G4UCNMicroRoughnessHelper.cc

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//
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//
// This file contains the source code of various functions all related to the
// calculation of microroughness.
//
// see A. Steyerl, Z. Physik 254 (1972) 169.
//
// A description of the functions can be found in the corresponding header file
//
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#include "G4UCNMicroRoughnessHelper.hh"

#include "globals.hh"

#include "G4SystemOfUnits.hh"
#include "G4PhysicalConstants.hh"

G4UCNMicroRoughnessHelper* G4UCNMicroRoughnessHelper::fpInstance = 0;

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// Constructor

G4UCNMicroRoughnessHelper::G4UCNMicroRoughnessHelper() {;}

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G4UCNMicroRoughnessHelper::~G4UCNMicroRoughnessHelper()
{
  delete fpInstance;
  fpInstance = 0;
}

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G4UCNMicroRoughnessHelper* G4UCNMicroRoughnessHelper::GetInstance()
{
  if (fpInstance == NULL) fpInstance = new G4UCNMicroRoughnessHelper;
  return fpInstance;
}

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G4double G4UCNMicroRoughnessHelper::S2(G4double costheta2, G4double klk2)
{
  // case 1: radicand is positive,
  // case 2: radicand is negative, cf. p. 174 of the Steyerl paper

  if (costheta2>=klk2)
     return 4*costheta2/(2*costheta2-klk2+2*std::sqrt(costheta2*(costheta2-klk2)));
  else
     return 4*costheta2/klk2;
}

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G4double G4UCNMicroRoughnessHelper::SS2(G4double costhetas2, G4double klks2)
{
  // cf. p. 175 of the Steyerl paper

  return 4*costhetas2/
                   (2*costhetas2+klks2+2*std::sqrt(costhetas2*(costhetas2+klks2)));
}

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G4double G4UCNMicroRoughnessHelper::Fmu(G4double k2, G4double thetai,
                                        G4double thetao, G4double phio,
                                        G4double b2, G4double w2,
                                        G4double AngCut)
{
  G4double mu_squared;

  // Checks if the distribution is peaked around the specular direction

  if ((std::fabs(thetai-thetao)<AngCut) && (std::fabs(phio)<AngCut))
    mu_squared=0.;
  else
    {
      // cf. p. 177 of the Steyerl paper

      G4double sinthetai=std::sin(thetai);
      G4double sinthetao=std::sin(thetao);
      mu_squared=k2*
          (sinthetai*sinthetai+sinthetao*sinthetao-
                   2.*sinthetai*sinthetao*std::cos(phio));
    }

  // cf. p. 177 of the Steyerl paper

  return b2*w2/twopi*std::exp(-mu_squared*w2/2);
}

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G4double G4UCNMicroRoughnessHelper::FmuS(G4double k, G4double kS,
                                         G4double thetai, G4double thetaSo,
                                         G4double phiSo,
                                         G4double b2, G4double w2,
                                         G4double AngCut, G4double thetarefract)
{
  G4double mu_squared;

  // Checks if the distribution is peaked around the direction of
  // unperturbed refraction

  if ((std::fabs(thetarefract-thetaSo)<AngCut) && (std::fabs(phiSo)<AngCut))
    mu_squared=0.;
  else
    {
      G4double sinthetai=std::sin(thetai);
      G4double sinthetaSo=std::sin(thetaSo);

      // cf. p. 177 of the Steyerl paper
      mu_squared=k*k*sinthetai*sinthetai+kS*kS*sinthetaSo*sinthetaSo-
                 2.*k*kS*sinthetai*sinthetaSo*std::cos(phiSo);
    }

  // cf. p. 177 of the Steyerl paper

  return b2*w2/twopi*std::exp(-mu_squared*w2/2);
}

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G4double G4UCNMicroRoughnessHelper::IntIplus(G4double E, G4double fermipot,
                                             G4double theta_i, G4int AngNoTheta,
                                             G4int AngNoPhi, G4double b2,
                                             G4double w2, G4double* max,
                                             G4double AngCut)
{
  *max=0.;

  // max_theta_o saves the theta-position of the max probability,
  // the previous value is saved in a_max_theta_o

  G4double a_max_theta_o, max_theta_o=theta_i, a_max_phi_o, max_phi_o=0.;

  // max_phi_o saves the phi-position of the max probability,
  // the previous value is saved in a_max_phi_o

  // Definition of the stepsizes in theta_o and phi_o

  G4double theta_o;
  G4double phi_o;
  G4double Intens;
  G4double ang_steptheta=90.*degree/(AngNoTheta-1);
  G4double ang_stepphi=360.*degree/(AngNoPhi-1);
  G4double costheta_i=std::cos(theta_i);
  G4double costheta_i_squared=costheta_i*costheta_i;

  // (k_l/k)^2
  G4double kl4d4=neutron_mass_c2/hbarc_squared*neutron_mass_c2/
                                 hbarc_squared*fermipot*fermipot;

  // (k_l/k)^2
  G4double klk2=fermipot/E;

  G4double costheta_o_squared;

  // k^2
  G4double k2=2*neutron_mass_c2*E/hbarc_squared;

  G4double wkeit=0.;

  // Loop through theta_o
 
  for (theta_o=0.*degree; theta_o<=90.*degree+1e-6; theta_o+=ang_steptheta)
    {
      costheta_o_squared=std::cos(theta_o)*std::cos(theta_o);

      // Loop through phi_o

      for (phi_o=-180.*degree; phi_o<=180.*degree+1e-6; phi_o+=ang_stepphi)
        {
          //calculates probability for a certain theta_o,phi_o pair

          Intens=kl4d4/costheta_i*S2(costheta_i_squared,klk2)*
                 S2(costheta_o_squared,klk2)*
                 Fmu(k2,theta_i,theta_o,phi_o,b2,w2,AngCut)*std::sin(theta_o);

          //G4cout << "S2:  " << S2(costheta_i_squared,klk2) << G4endl;
          //G4cout << "S2:  " << S2(costheta_o_squared,klk2) << G4endl;
          //G4cout << "Fmu: " << Fmu(k2,theta_i,theta_o,phi_o,b2,w2,AngCut)*sin(theta_o) << G4endl;
          // checks if the new probability is larger than the
          // maximum found so far

          if (Intens>*max)
            {
              *max=Intens;
              max_theta_o=theta_o;
              max_phi_o=phi_o;
            }

          // Adds the newly found probability to the integral probability

          wkeit+=Intens*ang_steptheta*ang_stepphi;
        }
    }

  // Fine-Iteration to find maximum of distribution
  // only if the energy is not zero

  if (E>1e-10*eV)
    {

  // Break-condition for refining

  while ((ang_stepphi>=AngCut*AngCut) || (ang_steptheta>=AngCut*AngCut))
    {
      a_max_theta_o=max_theta_o;
      a_max_phi_o=max_phi_o;
      ang_stepphi /= 2.;
      ang_steptheta /= 2.;

      //G4cout << ang_stepphi/degree << ", "
      //       << ang_steptheta/degree << ","
      //       << AngCut/degree << G4endl;

      for (theta_o=a_max_theta_o-ang_steptheta;
           theta_o<=a_max_theta_o-ang_steptheta+1e-6;
           theta_o+=ang_steptheta)
        {
          //G4cout << "theta_o: " << theta_o/degree << G4endl;
          costheta_o_squared=std::cos(theta_o)*std::cos(theta_o);
          for (phi_o=a_max_phi_o-ang_stepphi;
               phi_o<=a_max_phi_o+ang_stepphi+1e-6;
               phi_o+=ang_stepphi)
            {
              //G4cout << "phi_o: " << phi_o/degree << G4endl;
              Intens=kl4d4/costheta_i*S2(costheta_i_squared, klk2)*
                     S2(costheta_o_squared,klk2)*
                     Fmu(k2,theta_i,theta_o,phi_o,b2,w2,AngCut)*std::sin(theta_o);
              if (Intens>*max)
                {
                  *max=Intens;
                  max_theta_o=theta_o;
                  max_phi_o=phi_o;
                }
            }
        }
    }
    }
  return wkeit;
}

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G4double G4UCNMicroRoughnessHelper::IntIminus(G4double E, G4double fermipot,
                                              G4double theta_i,
                                              G4int AngNoTheta,
                                              G4int AngNoPhi, G4double b2,
                                              G4double w2, G4double* max,
                                              G4double AngCut)
{
  G4double a_max_thetas_o, max_thetas_o = theta_i;
  G4double a_max_phis_o, max_phis_o = 0.;
  G4double thetas_o;
  G4double phis_o;
  G4double IntensS;
  G4double ang_steptheta=180.*degree/(AngNoTheta-1);
  G4double ang_stepphi=180.*degree/(AngNoPhi-1);
  G4double costheta_i=std::cos(theta_i);
  G4double costheta_i_squared=costheta_i*costheta_i;

  *max = 0.;
  G4double wkeit=0.;

  if (E*costheta_i_squared < fermipot) return wkeit;

  //k_l^4/4
  G4double kl4d4=neutron_mass_c2/hbarc_squared*neutron_mass_c2/
                 hbarc_squared*fermipot*fermipot;
  // (k_l/k)^2
  G4double klk2=fermipot/E;

  // (k_l/k')^2
  G4double klks2=fermipot/(E-fermipot);

  // k'/k
  G4double ksdk=std::sqrt((E-fermipot)/E);

  G4double costhetas_o_squared;

  // k
  G4double k=std::sqrt(2*neutron_mass_c2*E/hbarc_squared);

  // k'
  G4double kS=ksdk*k;

  for (thetas_o=0.*degree; thetas_o<=90.*degree+1e-6; thetas_o+=ang_steptheta)
    {
      costhetas_o_squared=std::cos(thetas_o)*std::cos(thetas_o);

      for (phis_o=-180.*degree; phis_o<=180.*degree+1e-6; phis_o+=ang_stepphi)
        {
          //cf. Steyerl-paper p. 176, eq. 21
          if (costhetas_o_squared>=-klks2) {

            //calculates probability for a certain theta'_o, phi'_o pair

            G4double thetarefract = thetas_o;
            if (std::fabs(std::sin(theta_i)/ksdk) <= 1.)
                                        thetarefract = std::asin(std::sin(theta_i)/ksdk);

            IntensS = kl4d4/costheta_i*ksdk*S2(costheta_i_squared, klk2)*
                      SS2(costhetas_o_squared,klks2)*
                      FmuS(k,kS,theta_i,thetas_o,phis_o,b2,w2,AngCut,thetarefract)*
                      std::sin(thetas_o);
          } else {
            IntensS=0.;
          }
            // checks if the new probability is larger than
            // the maximum found so far
          if (IntensS>*max)
            {
              *max=IntensS;
            }
          wkeit+=IntensS*ang_steptheta*ang_stepphi;
        }
    }

  // Fine-Iteration to find maximum of distribution

  if (E>1e-10*eV)
    {

  // Break-condition for refining

  while (ang_stepphi>=AngCut*AngCut || ang_steptheta>=AngCut*AngCut)
    {
      a_max_thetas_o=max_thetas_o;
      a_max_phis_o=max_phis_o;
      ang_stepphi /= 2.;
      ang_steptheta /= 2.;
      //G4cout << ang_stepphi/degree << ", " << ang_steptheta/degree 
      //       << ", " << AngCut/degree << G4endl;
      for (thetas_o=a_max_thetas_o-ang_steptheta;
           thetas_o<=a_max_thetas_o-ang_steptheta+1e-6;
           thetas_o+=ang_steptheta)
        {
          costhetas_o_squared=std::cos(thetas_o)*std::cos(thetas_o);
          for (phis_o=a_max_phis_o-ang_stepphi;
               phis_o<=a_max_phis_o+ang_stepphi+1e-6;
               phis_o+=ang_stepphi)
            {
              G4double thetarefract = thetas_o;
              if (std::fabs(std::sin(theta_i)/ksdk) <= 1.)
                                       thetarefract = std::asin(std::sin(theta_i)/ksdk);

              IntensS=kl4d4/costheta_i*ksdk*S2(costheta_i_squared, klk2)*
                      SS2(costhetas_o_squared,klks2)*
                      FmuS(k,kS,theta_i,thetas_o,phis_o,b2,w2,AngCut,thetarefract)*
                      std::sin(thetas_o);
              if (IntensS>*max)
                {
                  *max=IntensS;
                  max_thetas_o=thetas_o;
                  max_phis_o=phis_o;
                }
            }
        }
    }
    }
  return wkeit;
}

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G4double G4UCNMicroRoughnessHelper::ProbIplus(G4double E, G4double fermipot,
                                              G4double theta_i,
                                              G4double theta_o,
                                              G4double phi_o,
                                              G4double b, G4double w,
                                              G4double AngCut)
{
  //k_l^4/4
  G4double kl4d4=neutron_mass_c2/hbarc_squared*neutron_mass_c2/
                 hbarc_squared*fermipot*fermipot;

  // (k_l/k)^2
  G4double klk2=fermipot/E;

  G4double costheta_i=std::cos(theta_i); 
  G4double costheta_o=std::cos(theta_o);

  // eq. 20 on page 176 in the steyerl paper

  return kl4d4/costheta_i*S2(costheta_i*costheta_i, klk2)*
         S2(costheta_o*costheta_o,klk2)*
   Fmu(2*neutron_mass_c2*E/hbarc_squared,theta_i,theta_o,phi_o,b*b,w*w,AngCut)*
   std::sin(theta_o);
}

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G4double G4UCNMicroRoughnessHelper::ProbIminus(G4double E, G4double fermipot,
                                               G4double theta_i,
                                               G4double thetas_o,
                                               G4double phis_o, G4double b,
                                               G4double w, G4double AngCut)
{
  //k_l^4/4
  G4double kl4d4=neutron_mass_c2/hbarc_squared*neutron_mass_c2/
                 hbarc_squared*fermipot*fermipot;
  // (k_l/k)^2
  G4double klk2=fermipot/E;

  // (k_l/k')^2
  G4double klks2=fermipot/(E-fermipot);

  if (E < fermipot) {
     G4cout << " ProbIminus E < fermipot " << G4endl;
     return 0.;
  }

  // k'/k
  G4double ksdk=std::sqrt((E-fermipot)/E);

  // k
  G4double k=std::sqrt(2*neutron_mass_c2*E/hbarc_squared);

  // k'/k
  G4double kS=ksdk*k;

  G4double costheta_i=std::cos(theta_i);
  G4double costhetas_o=std::cos(thetas_o);

  // eq. 20 on page 176 in the steyerl paper

  G4double thetarefract = thetas_o;
  if(std::fabs(std::sin(theta_i)/ksdk) <= 1.)thetarefract = std::asin(std::sin(theta_i)/ksdk);

  return kl4d4/costheta_i*ksdk*S2(costheta_i*costheta_i, klk2)*
         SS2(costhetas_o*costhetas_o,klks2)*
         FmuS(k,kS,theta_i,thetas_o,phis_o,b*b,w*w,AngCut,thetarefract)*
         std::sin(thetas_o);
}

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