v, sigma0, a1, a3;
  //
  G4double ame = 0.51099907e-3;  // GeV
  G4double lamu = 0.105658389;  // GeV
  G4double re = 2.81794092e-13;  // cm
  G4double avno = 6.022137e23;
  G4double alpha = 1. / 137.036;
  G4double lpi = 3.141592654;
  G4double bmu = lamu * lamu / (2. * ame);
  G4double coeff0 = avno * 2. * lpi * ame * re * re;
  G4double coeff1 = alpha / (2. * lpi);
  //***

  G4double e = tkin + lamu;
  G4double epmax = e / (1. + bmu / e);
  if (ep >= epmax) {
    return 0.0;
  }
  v = ep / e;
  sigma0 = coeff0 * (z / a) * (1. - ep / epmax + 0.5 * v * v) / (ep * ep);
  a1 = G4Log(1. + 2. * ep / ame);
  a3 = G4Log(4. * e * (e - ep) / (lamu * lamu));
  crk_g4 = sigma0 * (1. + coeff1 * a1 * (a3 - a1));
  return crk_g4;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CRN_Mephi(G4double, G4double a, G4double tkin, G4double ep)

//***********************************************************************
//***        Differential cross section for photonuclear muon interaction.
//***        Formulae from Borog & Petrukhin, 1975
//***        Real photon cross section: Caldwell e.a., 1979
//***        Nuclear shadowing: Brodsky e.a., 1972
//***        Units: cm^2 / g GeV.
//***        CRN_G4_1.inc        January 31st, 1998        R.P.Kokoulin
//***********************************************************************
{
  //    G4double Z,A,Tkin,EP;
  G4double crn_g4;
  G4double e, aeff, sigph, v, v1, v2, amu2, up, down;
  //***
  G4double lamu = 0.105658389;  // GeV
  G4double avno = 6.022137e23;
  G4double amp = 0.9382723;  // GeV
  G4double lpi = 3.14159265;
  G4double alpha = 1. / 137.036;
  //***
  G4double epmin_phn = 0.20;  // GeV
  G4double alam2 = 0.400000;  // GeV**2
  G4double alam = 0.632456;  // sqrt(alam2)
  G4double coeffn = alpha / lpi * avno * 1e-30;  // cm^2/microbarn
  //***
  e = tkin + lamu;
  crn_g4 = 0.;
  if (ep >= e - 0.5 * amp || ep <= epmin_phn) return crn_g4;
  aeff = 0.22 * a + 0.78 * pow(a, 0.89);  // shadowing
  sigph = 49.2 + 11.1 * G4Log(ep) + 151.8 / std::sqrt(ep);  // microbarn
  v = ep / e;
  v1 = 1. - v;
  v2 = v * v;
  amu2 = lamu * lamu;
  up = e * e * v1 / amu2 * (1. + amu2 * v2 / (alam2 * v1));
  down = 1. + ep / alam * (1. + alam / (2. * amp) + ep / alam);
  crn_g4 = coeffn * aeff / a * sigph / ep
           * (-v1 + (v1 + 0.5 * v2 * (1. + 2. * amu2 / alam2)) * log(up / down));
  if (crn_g4 < 0.) crn_g4 = 0.;
  return crn_g4;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CRP_Mephi(G4double z, G4double a, G4double tkin, G4double ep)

//**********************************************************************
//***        crp_g4_1.inc        in comparison with crp_m.inc, following
//***        changes are introduced (January 16th, 1998):
//***                1) Avno/A, cm^2/gram GeV
//***                2) zeta_loss(E,Z)         from Kelner 1997, Eqs.(53-54)
//***                3) function crp_g4 (Z,A,Tkin,EP), Tkin is kinetic energy
//***                4) bbb=183        (Thomas-Fermi)
//***                5) special case of hidrogen (Z<1.5), bbb,g1,g2
//***                6) expansions in 'xi' are simplified        (Jan.17th,1998)
//***
//***        Cross section for electron pair production by fast muon
//***        By R.P.Kokoulin, December 1997
//***        Formulae from Kokoulin & Petrukhin 1971, Hobart, Eqs.(1,8,9,10)
{
  //    G4double Z,A,Tkin,EP;
  G4double crp_g4;
  G4double bbbtf, bbbh, g1tf, g2tf, g1h, g2h, e, z13, e1, alf, a3, bbb;
  G4double g1, g2, zeta1, zeta2, zeta, z2, screen0, a0, a1, bet, xi0, del;
  G4double tmn, sum, a4, a5, a6, a7, a9, xi, xii, xi1, screen, yeu, yed, ye1;
  G4double ale, cre, be, fe, ymu, ymd, ym1, alm_crm, a10, bm, fm;
  //
  G4double ame = 0.51099907e-3;  // GeV
  G4double lamu = 0.105658389;  // GeV
  G4double re = 2.81794092e-13;  // cm
  G4double avno = 6.022137e23;
  G4double lpi = 3.14159265;
  G4double alpha = 1. / 137.036;
  G4double rmass = lamu / ame;  // "207"
  G4double coeff = 4. / (3. * lpi) * (alpha * re) * (alpha * re) * avno;  // cm^2
  G4double sqrte = 1.64872127;  // sqrt(2.71828...)
  G4double c3 = 3. * sqrte * lamu / 4.;  // for limits
  G4double c7 = 4. * ame;  // -"-
  G4double c8 = 6. * lamu * lamu;  // -"-

  G4double xgi[8] = {.0199, .1017, .2372, .4083, .5917, .7628, .8983, .9801};  // Gauss, 8
  G4double wgi[8] = {.0506, .1112, .1569, .1813, .1813, .1569, .1112, .0506};  // Gauss, 8
  bbbtf = 183.;  // for the moment...
  bbbh = 202.4;  // for the moment...
  g1tf = 1.95e-5;
  g2tf = 5.3e-5;
  g1h = 4.4e-5;
  g2h = 4.8e-5;

  e = tkin + lamu;
  z13 = fNist->GetZ13(G4lrint(z));
  e1 = e - ep;
  crp_g4 = 0.;
  if (e1 <= c3 * z13) return crp_g4;  // ep > max
  alf = c7 / ep;  // 4m/ep
  a3 = 1. - alf;
  if (a3 <= 0.) return crp_g4;  // ep < min
  //***                zeta calculation
  if (z <= 1.5)  // special case of hidrogen
  {
    bbb = bbbh;
    g1 = g1h;
    g2 = g2h;
  }
  else {
    bbb = bbbtf;
    g1 = g1tf;
    g2 = g2tf;
  }
  zeta1 = 0.073 * G4Log(e / (lamu + g1 * z13 * z13 * e)) - 0.26;
  if (zeta1 > 0.) {
    zeta2 = 0.058 * log(e / (lamu + g2 * z13 * e)) - 0.14;
    zeta = zeta1 / zeta2;
  }
  else {
    zeta = 0.;
  }
  z2 = z * (z + zeta);  //
  //***                just to check (for comparison with crp_m)
  //        z2=z*(z+1.)
  //        bbb=189.
  //***
  screen0 = 2. * ame * sqrte * bbb / (z13 * ep);  // be careful with "ame"
  a0 = e * e1;
  a1 = ep * ep / a0;  // 2*beta
  bet = 0.5 * a1;  // beta
  xi0 = 0.25 * rmass * rmass * a1;  // xi0
  del = c8 / a0;  // 6mu^2/EE'
  tmn = G4Log((alf + 2. * del * a3) / (1. + (1. - del) * sqrt(a3)));  // log(1-rmax)
  sum = 0.;
  for (G4int i = 0; i < 8; ++i) {
    a4 = G4Exp(tmn * xgi[i]);  // 1-r
    a5 = a4 * (2. - a4);  // 1-r2
    a6 = 1. - a5;  // r2
    a7 = 1. + a6;  // 1+r2
    a9 = 3. + a6;  // 3+r2
    xi = xi0 * a5;
    xii = 1. / xi;
    xi1 = 1. + xi;
    screen = screen0 * xi1 / a5;
    yeu = 5. - a6 + 4. * bet * a7;
    yed = 2. * (1. + 3. * bet) * G4Log(3. + xii) - a6 - a1 * (2. - a6);
    ye1 = 1. + yeu / yed;
    ale = G4Log(bbb / z13 * std::sqrt(xi1 * ye1) / (1. + screen * ye1));
    cre = 0.5 * G4Log(1. + (1.5 / rmass * z13) * (1.5 / rmass * z13) * xi1 * ye1);
    if (xi <= 1e3) {
      be = ((2. + a6) * (1. + bet) + xi * a9) * G4Log(1. + xii) + (a5 - bet) / xi1 - a9;
    }
    else {
      be = (3. - a6 + a1 * a7) / (2. * xi);  // -(6.-5.*a6+3.*bet*a6)/(6.*xi*xi);
    }
    fe = std::max(0., (ale - cre) * be);
    ymu = 4. + a6 + 3. * bet * a7;
    ymd = a7 * (1.5 + a1) * G4Log(3. + xi) + 1. - 1.5 * a6;
    ym1 = 1. + ymu / ymd;
    alm_crm = G4Log(bbb * rmass / (1.5 * z13 * z13 * (1. + screen * ym1)));
    if (xi >= 1e-3) {
      a10 = (1. + a1) * a5;  // (1+2b)(1-r2)
      bm = (a7 * (1. + 1.5 * bet) - a10 * xii) * G4Log(xi1) + xi * (a5 - bet) / xi1 + a10;
    }
    else {
      bm = (5. - a6 + bet * a9) * (xi / 2.);  // -(11.-5.*a6+.5*bet*(5.+a6))*(xi*xi/6.)
    }
    fm = max(0., (alm_crm)*bm);
    //***
    sum = sum + a4 * (fe + fm / (rmass * rmass)) * wgi[i];
  }
  crp_g4 = -tmn * sum * (z2 / a) * coeff * e1 / (e * ep);
  return crp_g4;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::CRM_Mephi(G4double Z, G4double tkin, G4double pairEnergy)
{
  /*
      ||Cross section for pair production of muons by fast muon
      ||By Siddharth Yajaman 19-07-2022
      ||Based on the formulae from Kelner, Kokoulin and Petrukhin,
      ||Physics of Atomic Nuclei, Vol. 63, No. 9, 2000, pp. 1603-1611
      ||Equations (15) - (22)
  */

  const G4double xgi[] = {0.0198550717512320, 0.1016667612931865, 0.2372337950418355,
                          0.4082826787521750, 0.5917173212478250, 0.7627662049581645,
                          0.8983332387068135, 0.9801449282487680};

  const G4double wgi[] = {0.0506142681451880, 0.1111905172266870, 0.1568533229389435,
                          0.1813418916891810, 0.1813418916891810, 0.1568533229389435,
                          0.1111905172266870, 0.0506142681451880};

  static const G4double factorForCross =
    2. / (3 * CLHEP::pi)
    * pow(CLHEP::fine_structure_const * CLHEP::classic_electr_radius / fMueRatio, 2);

  if (pairEnergy <= 2. * fMuonMass) return 0.0;

  G4double totalEnergy = tkin + fMuonMass;
  G4double residEnergy = totalEnergy - pairEnergy;

  if (residEnergy <= fMuonMass) return 0.0;

  G4double a0 = 1.0 / (totalEnergy * residEnergy);
  G4double rhomax = 1.0 - 2 * fMuonMass / pairEnergy;
  G4double tmnexp = 1. - rhomax;

  if (tmnexp >= 1.0) {
    return 0.0;
  }

  G4double tmn = G4Log(tmnexp);

  G4double z2 = Z * Z;
  G4double beta = 0.5 * pairEnergy * pairEnergy * a0;
  G4double xi0 = 0.5 * beta;

  // Gaussian integration in ln(1-ro) ( with 8 points)
  G4double rho[8];
  G4double rho2[8];
  G4double xi[8];
  G4double xi1[8];
  G4double xii[8];

  for (G4int i = 0; i < 8; ++i) {
    rho[i] = G4Exp(tmn * xgi[i]) - 1.0;  // rho = -asymmetry
    rho2[i] = rho[i] * rho[i];
    xi[i] = xi0 * (1.0 - rho2[i]);
    xi1[i] = 1.0 + xi[i];
    xii[i] = 1.0 / xi[i];
  }

  G4double ximax = xi0 * (1. - rhomax * rhomax);

  G4double Y = 10 * sqrt(fMuonMass / totalEnergy);
  G4double U[8];

  for (G4int i = 0; i < 8; ++i) {
    U[i] = U_func(Z, rho2[i], xi[i], Y, pairEnergy);
  }

  G4double UMax = U_func(Z, rhomax * rhomax, ximax, Y, pairEnergy);

  G4double sum = 0.0;

  for (G4int i = 0; i < 8; ++i) {
    G4double X = 1 + U[i] - UMax;
    G4double lnX = G4Log(X);
    G4double phi = ((2 + rho2[i]) * (1 + beta) + xi[i] * (3 + rho2[i])) * G4Log(1 + xii[i]) - 1
                   - 3 * rho2[i] + beta * (1 - 2 * rho2[i])
                   + ((1 + rho2[i]) * (1 + 1.5 * beta) - xii[i] * (1 + 2 * beta) * (1 - rho2[i]))
                       * G4Log(xi1[i]);
    sum += wgi[i] * (1.0 + rho[i]) * phi * lnX;
  }

  return -tmn * sum * factorForCross * z2 * residEnergy / (totalEnergy * pairEnergy);
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double MuCrossSections::U_func(G4double Z, G4double rho2, G4double xi, G4double Y,
                                 G4double pairEnergy, const G4double B)
{
  G4int z = G4lrint(Z);
  G4double A27 = fNist->GetA27(z);
  G4double Z13 = fNist->GetZ13(z);
  static const G4double sqe = 2 * std::sqrt(G4Exp(1.0)) * fMuonMass * fMuonMass;
  G4double res = (0.65 * B / (A27 * Z13) * fMueRatio)
                 / (1
                    + (sqe * B * (1 + xi) * (1 + Y))
                        / (Z13 * CLHEP::electron_mass_c2 * pairEnergy * (1 - rho2)));
  return res;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......