clebschgordan.cc

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/*
 *    Copyright (c) 2015-2018
 *      SMASH Team
 *
 *    GNU General Public License (GPLv3 or later)
 */

#include "smash/clebschgordan.h"

#include <gsl/gsl_sf_coupling.h>
#include <numeric>
#include "smash/constants.h"
#include "smash/logging.h"

namespace smash {

double clebsch_gordan(const int j_a, const int j_b, const int j_c,
                      const int m_a, const int m_b, const int m_c) {
  const double wigner_3j = gsl_sf_coupling_3j(j_a, j_b, j_c, m_a, m_b, -m_c);
  if (std::abs(wigner_3j) < really_small) {
    return 0.;
  }
  assert((j_a - j_b + m_c) % 2 == 0);
  const int j = (j_a - j_b + m_c) / 2;
  double result = std::sqrt(j_c + 1) * wigner_3j;
  result *= (j % 2 == 0) * 2 - 1;  // == (-1)**j

#ifndef NDEBUG
  const auto &log = logger<LogArea::Resonances>();
  log.debug("CG: ", result, " I1: ", j_a, " I2: ", j_b, " IR: ", j_c,
            " iz1: ", m_a, " iz2: ", m_b, " izR: ", m_c);
#endif

  return result;
}

static double isospin_clebsch_gordan_2to1(const ParticleType &p_a,
                                          const ParticleType &p_b,
                                          const int I_tot, const int I_z) {
  return clebsch_gordan(p_a.isospin(), p_b.isospin(), I_tot, p_a.isospin3(),
                        p_b.isospin3(), I_z);
}

double isospin_clebsch_gordan_sqr_3to1(const ParticleType &p_a,
                                       const ParticleType &p_b,
                                       const ParticleType &p_c,
                                       const ParticleType &Res) {
  // Calculate allowed isospin range for 3->1 reaction I_ab
  const auto min_I_ab = std::abs(p_a.isospin() - p_b.isospin());
  const auto max_I_ab = p_a.isospin() + p_b.isospin();
  std::vector<int> possible_I_ab(max_I_ab - min_I_ab + 1);
  std::iota(possible_I_ab.begin(), possible_I_ab.end(), min_I_ab);
  std::vector<int> allowed_I_ab;
  allowed_I_ab.reserve(possible_I_ab.size());
  for (const auto Iab : possible_I_ab) {
    const auto min_I = std::abs(Iab - p_c.isospin());
    const auto max_I = Iab + p_c.isospin();
    if (min_I <= Res.isospin() && Res.isospin() <= max_I) {
      allowed_I_ab.push_back(Iab);
    }
  }
  if (allowed_I_ab.size() != 1) {
    throw std::runtime_error(
        "The coupled 3-body isospin state is not uniquely defined for " +
        Res.name() + " -> " + p_a.name() + " " + p_b.name() + " " + p_c.name());
  }
  const auto I_ab = allowed_I_ab[0];

  const int I_abz = p_a.isospin3() + p_b.isospin3();
  const double cg = clebsch_gordan(I_ab, p_c.isospin(), Res.isospin(), I_abz,
                                   p_c.isospin3(), Res.isospin3()) *
                    clebsch_gordan(p_a.isospin(), p_b.isospin(), I_ab,
                                   p_a.isospin3(), p_b.isospin3(), I_abz);
  return cg * cg;
}

double isospin_clebsch_gordan_sqr_2to2(const ParticleType &p_a,
                                       const ParticleType &p_b,
                                       const ParticleType &p_c,
                                       const ParticleType &p_d, const int I) {
  const int I_z = p_a.isospin3() + p_b.isospin3();

  /* Loop over total isospin in allowed range. */
  double isospin_factor = 0.;
  for (const int I_tot : I_tot_range(p_a, p_b, p_c, p_d)) {
    if (I < 0 || I_tot == I) {
      const double cg_in = isospin_clebsch_gordan_2to1(p_a, p_b, I_tot, I_z);
      const double cg_out = isospin_clebsch_gordan_2to1(p_c, p_d, I_tot, I_z);
      isospin_factor = isospin_factor + cg_in * cg_in * cg_out * cg_out;
    }
  }
  return isospin_factor;
}

}  // namespace smash