nucleus.cc

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/*
 *    Copyright (c) 2014-2023
 *      SMASH Team
 *
 *    GNU General Public License (GPLv3 or later)
 */
#include "smash/nucleus.h"
 
#include <fstream>
#include <iostream>
#include <limits>
#include <map>
#include <string>
 
#include "smash/angles.h"
#include "smash/constants.h"
#include "smash/fourvector.h"
#include "smash/logging.h"
#include "smash/random.h"
#include "smash/threevector.h"
 
namespace smash {
static constexpr int LNucleus = LogArea::Nucleus::id;
 
Nucleus::Nucleus(const std::map<PdgCode, int> &particle_list, int nTest) {
  fill_from_list(particle_list, nTest);
  set_parameters_automatic();
  set_saturation_density(calculate_saturation_density());
}
 
Nucleus::Nucleus(Configuration &config, int nTest) {
  // Fill nuclei with particles.
  std::map<PdgCode, int> part = config.take({"Particles"});
  fill_from_list(part, nTest);
  // Look for user-defined values or take the default parameters.
  if (config.has_value({"Diffusiveness"}) && config.has_value({"Radius"}) &&
      config.has_value({"Saturation_Density"})) {
    set_parameters_from_config(config);
  } else if (!config.has_value({"Diffusiveness"}) &&
             !config.has_value({"Radius"}) &&
             !config.has_value({"Saturation_Density"})) {
    set_parameters_automatic();
    set_saturation_density(calculate_saturation_density());
  } else {
    throw std::invalid_argument(
        "Diffusiveness, Radius and Saturation_Density "
        "required to manually configure the Woods-Saxon"
        " distribution. Only one/two were provided. \n"
        "Providing none of the above mentioned "
        "parameters automatically configures the "
        "distribution based on the atomic number.");
  }
}
 
double Nucleus::mass() const {
  double total_mass = 0.;
  for (auto i = cbegin(); i != cend(); i++) {
    total_mass += i->momentum().abs();
  }
  return total_mass / (testparticles_ + 0.0);
}
 
ThreeVector Nucleus::distribute_nucleon() {
  // Get the solid angle of the nucleon.
  Angles dir;
  dir.distribute_isotropically();
  // diffusiveness_ zero or negative? Use hard sphere.
  if (almost_equal(diffusiveness_, 0.)) {
    return dir.threevec() * nuclear_radius_ * std::cbrt(random::canonical());
  }
  if (almost_equal(nuclear_radius_, 0.)) {
    return smash::ThreeVector();
  }
  double radius_scaled = nuclear_radius_ / diffusiveness_;
  double prob_range1 = 1.0;
  double prob_range2 = 3. / radius_scaled;
  double prob_range3 = 2. * prob_range2 / radius_scaled;
  double prob_range4 = 1. * prob_range3 / radius_scaled;
  double ranges234 = prob_range2 + prob_range3 + prob_range4;
  double t;
  do {
    double which_range = random::uniform(-prob_range1, ranges234);
    if (which_range < 0.0) {
      t = radius_scaled * (std::cbrt(random::canonical()) - 1.);
    } else {
      t = -std::log(random::canonical());
      if (which_range >= prob_range2) {
        t -= std::log(random::canonical());
        if (which_range >= prob_range2 + prob_range3) {
          t -= std::log(random::canonical());
        }
      }
    }
  } while (random::canonical() > 1. / (1. + std::exp(-std::abs(t))));
  double position_scaled = t + radius_scaled;
  double position = position_scaled * diffusiveness_;
  return dir.threevec() * position;
}
 
double Nucleus::woods_saxon(double r) {
  return r * r / (std::exp((r - nuclear_radius_) / diffusiveness_) + 1);
}
 
void Nucleus::arrange_nucleons() {
  for (auto i = begin(); i != end(); i++) {
    // Initialize momentum
    i->set_4momentum(i->pole_mass(), 0.0, 0.0, 0.0);
    /* Sampling the Woods-Saxon, get the radial
     * position and solid angle for the nucleon. */
    ThreeVector pos = distribute_nucleon();
 
    // Set the position of the nucleon.
    i->set_4position(FourVector(0.0, pos));
  }
 
  // Recenter and rotate
  align_center();
  rotate();
}
 
void Nucleus::set_parameters_automatic() {
  int A = Nucleus::number_of_particles();
  int Z = Nucleus::number_of_protons();
  if (A == 1) {  // single particle
    /* In case of testparticles, an infinite reaction loop will be
     * avoided by a small finite spread according to a single particles
     * 'nucleus'. The proper solution will be to introduce parallel
     * ensembles. */
    set_nuclear_radius(
        testparticles_ == 1 ? 0. : 1. - std::exp(-(testparticles_ - 1.) * 0.1));
    set_diffusiveness(testparticles_ == 1 ? -1. : 0.02);
  } else if ((A == 238) && (Z == 92)) {  // Uranium
    // Default values.
    set_diffusiveness(0.556);
    set_nuclear_radius(6.86);
  } else if ((A == 208) && (Z == 82)) {  // Lead
    // Default values.
    set_diffusiveness(0.54);
    set_nuclear_radius(6.67);
  } else if ((A == 197) && (Z == 79)) {  // Gold
    // Default values from \iref{Schopper:2004qco}
    set_diffusiveness(0.523);
    set_nuclear_radius(6.55);
  } else if ((A == 129) && (Z == 54)) {  // Xenon
    // Default values.
    set_diffusiveness(0.59);
    set_nuclear_radius(5.36);
  } else if ((A == 63) && (Z == 29)) {  // Copper
    // Default values.
    set_diffusiveness(0.5977);
    set_nuclear_radius(4.20641);
  } else if (A == 96) {
    if (Z == 40) {  // Zirconium
      // Default values.
      set_diffusiveness(0.46);
      set_nuclear_radius(5.02);
    } else if (Z == 44) {  // Ruthenium
      // Default values.
      set_diffusiveness(0.46);
      set_nuclear_radius(5.085);
    } else {
      // radius and diffusiveness taken from \iref{Rybczynski:2013yba}
      set_diffusiveness(0.54);
      set_nuclear_radius(1.12 * std::pow(A, 1.0 / 3.0) -
                         0.86 * std::pow(A, -1.0 / 3.0));
    }
  } else {
    // saturation density already has reasonable default
    set_nuclear_radius(default_nuclear_radius());
    if (A <= 16) {
      set_diffusiveness(0.545);
    } else {
      // diffusiveness taken from \iref{Rybczynski:2013yba}
      set_diffusiveness(0.54);
    }
  }
}
 
void Nucleus::set_parameters_from_config(Configuration &config) {
  set_diffusiveness(static_cast<double>(config.take({"Diffusiveness"})));
  set_nuclear_radius(static_cast<double>(config.take({"Radius"})));
  // Saturation density (normalization for accept/reject sampling)
  set_saturation_density(
      static_cast<double>(config.take({"Saturation_Density"})));
}
 
void Nucleus::generate_fermi_momenta() {
  const int N_n = std::count_if(begin(), end(), [](const ParticleData i) {
    return i.pdgcode() == pdg::n;
  });
  const int N_p = std::count_if(begin(), end(), [](const ParticleData i) {
    return i.pdgcode() == pdg::p;
  });
  const FourVector nucleus_center = center();
  const int A = N_n + N_p;
  constexpr double pi2_3 = 3.0 * M_PI * M_PI;
  logg[LNucleus].debug() << N_n << " neutrons, " << N_p << " protons.";
 
  ThreeVector ptot = ThreeVector(0.0, 0.0, 0.0);
  for (auto i = begin(); i != end(); i++) {
    // Only protons and neutrons get Fermi momenta
    if (i->pdgcode() != pdg::p && i->pdgcode() != pdg::n) {
      if (i->is_baryon()) {
        logg[LNucleus].warn() << "No rule to calculate Fermi momentum "
                              << "for particle " << i->pdgcode();
      }
      continue;
    }
    const double r = (i->position() - nucleus_center).abs3();
    const double theta = (i->position().threevec().get_theta());
    const double phi = (i->position().threevec().get_phi());
    double rho = nucleon_density(r, std::cos(theta), phi);
 
    if (i->pdgcode() == pdg::p) {
      rho = rho * N_p / A;
    }
    if (i->pdgcode() == pdg::n) {
      rho = rho * N_n / A;
    }
    const double p =
        hbarc * std::pow(pi2_3 * rho * random::uniform(0.0, 1.0), 1.0 / 3.0);
    Angles phitheta;
    phitheta.distribute_isotropically();
    const ThreeVector ith_3momentum = phitheta.threevec() * p;
    ptot += ith_3momentum;
    i->set_3momentum(ith_3momentum);
    logg[LNucleus].debug() << "Particle: " << *i << ", pF[GeV]: "
                           << hbarc * std::pow(pi2_3 * rho, 1.0 / 3.0)
                           << " r[fm]: " << r
                           << " Nuclear radius[fm]: " << nuclear_radius_;
  }
  if (A == 0) {
    // No Fermi momenta should be assigned
    assert(ptot.x1() == 0.0 && ptot.x2() == 0.0 && ptot.x3() == 0.0);
  } else {
    /* Ensure zero total momentum of nucleus - redistribute ptot equally
     * among protons and neutrons */
    const ThreeVector centralizer = ptot / A;
    for (auto i = begin(); i != end(); i++) {
      if (i->pdgcode() == pdg::p || i->pdgcode() == pdg::n) {
        i->set_4momentum(i->pole_mass(),
                         i->momentum().threevec() - centralizer);
      }
    }
  }
}
 
void Nucleus::boost(double beta_scalar) {
  double beta_squared = beta_scalar * beta_scalar;
  double one_over_gamma = std::sqrt(1.0 - beta_squared);
  double gamma = 1.0 / one_over_gamma;
  /* We are talking about a /passive/ lorentz transformation here, as
   * far as I can see, so we need to boost in the direction opposite to
   * where we want to go
   *     ( The vector we transform - p - stays unchanged, but we go into
   *       a system that moves with -beta. Now in this frame, it seems
   *       like p has been accelerated with +beta.
   *     ) */
  for (auto i = begin(); i != end(); i++) {
    /* a real Lorentz Transformation would leave the particles at
     * different times here, which we would then have to propagate back
     * to equal times. Since we know the result, we can simply multiply
     * the z-value with 1/gamma. */
    FourVector this_position = i->position();
    this_position.set_x3(this_position.x3() * one_over_gamma);
    i->set_4position(this_position);
    /* The simple Lorentz transformation of momenta does not take into account
     * that nucleus has binding energy. Here we apply the method used
     * in the JAM code \iref{Nara:1999dz}: p' = p_beam + gamma*p_F.
     * This formula is derived under assumption that all nucleons have
     * the same binding energy. */
    FourVector mom_i = i->momentum();
    i->set_4momentum(i->pole_mass(), mom_i.x1(), mom_i.x2(),
                     gamma * (beta_scalar * mom_i.x0() + mom_i.x3()));
  }
}
 
void Nucleus::fill_from_list(const std::map<PdgCode, int> &particle_list,
                             int testparticles) {
  testparticles_ = testparticles;
  for (auto n = particle_list.cbegin(); n != particle_list.cend(); ++n) {
    const ParticleType &current_type = ParticleType::find(n->first);
    double current_mass = current_type.mass();
    for (unsigned int i = 0; i < n->second * testparticles_; i++) {
      // append particle to list and set its PDG code.
      particles_.emplace_back(current_type);
      particles_.back().set_4momentum(current_mass, 0.0, 0.0, 0.0);
    }
  }
}
 
void Nucleus::shift(double z_offset, double x_offset, double simulation_time) {
  // Move the nucleus in z and x directions, and set the time.
  for (auto i = begin(); i != end(); i++) {
    FourVector this_position = i->position();
    this_position.set_x3(this_position.x3() + z_offset);
    this_position.set_x1(this_position.x1() + x_offset);
    this_position.set_x0(simulation_time);
    i->set_4position(this_position);
    i->set_formation_time(simulation_time);
  }
}
 
void Nucleus::copy_particles(Particles *external_particles) {
  for (auto p = begin(); p != end(); p++) {
    external_particles->insert(*p);
  }
}
 
FourVector Nucleus::center() const {
  FourVector centerpoint(0.0, 0.0, 0.0, 0.0);
  for (auto p = cbegin(); p != cend(); p++) {
    centerpoint += p->position();
  }
  centerpoint /= size();
  return centerpoint;
}
 
void Nucleus::random_euler_angles() {
  // Sample euler_theta_ such that cos(theta) is uniform
  euler_phi_ = twopi * random::uniform(0., 1.);
  euler_theta_ = std::acos(2 * random::uniform(0., 1.) - 1);
  euler_psi_ = twopi * random::uniform(0., 1.);
}
 
double Nucleus::nucleon_density(double r, double, double) const {
  return get_saturation_density() /
         (std::exp((r - nuclear_radius_) / diffusiveness_) + 1.);
}
 
double Nucleus::nucleon_density_unnormalized(double r, double, double) const {
  return 1.0 / (std::exp((r - nuclear_radius_) / diffusiveness_) + 1.);
}
 
double Nucleus::calculate_saturation_density() const {
  Integrator2d integrate;
  // Transform integral from (0, oo) to (0, 1) via r = (1 - t) / t.
  // To prevent overflow, the integration is only performed to t = 0.01 which
  // corresponds to r = 99fm. Additionally the precision settings in the
  // Integrator2d scheme are equally important. However both these point affect
  // the result only after the seventh digit which should not be relevant here.
  const auto result = integrate(0.01, 1, -1, 1, [&](double t, double cosx) {
    const double r = (1 - t) / t;
    return twopi * std::pow(r, 2.0) *
           nucleon_density_unnormalized(r, cosx, 0.0) / std::pow(t, 2.0);
  });
  const auto rho0 = number_of_particles() / result.value();
  return rho0;
}
 
std::ostream &operator<<(std::ostream &out, const Nucleus &n) {
  return out << "  #particles   #testparticles   mass [GeV]   "
                "radius [fm]  diffusiveness [fm]\n"
             << format(n.number_of_particles(), nullptr, 12)
             << format(n.size(), nullptr, 17) << format(n.mass(), nullptr, 13)
             << format(n.get_nuclear_radius(), nullptr, 14)
             << format(n.get_diffusiveness(), nullptr, 20);
}
 
}  // namespace smash