MagneticIon.cpp

#include "MantidKernel/MagneticIon.h"
#include "MantidKernel/Exception.h"

#include <sstream>

namespace Mantid {
namespace PhysicalConstants {
/// Default Constructor
MagneticIon::MagneticIon()
    : symbol(""), charge(0), j0(8, 0.0), j2(8, 0.0), j4(8, 0.0), j6(8, 0.0) {}

/**
 * Constructor from symbol, charge, and 4 vectors of 8 doubles each
 * @param symbol :: A string symbol defining the element
 * @param charge :: The value of the charge
 * @param j0i :: Form factor coefficients for n = 0
 * @param j2i :: Form factor coefficients for n = 2
 * @param j4i :: Form factor coefficients for n = 4
 * @param j6i :: Form factor coefficients for n = 6
 */
MagneticIon::MagneticIon(const std::string symbol, const uint16_t charge,
                         const double j0i[8], const double j2i[8],
                         const double j4i[8], const double j6i[8])
    : symbol(symbol), charge(charge), j0(j0i, j0i + 8), j2(j2i, j2i + 8),
      j4(j4i, j4i + 8), j6(j6i, j6i + 8) {}

/**
 * Returns the value of the form factor for the given \f$Q^2\f$ in
 * \f$\mbox{\AA}^-2\f$ taking into account the
 * number of terms given by the value of j & l
 * @param qsqr :: The square of the momentum transfer in \f$\mbox{\AA}^-2\f$
 * @param j :: The total angular momentum
 * @param l :: The orbital angular momentum
 * @return
 */
double MagneticIon::analyticalFormFactor(const double qsqr, const uint16_t j,
                                         const uint16_t l) const {
  if (j != 0 || l != 0) {
    throw Kernel::Exception::NotImplementedError(
        "MagneticIon::analyticalFormFactor - Only j=0 & l=0 terms have been "
        "implemented.");
  }
  if (qsqr < MagneticIon::formFactorCutOff(
                 j, l)) // Simplest approximation taking only j0 terms for low Q
  {
    static double fourPiSq = 16.0 * M_PI * M_PI;
    const double A = j0[0];
    const double alpha = j0[1] / fourPiSq;
    const double B = j0[2];
    const double beta = j0[3] / fourPiSq;
    const double C = j0[4];
    const double gamma = j0[5] / fourPiSq;
    const double D = j0[6];
    return A * std::exp(-alpha * qsqr) + B * std::exp(-beta * qsqr) +
           C * std::exp(-gamma * qsqr) + D;
  } else
    return 0.0; // Outside simple model range
}

/**
 * Returns the cutoff value for the given form factor approximation
 * @param j :: The total angular momentum
 * @param l :: The orbital angular momentum (default=0)
 * @return
 */
double MagneticIon::formFactorCutOff(const uint16_t j, const uint16_t l) {
  UNUSED_ARG(l);
  if (j == 0) {
    static double cutoff(36.0 * M_PI * M_PI);
    return cutoff;
  } else {
    throw Kernel::Exception::NotImplementedError(
        "MagneticIon::formFactorCutOff - Only j=0 & l=0 cutoff have been "
        "implemented.");
  }
}

namespace {
// Windows will not accept array initializer syntax within a constructor so put
// the various j_i definitions here
// The format is { j0, j2, j4, j6 }
double j_Sc0[4][8] = {
    {0.2512, 90.03, 0.329, 39.402, 0.4235, 14.322, -0.0043, 0.2029},  // <j0>
    {10.8172, 54.327, 4.7353, 14.847, 0.6071, 4.218, 0.0011, 0.1212}, // <j2>
    {1.342, 10.2, 0.3837, 3.079, 0.0468, 0.118, -0.0328, 0.1343},     // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Sc1[4][8] = {
    {0.4889, 51.16, 0.5203, 14.076, -0.0286, 0.179, 0.0185, 0.1217}, // <j0>
    {8.5021, 34.285, 3.2116, 10.994, 0.4244, 3.605, 0.0009, 0.1037}, // <j2>
    {7.1167, 15.487, -6.6671, 18.269, 0.49, 2.992, 0.0047, 0.1624},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Sc2[4][8] = {
    {0.5048, 31.403, 0.5186, 10.99, -0.0241, 1.183, 0, 0.0578},      // <j0>
    {4.3683, 28.654, 3.7231, 10.823, 0.6074, 3.668, 0.0014, 0.0681}, // <j2>
    {-1.6684, 15.648, 1.7742, 9.062, 0.4075, 2.412, 0.0042, 0.1105}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Ti0[4][8] = {
    {0.4657, 33.59, 0.549, 9.879, -0.0291, 0.323, 0.0123, 0.1088},   // <j0>
    {4.3583, 36.056, 3.823, 11.133, 0.6855, 3.469, 0.002, 0.0967},   // <j2>
    {-2.1515, 11.271, 2.5149, 8.859, 0.3555, 2.149, 0.0045, 0.1244}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Ti1[4][8] = {
    {0.5093, 36.703, 0.5032, 10.371, -0.0263, 0.311, 0.0116, 0.1125}, // <j0>
    {6.1567, 27.275, 2.6833, 8.983, 0.407, 3.052, 0.0011, 0.0902},    // <j2>
    {-1.0383, 16.19, 1.4699, 8.924, 0.3631, 2.283, 0.0044, 0.127},    // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Ti2[4][8] = {
    {0.5091, 24.976, 0.5162, 8.757, -0.0281, 0.916, 0.0015, 0.0589}, // <j0>
    {4.3107, 18.348, 2.096, 6.797, 0.2984, 2.548, 0.0007, 0.064},    // <j2>
    {-1.3242, 15.31, 1.2042, 7.899, 0.3976, 2.156, 0.0051, 0.082},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Ti3[4][8] = {
    {0.3571, 22.841, 0.6688, 8.931, -0.0354, 0.483, 0.0099, 0.0575}, // <j0>
    {3.3717, 14.444, 1.8258, 5.713, 0.247, 2.265, 0.0005, 0.0491},   // <j2>
    {-1.1117, 14.635, 0.7689, 6.927, 0.4385, 2.089, 0.006, 0.0572},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_V0[4][8] = {
    {0.4086, 28.811, 0.6077, 8.544, -0.0295, 0.277, 0.0123, 0.097}, // <j0>
    {3.76, 21.831, 2.4026, 7.546, 0.4464, 2.663, 0.0017, 0.0556},   // <j2>
    {-0.9633, 15.273, 0.9274, 7.732, 0.3891, 2.053, 0.0063, 0.084}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_V1[4][8] = {
    {0.4444, 32.648, 0.5683, 9.097, -0.2285, 0.022, 0.215, 0.1111},  // <j0>
    {4.7474, 23.323, 2.3609, 7.808, 0.4105, 2.706, 0.0014, 0.08},    // <j2>
    {-0.9606, 15.545, 1.1278, 8.118, 0.3653, 2.097, 0.0056, 0.1027}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_V2[4][8] = {
    {0.4085, 23.853, 0.6091, 8.246, -0.1676, 0.041, 0.1496, 0.0593}, // <j0>
    {3.4386, 16.53, 1.9638, 6.141, 0.2997, 2.267, 0.0009, 0.0565},   // <j2>
    {-1.1729, 14.973, 0.9092, 7.613, 0.4105, 2.039, 0.0067, 0.0719}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_V3[4][8] = {
    {0.3598, 19.336, 0.6632, 7.617, -0.3064, 0.03, 0.2835, 0.0515},  // <j0>
    {2.3005, 14.682, 2.0364, 6.13, 0.4099, 2.382, 0.0014, 0.0252},   // <j2>
    {-0.9417, 14.205, 0.5284, 6.607, 0.4411, 1.967, 0.0076, 0.0569}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_V4[4][8] = {
    {0.3106, 16.816, 0.7198, 7.049, -0.0521, 0.302, 0.0221, 0.0433}, // <j0>
    {1.8377, 12.267, 1.8247, 5.458, 0.3979, 2.248, 0.0012, 0.0399},  // <j2>
    {-0.7654, 13.097, 0.3071, 5.674, 0.4476, 1.871, 0.0081, 0.0518}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Cr0[4][8] = {
    {0.1135, 45.199, 0.3481, 19.493, 0.5477, 7.354, -0.0092, 0.1975}, // <j0>
    {3.4085, 20.127, 2.1006, 6.802, 0.4266, 2.394, 0.0019, 0.0662},   // <j2>
    {-0.667, 19.613, 0.5342, 6.478, 0.3641, 1.905, 0.0073, 0.0628},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Cr1[4][8] = {
    {-0.0977, 0.047, 0.4544, 26.005, 0.5579, 7.489, 0.0831, 0.1114}, // <j0>
    {3.7768, 20.346, 2.1028, 6.893, 0.401, 2.411, 0.0017, 0.0686},   // <j2>
    {-0.8309, 18.043, 0.7252, 7.531, 0.3828, 2.003, 0.0073, 0.0781}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Cr2[4][8] = {
    {1.2024, -0.005, 0.4158, 20.548, 0.6032, 6.956, -1.2218, 0.0572}, // <j0>
    {2.6422, 16.06, 1.9198, 6.253, 0.4446, 2.372, 0.002, 0.048},      // <j2>
    {-0.893, 15.664, 0.559, 7.033, 0.4093, 1.924, 0.0081, 0.0631},    // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Cr3[4][8] = {
    {-0.3094, 0.027, 0.368, 17.035, 0.6559, 6.524, 0.2856, 0.0436}, // <j0>
    {1.6262, 15.066, 2.0618, 6.284, 0.5281, 2.368, 0.0023, 0.0263}, // <j2>
    {-0.7327, 14.073, 0.3268, 5.674, 0.4114, 1.81, 0.0085, 0.0505}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Cr4[4][8] = {
    {-0.232, 0.043, 0.3101, 14.952, 0.7182, 6.173, 0.2042, 0.0419}, // <j0>
    {1.0293, 13.95, 1.9933, 6.059, 0.5974, 2.346, 0.0027, 0.0366},  // <j2>
    {-0.6748, 12.946, 0.1805, 6.753, 0.4526, 1.8, 0.0098, 0.0644},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Mn0[4][8] = {
    {0.2438, 24.963, 0.1472, 15.673, 0.6189, 6.54, -0.0105, 0.1748}, // <j0>
    {2.6681, 16.06, 1.7561, 5.64, 0.3675, 2.049, 0.0017, 0.0595},    // <j2>
    {-0.5452, 15.471, 0.4406, 4.902, 0.2884, 1.543, 0.0059, 0.0488}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Mn1[4][8] = {
    {-0.0138, 0.421, 0.4231, 24.668, 0.5905, 6.655, -0.001, 0.1242}, // <j0>
    {3.2953, 18.695, 1.8792, 6.24, 0.3927, 2.201, 0.0022, 0.0659},   // <j2>
    {-0.7947, 17.867, 0.6078, 7.704, 0.3798, 1.905, 0.0087, 0.0737}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Mn2[4][8] = {
    {0.422, 17.684, 0.5948, 6.005, 0.0043, -0.609, -0.0219, 0.0589}, // <j0>
    {2.0515, 15.556, 1.8841, 6.063, 0.4787, 2.232, 0.0027, 0.0306},  // <j2>
    {-0.7416, 15.255, 0.3831, 6.469, 0.3935, 1.8, 0.0093, 0.0577},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Mn3[4][8] = {
    {0.4198, 14.283, 0.6054, 5.469, 0.9241, -0.009, -0.9498, 0.0392}, // <j0>
    {1.2427, 14.997, 1.9567, 6.118, 0.5732, 2.258, 0.0031, 0.0336},   // <j2>
    {-0.6603, 13.607, 0.2322, 6.218, 0.4104, 1.74, 0.0101, 0.0579},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Mn4[4][8] = {
    {0.376, 12.566, 0.6602, 5.133, -0.0372, 0.563, 0.0011, 0.0393},  // <j0>
    {0.7879, 13.886, 1.8717, 5.743, 0.5981, 2.182, 0.0034, 0.0434},  // <j2>
    {-0.5127, 13.461, 0.0313, 7.763, 0.4282, 1.701, 0.0113, 0.0693}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Fe0[4][8] = {
    {0.0706, 35.008, 0.3589, 15.358, 0.5819, 5.561, -0.0114, 0.1398}, // <j0>
    {1.9405, 18.473, 1.9566, 6.323, 0.5166, 2.161, 0.0036, 0.0394},   // <j2>
    {-0.5029, 19.677, 0.2999, 3.776, 0.2576, 1.424, 0.0071, 0.0292},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Fe1[4][8] = {
    {0.1251, 34.963, 0.3629, 15.514, 0.5223, 5.591, -0.0105, 0.1301}, // <j0>
    {2.629, 18.66, 1.8704, 6.331, 0.469, 2.163, 0.0031, 0.0491},      // <j2>
    {-0.5109, 19.25, 0.3896, 4.891, 0.281, 1.526, 0.0069, 0.0375},    // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Fe2[4][8] = {
    {0.0263, 34.96, 0.3668, 15.943, 0.6188, 5.594, -0.0119, 0.1437}, // <j0>
    {1.649, 16.559, 1.9064, 6.133, 0.5206, 2.137, 0.0035, 0.0335},   // <j2>
    {-0.5401, 17.227, 0.2865, 3.742, 0.2658, 1.424, 0.0076, 0.0278}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Fe3[4][8] = {
    {0.3972, 13.244, 0.6295, 4.903, -0.0314, 0.35, 0.0044, 0.0441},  // <j0>
    {1.3602, 11.998, 1.5188, 5.003, 0.4705, 1.991, 0.0038, 0.0374},  // <j2>
    {-0.5507, 11.493, 0.2153, 4.906, 0.3468, 1.523, 0.0095, 0.0314}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Fe4[4][8] = {
    {0.3782, 11.38, 0.6556, 4.592, -0.0346, 0.483, 0.0005, 0.0362}, // <j0>
    {1.5582, 8.275, 1.1863, 3.279, 0.1366, 1.107, -0.0022, 0.0327}, // <j2>
    {-0.5352, 9.507, 0.1783, 5.175, 0.3584, 1.469, 0.0097, 0.036},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Co0[4][8] = {
    {0.4139, 16.162, 0.6013, 4.78, -0.1518, 0.021, 0.1345, 0.1033}, // <j0>
    {1.9678, 14.17, 1.4911, 4.948, 0.3844, 1.797, 0.0027, 0.0452},  // <j2>
    {-0.4221, 14.195, 0.29, 3.979, 0.2469, 1.286, 0.0063, 0.04},    // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Co1[4][8] = {
    {0.099, 33.125, 0.3645, 15.177, 0.547, 5.008, -0.0109, 0.0983}, // <j0>
    {2.4097, 16.161, 1.578, 5.46, 0.4095, 1.914, 0.0031, 0.0581},   // <j2>
    {-0.4115, 14.561, 0.358, 4.717, 0.2644, 1.418, 0.0074, 0.0541}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Co2[4][8] = {
    {0.4332, 14.355, 0.5857, 4.608, -0.0382, 0.134, 0.0179, 0.0711}, // <j0>
    {1.9049, 11.644, 1.3159, 4.357, 0.3146, 1.645, 0.0017, 0.0459},  // <j2>
    {0.4759, 14.046, 0.2747, 3.731, 0.2458, 1.25, 0.0057, 0.0282},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Co3[4][8] = {
    {0.3902, 12.508, 0.6324, 4.457, -0.15, 0.034, 0.1272, 0.0515},   // <j0>
    {1.7058, 8.859, 1.1409, 3.309, 0.1474, 1.09, -0.0025, 0.0462},   // <j2>
    {-0.4466, 13.391, 0.1419, 3.011, 0.2773, 1.335, 0.0093, 0.0341}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Co4[4][8] = {
    {0.3515, 10.778, 0.6778, 4.234, -0.0389, 0.241, 0.0098, 0.039},   // <j0>
    {1.311, 8.025, 1.1551, 3.179, 0.1608, 1.13, -0.0011, 0.0374},     // <j2>
    {-0.4091, 13.194, -0.0194, 3.417, 0.3534, 1.421, 0.0112, 0.0622}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Ni0[4][8] = {
    {-0.0172, 35.739, 0.3174, 14.269, 0.7136, 4.566, -0.0143, 0.1072}, // <j0>
    {1.0302, 12.252, 1.4669, 4.745, 0.4521, 1.744, 0.0036, 0.0338},    // <j2>
    {-0.4428, 14.485, 0.087, 3.234, 0.2932, 1.331, 0.0096, 0.0554},    // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Ni1[4][8] = {
    {0.0705, 35.856, 0.3984, 13.804, 0.5427, 4.397, -0.0118, 0.0738}, // <j0>
    {2.104, 14.866, 1.4302, 5.071, 0.4031, 1.778, 0.0034, 0.0561},    // <j2>
    {-0.3836, 13.425, 0.3116, 4.462, 0.2471, 1.309, 0.0079, 0.0515},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Ni2[4][8] = {
    {0.0163, 35.883, 0.3916, 13.223, 0.6052, 4.339, -0.0133, 0.0817}, // <j0>
    {1.708, 11.016, 1.2147, 4.103, 0.315, 1.533, 0.0018, 0.0446},     // <j2>
    {-0.3803, 10.403, 0.2838, 3.378, 0.2108, 1.104, 0.005, 0.0474},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Ni3[4][8] = {
    {0.0012, 35, 0.3468, 11.987, 0.6667, 4.252, -0.0148, 0.0883},   // <j0>
    {1.4683, 8.671, 0.1794, 1.106, 1.1068, 3.257, -0.0023, 0.0373}, // <j2>
    {-0.4014, 9.046, 0.2314, 3.075, 0.2192, 1.084, 0.006, 0.0323},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Ni4[4][8] = {
    {-0.009, 35.861, 0.2776, 11.79, 0.7474, 4.201, -0.0163, 0.0966}, // <j0>
    {1.1612, 7.7, 1.0027, 3.263, 0.2719, 1.378, 0.0025, 0.0326},     // <j2>
    {-0.3509, 8.157, 0.222, 2.106, 0.1567, 0.925, 0.0065, 0.0352},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Cu0[4][8] = {
    {0.0909, 34.984, 0.4088, 11.443, 0.5128, 3.825, -0.0124, 0.0513}, // <j0>
    {1.9182, 14.49, 1.3329, 4.73, 0.3842, 1.639, 0.0035, 0.0617},     // <j2>
    {-0.3204, 15.132, 0.2335, 4.021, 0.2312, 1.196, 0.0068, 0.0457},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Cu1[4][8] = {
    {0.0749, 34.966, 0.4147, 11.764, 0.5238, 3.85, -0.0127, 0.0591}, // <j0>
    {1.8814, 13.433, 1.2809, 4.545, 0.3646, 1.602, 0.0033, 0.059},   // <j2>
    {-0.3572, 15.125, 0.2336, 3.966, 0.2315, 1.197, 0.007, 0.0397},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Cu2[4][8] = {
    {0.0232, 34.969, 0.4023, 11.564, 0.5882, 3.843, -0.0137, 0.0532}, // <j0>
    {1.5189, 10.478, 1.1512, 3.813, 0.2918, 1.398, 0.0017, 0.0429},   // <j2>
    {-0.3914, 14.74, 0.1275, 3.384, 0.2548, 1.255, 0.0103, 0.0394},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Cu3[4][8] = {
    {0.0031, 34.907, 0.3582, 10.914, 0.6531, 3.828, -0.0147, 0.0665}, // <j0>
    {1.2797, 8.45, 1.0315, 3.28, 0.2401, 1.25, 0.0015, 0.0389},       // <j2>
    {-0.3671, 14.082, -0.0078, 3.315, 0.3154, 1.377, 0.0132, 0.0534}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Cu4[4][8] = {
    {-0.0132, 30.682, 0.2801, 11.163, 0.749, 3.817, -0.0165, 0.0767}, // <j0>
    {0.9568, 7.448, 0.9099, 3.396, 0.3729, 1.494, 0.0049, 0.033},     // <j2>
    {-0.2915, 14.124, -0.1065, 4.201, 0.3247, 1.352, 0.0148, 0.0579}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Y0[4][8] = {
    {0.5915, 67.608, 1.5123, 17.9, -1.113, 14.136, 0.008, 0.3272},     // <j0>
    {14.4084, 44.658, 5.1045, 14.904, -0.0535, 3.319, 0.0028, 0.1093}, // <j2>
    {-8.0767, 32.201, 7.9197, 25.156, 1.4067, 6.827, -0.0001, 0.1031}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Zr0[4][8] = {
    {0.4106, 59.996, 1.0543, 18.648, -0.4751, 10.54, 0.0106, 0.3667},  // <j0>
    {10.1378, 35.337, 4.7734, 12.545, -0.0489, 2.672, 0.0036, 0.0912}, // <j2>
    {-5.2697, 32.868, 4.193, 24.183, 1.5202, 6.048, -0.0002, 0.0855},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Zr1[4][8] = {
    {0.4532, 59.595, 0.7834, 21.436, -0.2451, 9.036, 0.0098, 0.3639},  // <j0>
    {11.8722, 34.92, 4.0502, 12.127, -0.0632, 2.828, 0.0034, 0.0737},  // <j2>
    {-5.6384, 33.607, 4.6729, 22.338, 1.3258, 5.924, -0.0003, 0.0674}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Nb0[4][8] = {
    {0.3946, 49.23, 1.3197, 14.822, -0.7269, 9.616, 0.0129, 0.3659},  // <j0>
    {7.4796, 33.179, 5.0884, 11.571, -0.0281, 1.564, 0.0047, 0.0944}, // <j2>
    {-3.1377, 25.595, 2.3411, 16.569, 1.2304, 4.99, -0.0005, 0.0615}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Nb1[4][8] = {
    {0.4572, 49.918, 1.0274, 15.726, -0.4962, 9.157, 0.0118, 0.3403}, // <j0>
    {8.7735, 33.285, 4.6556, 11.605, -0.0268, 1.539, 0.0044, 0.0855}, // <j2>
    {-3.3598, 25.82, 2.8297, 16.427, 1.1203, 4.982, -0.0005, 0.0724}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Mo0[4][8] = {
    {0.1806, 49.057, 1.2306, 14.786, -0.4268, 6.987, 0.0171, 0.4135}, // <j0>
    {5.118, 23.422, 4.1809, 9.208, -0.0505, 1.743, 0.0053, 0.0655},   // <j2>
    {-2.886, 20.572, 1.813, 14.628, 1.1899, 4.264, -0.0008, 0.041},   // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Mo1[4][8] = {
    {0.35, 48.035, 1.0305, 15.06, -0.3929, 7.479, 0.0139, 0.351},      // <j0>
    {7.2367, 28.128, 4.0705, 9.923, -0.0317, 1.455, 0.0049, 0.0798},   // <j2>
    {-3.2618, 25.486, 2.3596, 16.462, 1.1164, 4.491, -0.0007, 0.0592}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Tc0[4][8] = {
    {0.1298, 49.661, 1.1656, 14.131, -0.3134, 5.513, 0.0195, 0.3869}, // <j0>
    {4.2441, 21.397, 3.9439, 8.375, -0.0371, 1.187, 0.0066, 0.0645},  // <j2>
    {-2.7975, 20.159, 1.652, 16.261, 1.1726, 3.943, -0.0008, 0.0657}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Tc1[4][8] = {
    {0.2674, 48.957, 0.9569, 15.141, -0.2387, 5.458, 0.016, 0.3412}, // <j0>
    {6.4056, 24.824, 3.54, 8.611, -0.0366, 1.485, 0.0044, 0.0806},   // <j2>
    {-2.047, 19.683, 1.6306, 11.592, 0.8698, 3.769, -0.001, 0.0723}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                       // <j6>
double j_Ru0[4][8] = {
    {0.1069, 49.424, 1.1912, 12.742, -0.3176, 4.912, 0.0213, 0.3597}, // <j0>
    {3.7445, 18.613, 3.4749, 7.42, -0.0363, 1.007, 0.0073, 0.0533},   // <j2>
    {-1.5042, 17.949, 0.6027, 9.961, 0.97, 3.393, -0.001, 0.0338},    // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Ru1[4][8] = {
    {0.441, 33.309, 1.4775, 9.553, -0.9361, 6.722, 0.0176, 0.2608},   // <j0>
    {5.2826, 23.683, 3.5813, 8.152, -0.0257, 0.426, 0.0131, 0.083},   // <j2>
    {1.6278, 18.506, 1.1828, 10.189, 0.8138, 3.418, -0.0009, 0.0673}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Rh0[4][8] = {
    {0.0976, 49.882, 1.1601, 11.831, -0.2789, 4.127, 0.0234, 0.3263},  // <j0>
    {3.3651, 17.344, 3.2121, 6.804, -0.035, 0.503, 0.0146, 0.0545},    // <j2>
    {-1.3492, 17.577, 0.4527, 10.507, 0.9285, 3.155, -0.0009, 0.0483}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Rh1[4][8] = {
    {0.3342, 29.756, 1.2209, 9.438, -0.5755, 5.332, 0.021, 0.2574},   // <j0>
    {4.026, 18.95, 3.1663, 7, -0.0296, 0.486, 0.0127, 0.0629},        // <j2>
    {-1.4673, 17.957, 0.7381, 9.944, 0.8485, 3.126, -0.0012, 0.0487}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                        // <j6>
double j_Pd0[4][8] = {
    {0.2003, 29.363, 1.1446, 9.599, -0.3689, 4.042, 0.0251, 0.2453},   // <j0>
    {3.3105, 14.726, 2.6332, 5.862, -0.0437, 1.13, 0.0053, 0.0492},    // <j2>
    {-1.1955, 17.628, 0.3183, 11.309, 0.8696, 2.909, -0.0006, 0.0555}, // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                         // <j6>
double j_Pd1[4][8] = {
    {0.5033, 24.504, 1.9982, 6.908, -1.524, 5.513, 0.0213, 0.1909}, // <j0>
    {4.2749, 17.9, 2.7021, 6.354, -0.0258, 0.7, 0.0071, 0.0768},    // <j2>
    {-1.4098, 17.765, 0.7927, 9.999, 0.771, 2.93, -0.0006, 0.053},  // <j4>
    {0, 0, 0, 0, 0, 0, 0, 0}};                                      // <j6>
double j_Ce2[4][8] = {
    {0.2953, 17.685, 0.2923, 6.733, 0.4313, 5.383, -0.0194, 0.0845},  // <j0>
    {0.9809, 18.063, 1.8413, 7.769, 0.9905, 2.845, 0.012, 0.0448},    // <j2>
    {-0.6468, 10.533, 0.4052, 5.624, 0.3412, 1.535, 0.008, 0.0522},   // <j4>
    {-0.1212, 7.994, -0.0639, 4.024, 0.1519, 1.096, 0.0078, 0.0388}}; // <j6>
double j_Nd2[4][8] = {
    {0.1645, 25.045, 0.2522, 11.978, 0.6012, 4.946, -0.018, 0.0668}, // <j0>
    {1.453, 18.34, 1.6196, 7.285, 0.8752, 2.622, 0.0126, 0.0461},    // <j2>
    {-0.5416, 12.204, 0.3571, 6.169, 0.3154, 1.485, 0.0098, 0.0519}, // <j4>
    {-0.16, 8.009, 0.0272, 4.028, 0.1104, 1.068, 0.0139, 0.0363}};   // <j6>
double j_Nd3[4][8] = {
    {0.054, 25.029, 0.3101, 12.102, 0.6575, 4.722, -0.0216, 0.0478}, // <j0>
    {0.6751, 18.342, 1.6272, 7.26, 0.9644, 2.602, 0.015, 0.045},     // <j2>
    {-0.4053, 14.014, 0.0329, 7.005, 0.3759, 1.707, 0.0209, 0.0372}, // <j4>
    {0.0416, 8.014, -0.1261, 4.04, 0.14, 1.087, 0.0102, 0.0367}};    // <j6>
double j_Sm2[4][8] = {
    {0.0909, 25.203, 0.3037, 11.856, 0.625, 4.237, -0.02, 0.0408},  // <j0>
    {1.036, 18.425, 1.4769, 7.032, 0.881, 2.437, 0.0152, 0.0345},   // <j2>
    {-0.415, 14.057, 0.1368, 7.032, 0.3272, 1.582, 0.0192, 0.0319}, // <j4>
    {0.1428, 6.041, 0.0723, 2.033, 0.055, 0.513, 0.0081, 0.045}};   // <j6>
double j_Sm3[4][8] = {
    {0.0288, 25.207, 0.2973, 11.831, 0.6954, 4.212, -0.0213, 0.051},  // <j0>
    {0.4707, 18.43, 1.4261, 7.034, 0.9574, 2.439, 0.0182, 0.051},     // <j2>
    {-0.4288, 10.052, 0.1782, 5.019, 0.2833, 1.236, 0.0088, 0.0328},  // <j4>
    {-0.0944, 6.03, -0.0498, 2.074, 0.1372, 0.645, -0.0132, 0.0387}}; // <j6>
double j_Eu2[4][8] = {
    {0.0755, 25.296, 0.3001, 11.599, 0.6438, 4.025, -0.0196, 0.0488}, // <j0>
    {0.897, 18.443, 1.3769, 7.005, 0.906, 2.421, 0.019, 0.0511},      // <j2>
    {-0.4145, 10.193, 0.2447, 5.164, 0.2661, 1.205, 0.0065, 0.0516},  // <j4>
    {-0.1252, 6.049, 0.0507, 2.085, 0.0572, 0.646, 0.0132, 0.0403}};  // <j6>
double j_Eu3[4][8] = {
    {0.0204, 25.308, 0.301, 11.474, 0.7005, 3.942, -0.022, 0.0356},   // <j0>
    {0.3985, 18.451, 1.3307, 6.956, 0.9603, 2.378, 0.0197, 0.0447},   // <j2>
    {-0.4095, 10.211, 0.1485, 5.175, 0.272, 1.237, 0.0131, 0.0494},   // <j4>
    {-0.0817, 6.039, -0.0596, 2.12, 0.1243, 0.764, -0.0001, 0.0206}}; // <j6>
double j_Gd2[4][8] = {
    {0.0636, 25.382, 0.3033, 11.212, 0.6528, 3.788, -0.0199, 0.0486}, // <j0>
    {0.7756, 18.469, 1.3124, 6.899, 0.8956, 2.338, 0.0199, 0.0441},   // <j2>
    {-0.3824, 10.344, 0.1955, 5.306, 0.2622, 1.203, 0.0097, 0.0363},  // <j4>
    {-0.1351, 5.03, 0.0828, 2.025, 0.0315, 0.503, 0.0187, 0.0453}};   // <j6>
double j_Gd3[4][8] = {
    {0.0186, 25.387, 0.2895, 11.142, 0.7135, 3.752, -0.0217, 0.0489}, // <j0>
    {0.3347, 18.476, 1.2465, 6.877, 0.9537, 2.318, 0.0217, 0.0484},   // <j2>
    {-0.3621, 10.353, 0.1016, 5.31, 0.2649, 1.219, 0.0147, 0.0494},   // <j4>
    {-0.0662, 6.031, -0.085, 2.154, 0.1323, 0.891, 0.0048, 0.0371}};  // <j6>
double j_Tb2[4][8] = {
    {0.0547, 25.509, 0.3171, 10.591, 0.649, 3.517, -0.0212, 0.0342}, // <j0>
    {0.6688, 18.491, 1.2487, 6.822, 0.8888, 2.275, 0.0215, 0.0439},  // <j2>
    {-0.3443, 10.469, 0.1481, 5.416, 0.2575, 1.182, 0.0104, 0.028},  // <j4>
    {-0.0758, 6.032, -0.054, 2.158, 0.1199, 0.89, 0.0051, 0.0488}};  // <j6>
double j_Tb3[4][8] = {
    {0.0177, 25.51, 0.2921, 10.577, 0.7133, 3.512, -0.0231, 0.0512}, // <j0>
    {0.2892, 18.497, 1.1678, 6.797, 0.9437, 2.257, 0.0232, 0.0458},  // <j2>
    {-0.3228, 10.476, 0.0638, 5.419, 0.2566, 1.196, 0.0159, 0.0439}, // <j4>
    {-0.0559, 6.031, -0.102, 2.237, 0.1264, 1.107, 0.0167, 0.017}};  // <j6>
double j_Dy2[4][8] = {
    {0.1308, 18.316, 0.3118, 7.665, 0.5795, 3.147, -0.0226, 0.0315}, // <j0>
    {0.5917, 18.511, 1.1828, 6.747, 0.8801, 2.214, 0.0229, 0.0439},  // <j2>
    {-0.3206, 12.071, 0.0904, 8.026, 0.2616, 1.23, 0.0143, 0.0767},  // <j4>
    {-0.0568, 6.032, -0.1003, 2.24, 0.1401, 1.106, 0.0109, 0.0463}}; // <j6>
double j_Dy3[4][8] = {
    {0.1157, 15.073, 0.327, 6.799, 0.5821, 3.02, -0.0249, 0.0146},  // <j0>
    {0.2523, 18.517, 1.0914, 6.736, 0.9345, 2.208, 0.025, 0.0476},  // <j2>
    {-0.2829, 9.525, 0.0565, 4.429, 0.2437, 1.066, 0.0092, 0.0181}, // <j4>
    {-0.0423, 6.038, -0.1248, 2.244, 0.1359, 1.2, 0.0188, 0.035}};  // <j6>
double j_Ho2[4][8] = {
    {0.0995, 18.176, 0.3305, 7.856, 0.5921, 2.98, -0.023, 0.124},     // <j0>
    {0.5094, 18.515, 1.1234, 6.706, 0.8727, 2.159, 0.0242, 0.056},    // <j2>
    {-0.2976, 9.719, 0.1224, 4.635, 0.2279, 1.005, 0.0063, 0.0452},   // <j4>
    {-0.0725, 6.045, -0.0318, 2.243, 0.0738, 1.202, 0.0252, 0.0634}}; // <j6>
double j_Ho3[4][8] = {
    {0.0566, 18.318, 0.3365, 7.688, 0.6317, 2.943, -0.0248, 0.0068}, // <j0>
    {0.2188, 18.516, 1.024, 6.707, 0.9251, 2.161, 0.0268, 0.0503},   // <j2>
    {-0.2717, 9.731, 0.0474, 4.638, 0.2292, 1.047, 0.0124, 0.031},   // <j4>
    {-0.0289, 6.05, -0.1545, 2.23, 0.155, 1.26, 0.0177, 0.0351}};    // <j6>
double j_Er2[4][8] = {
    {0.1122, 18.122, 0.3462, 6.911, 0.5649, 2.761, -0.0235, 0.0207}, // <j0>
    {0.4693, 18.528, 1.0545, 6.649, 0.8679, 2.12, 0.0261, 0.0413},   // <j2>
    {-0.2975, 9.829, 0.1189, 4.741, 0.2116, 1.004, 0.0117, 0.0524},  // <j4>
    {0.0648, 6.056, -0.0515, 2.23, 0.0825, 1.264, 0.025, 0.0409}};   // <j6>
double j_Er3[4][8] = {
    {0.0586, 17.98, 0.354, 7.096, 0.6126, 2.748, -0.0251, 0.0171},   // <j0>
    {0.171, 18.534, 0.9879, 6.625, 0.9044, 2.1, 0.0278, 0.0489},     // <j2>
    {-0.2568, 9.834, 0.0356, 4.741, 0.2172, 1.028, 0.0148, 0.0434},  // <j4>
    {-0.011, 6.061, -0.1954, 2.224, 0.1818, 1.296, 0.0149, 0.0455}}; // <j6>
double j_Tm2[4][8] = {
    {0.0983, 18.324, 0.338, 6.918, 0.5875, 2.662, -0.0241, 0.0404}, // <j0>
    {0.4198, 18.542, 0.9959, 6.6, 0.8593, 2.082, 0.0284, 0.0457},   // <j2>
    {-0.2677, 9.888, 0.0925, 4.784, 0.2056, 0.99, 0.0124, 0.0396},  // <j4>
    {0.0842, 4.07, 0.0807, 0.849, -0.2087, 0.039, 0.2095, 0.036}};  // <j6>
double j_Tm3[4][8] = {
    {0.0581, 15.092, 0.2787, 7.801, 0.6854, 2.793, -0.0224, 0.0351}, // <j0>
    {0.176, 18.542, 0.9105, 6.579, 0.897, 2.062, 0.0294, 0.0468},    // <j2>
    {-0.2292, 9.895, 0.0124, 4.785, 0.2108, 1.007, 0.0151, 0.0334},  // <j4>
    {0.0727, 4.073, 0.0243, 0.689, 3.9459, 0.002, -3.9076, 0.0502}}; // <j6>
double j_Yb2[4][8] = {
    {0.0855, 18.512, 0.2943, 7.373, 0.6412, 2.678, -0.0213, 0.0421}, // <j0>
    {0.3852, 18.55, 0.9415, 6.551, 0.8492, 2.043, 0.0301, 0.0478},   // <j2>
    {-0.2393, 9.947, 0.0663, 4.823, 0.2009, 0.965, 0.0122, 0.0311},  // <j4>
    {-0.0739, 5.031, 0.014, 2.03, 0.0351, 0.508, 0.0174, 0.0434}};   // <j6>
double j_Yb3[4][8] = {
    {0.0416, 16.095, 0.2849, 7.834, 0.6961, 2.672, -0.0229, 0.0344},  // <j0>
    {0.157, 18.555, 0.8484, 6.54, 0.888, 2.037, 0.0318, 0.0498},      // <j2>
    {-0.2121, 8.197, 0.0325, 3.153, 0.1975, 0.884, 0.0093, 0.0435},   // <j4>
    {-0.0345, 5.007, -0.0677, 2.02, 0.0985, 0.549, -0.0076, 0.0359}}; // <j6>
double j_U3[4][8] = {
    {0.5058, 23.288, 1.3464, 7.003, -0.8724, 4.868, 0.0192, 0.1507}, // <j0>
    {4.1582, 16.534, 2.4675, 5.952, -0.0252, 0.765, 0.0057, 0.0822}, // <j2>
    {-0.9859, 16.601, 0.6116, 6.515, 0.602, 2.597, -0.001, 0.0599},  // <j4>
    {-0.3797, 9.953, 0.0459, 5.038, 0.2748, 1.607, 0.0016, 0.0345}}; // <j6>
double j_U4[4][8] = {
    {0.3291, 23.548, 1.0836, 8.454, -0.434, 4.12, 0.0214, 0.1757},    // <j0>
    {3.7449, 13.894, 2.6453, 4.863, -0.5218, 3.192, 0.0009, 0.0928},  // <j2>
    {-1.054, 16.605, 0.4339, 6.512, 0.6746, 2.599, -0.0011, 0.0471},  // <j4>
    {-0.1793, 11.896, -0.2269, 5.428, 0.3291, 1.701, 0.003, 0.0472}}; // <j6>
double j_U5[4][8] = {
    {0.365, 19.804, 3.2199, 6.282, -2.6077, 5.301, 0.0233, 0.175},   // <j0>
    {3.0724, 12.546, 2.3076, 5.231, -0.0644, 1.474, 0.0035, 0.0477}, // <j2>
    {-0.9588, 16.485, 0.1576, 6.44, 0.7785, 2.64, -0.001, 0.0493},   // <j4>
    {-0.0399, 11.891, -0.3458, 5.58, 0.334, 1.645, 0.0029, 0.0444}}; // <j6>
double j_Np3[4][8] = {
    {0.5157, 20.865, 2.2784, 5.893, -1.8163, 4.846, 0.0211, 0.1378},   // <j0>
    {3.717, 15.133, 2.3216, 5.503, -0.0275, 0.8, 0.0052, 0.0948},      // <j2>
    {0.9029, 16.586, 0.4006, 6.47, 0.6545, 2.563, -0.0004, 0.047},     // <j4>
    {-0.2427, 11.844, -0.1129, 5.377, 0.2848, 1.568, 0.0022, 0.0368}}; // <j6>
double j_Np4[4][8] = {
    {0.4206, 19.805, 2.8004, 5.978, -2.2436, 4.985, 0.0228, 0.1408},  // <j0>
    {2.9203, 14.646, 2.5979, 5.559, -0.0301, 0.367, 0.0141, 0.0532},  // <j2>
    {-0.9887, 12.441, 0.5918, 5.294, 0.5306, 2.263, -0.0021, 0.0583}, // <j4>
    {-0.2436, 9.599, -0.1317, 4.101, 0.3029, 1.545, 0.0019, 0.05}};   // <j6>
double j_Np5[4][8] = {
    {0.3692, 18.19, 3.151, 5.85, -2.5446, 4.916, 0.0248, 0.1515},    // <j0>
    {2.3308, 13.654, 2.7219, 5.494, -0.1357, 0.049, 0.1224, 0.0553}, // <j2>
    {-0.8146, 16.581, -0.0055, 6.475, 0.7956, 2.562, -0.0004, 0.06}, // <j4>
    {-0.1157, 9.565, -0.2654, 4.26, 0.3298, 1.549, 0.0025, 0.0495}}; // <j6>
double j_Np6[4][8] = {
    {0.2929, 17.561, 3.4866, 5.785, -2.8066, 4.871, 0.0267, 0.1698},  // <j0>
    {1.8245, 13.18, 2.8508, 5.407, -0.1579, 0.044, 0.1438, 0.0585},   // <j2>
    {0.6738, 16.553, -0.2297, 6.505, 0.8513, 2.553, -0.0003, 0.0623}, // <j4>
    {-0.0128, 9.569, -0.3611, 4.304, 0.3419, 1.541, 0.0032, 0.052}};  // <j6>
double j_Pu3[4][8] = {
    {0.384, 16.679, 3.1049, 5.421, -2.5148, 4.551, 0.0263, 0.128},   // <j0>
    {2.0885, 12.871, 2.5961, 5.19, -0.1465, 0.039, 0.1343, 0.0866},  // <j2>
    {-0.7014, 16.369, -0.1162, 6.697, 0.7778, 2.45, 0, 0.0546},      // <j4>
    {-0.0364, 9.572, -0.3181, 4.342, 0.321, 1.523, 0.0041, 0.0496}}; // <j6>
double j_Pu4[4][8] = {
    {0.4934, 16.836, 1.6394, 5.638, -1.1581, 4.14, 0.0248, 0.1242},   // <j0>
    {2.7244, 12.926, 2.3387, 5.163, -0.13, 0.046, 0.1177, 0.049},     // <j2>
    {-0.916, 12.203, 0.4891, 5.127, 0.529, 2.149, -0.0022, 0.052},    // <j4>
    {-0.2394, 7.837, -0.0785, 4.024, 0.2643, 1.378, 0.0012, 0.0414}}; // <j6>
double j_Pu5[4][8] = {
    {0.3888, 16.559, 2.0362, 5.657, -1.4515, 4.255, 0.0267, 0.1287}, // <j0>
    {2.1409, 12.832, 2.5664, 5.152, -0.1338, 0.046, 0.121, 0.0491},  // <j2>
    {-0.7035, 16.36, -0.0979, 6.706, 0.7726, 2.447, 0, 0.061},       // <j4>
    {-0.109, 7.819, -0.2243, 4.1, 0.2947, 1.404, 0.0015, 0.0477}};   // <j6>
double j_Pu6[4][8] = {
    {0.3172, 16.051, 3.4654, 5.351, -2.8102, 4.513, 0.0281, 0.1382}, // <j0>
    {1.7262, 12.324, 2.6652, 5.066, -0.1695, 0.041, 0.155, 0.0502},  // <j2>
    {-0.556, 16.322, -0.3046, 6.768, 0.8146, 2.426, 0.0001, 0.0596}, // <j4>
    {-0.0001, 7.82, -0.3354, 4.144, 0.3097, 1.403, 0.002, 0.0513}};  // <j6>
double j_Am2[4][8] = {
    {0.4743, 21.776, 1.58, 5.69, -1.0779, 4.145, 0.0218, 0.1253},    // <j0>
    {3.5237, 15.955, 2.2855, 5.195, -0.0142, 0.585, 0.0033, 0.112},  // <j2>
    {-0.7433, 16.416, 0.3481, 6.788, 0.6014, 2.346, 0, 0.0566},      // <j4>
    {-0.3176, 7.864, 0.0771, 4.161, 0.2194, 1.339, 0.0018, 0.0374}}; // <j6>
double j_Am3[4][8] = {
    {0.4239, 19.574, 1.4573, 5.872, -0.9052, 3.968, 0.0238, 0.1054},  // <j0>
    {2.8622, 14.733, 2.4099, 5.144, -0.1326, 0.031, 0.1233, 0.0727},  // <j2>
    {0.8092, 12.854, 0.4161, 5.459, 0.5476, 2.172, -0.0011, 0.053},   // <j4>
    {-0.3159, 6.982, 0.0682, 3.995, 0.2141, 1.188, -0.0015, 0.0281}}; // <j6>
double j_Am4[4][8] = {
    {0.3737, 17.862, 1.3521, 6.043, -0.7514, 3.72, 0.0258, 0.1113},   // <j0>
    {2.4141, 12.948, 2.3687, 4.945, -0.249, 0.022, 0.2371, 0.0502},   // <j2>
    {-0.8548, 12.226, 0.3037, 5.909, 0.6173, 2.188, -0.0016, 0.0456}, // <j4>
    {-0.1787, 7.88, -0.1274, 4.09, 0.2565, 1.315, 0.0017, 0.0419}};   // <j6>
double j_Am5[4][8] = {
    {0.2956, 17.372, 1.4525, 6.073, -0.7755, 3.662, 0.0277, 0.1202},  // <j0>
    {2.0109, 12.053, 2.4155, 4.836, -0.2264, 0.027, 0.2128, 0.0414},  // <j2>
    {-0.6538, 15.462, -0.0948, 5.997, 0.7295, 2.297, 0, 0.0594},      // <j4>
    {-0.0927, 6.073, -0.2227, 3.784, 0.2916, 1.372, 0.0026, 0.0485}}; // <j6>
double j_Am6[4][8] = {
    {0.2302, 16.953, 1.4864, 6.116, -0.7457, 3.543, 0.0294, 0.1323}, // <j0>
    {1.6778, 11.337, 2.4531, 4.725, -0.2043, 0.034, 0.1892, 0.0387}, // <j2>
    {-0.539, 15.449, -0.2689, 6.017, 0.7711, 2.297, 0.0002, 0.0729}, // <j4>
    {0.0152, 6.079, -0.3549, 3.861, 0.3125, 1.403, 0.0036, 0.0732}}; // <j6>
double j_Am7[4][8] = {
    {0.3601, 12.73, 1.964, 5.12, -1.356, 3.714, 0.0316, 0.1232},       // <j0>
    {1.8845, 9.161, 2.0746, 4.042, -0.1318, 1.723, 0.002, 0.0379},     // <j2>
    {-0.4688, 12.019, -0.2692, 7.042, 0.7297, 2.164, -0.0011, 0.0262}, // <j4>
    {0.1292, 6.082, -0.4689, 3.879, 0.3234, 1.393, 0.0042, 0.0475}};   // <j6>
}

/// Typedef the map type
typedef std::map<std::string, MagneticIon> IonIndex;

/// Forward decalre intializer
void createIonLookup(IonIndex &ion_map);

/// Returns a reference to the static lookup map
const IonIndex &ionMap() {
  static IonIndex ionMap;
  if (ionMap.empty()) {
    createIonLookup(ionMap);
  }
  return ionMap;
}

/**
 * Creates the lookup table
 * @param ion_map A reference to the static lookup
 */
void createIonLookup(IonIndex &ion_map) {
  static const MagneticIon Sc0((std::string) "Sc", (uint16_t)0, j_Sc0[0],
                               j_Sc0[1], j_Sc0[2], j_Sc0[3]);
  ion_map["Sc0"] = Sc0;
  static const MagneticIon Sc1((std::string) "Sc", (uint16_t)1, j_Sc1[0],
                               j_Sc1[1], j_Sc1[2], j_Sc1[3]);
  ion_map["Sc1"] = Sc1;
  static const MagneticIon Sc2((std::string) "Sc", (uint16_t)2, j_Sc2[0],
                               j_Sc2[1], j_Sc2[2], j_Sc2[3]);
  ion_map["Sc2"] = Sc2;
  static const MagneticIon Ti0((std::string) "Ti", (uint16_t)0, j_Ti0[0],
                               j_Ti0[1], j_Ti0[2], j_Ti0[3]);
  ion_map["Ti0"] = Ti0;
  static const MagneticIon Ti1((std::string) "Ti", (uint16_t)1, j_Ti1[0],
                               j_Ti1[1], j_Ti1[2], j_Ti1[3]);
  ion_map["Ti1"] = Ti1;
  static const MagneticIon Ti2((std::string) "Ti", (uint16_t)2, j_Ti2[0],
                               j_Ti2[1], j_Ti2[2], j_Ti2[3]);
  ion_map["Ti2"] = Ti2;
  static const MagneticIon Ti3((std::string) "Ti", (uint16_t)3, j_Ti3[0],
                               j_Ti3[1], j_Ti3[2], j_Ti3[3]);
  ion_map["Ti3"] = Ti3;
  static const MagneticIon V0((std::string) "V", (uint16_t)0, j_V0[0], j_V0[1],
                              j_V0[2], j_V0[3]);
  ion_map["V0"] = V0;
  static const MagneticIon V1((std::string) "V", (uint16_t)1, j_V1[0], j_V1[1],
                              j_V1[2], j_V1[3]);
  ion_map["V1"] = V1;
  static const MagneticIon V2((std::string) "V", (uint16_t)2, j_V2[0], j_V2[1],
                              j_V2[2], j_V2[3]);
  ion_map["V2"] = V2;
  static const MagneticIon V3((std::string) "V", (uint16_t)3, j_V3[0], j_V3[1],
                              j_V3[2], j_V3[3]);
  ion_map["V3"] = V3;
  static const MagneticIon V4((std::string) "V", (uint16_t)4, j_V4[0], j_V4[1],
                              j_V4[2], j_V4[3]);
  ion_map["V4"] = V4;
  static const MagneticIon Cr0((std::string) "Cr", (uint16_t)0, j_Cr0[0],
                               j_Cr0[1], j_Cr0[2], j_Cr0[3]);
  ion_map["Cr0"] = Cr0;
  static const MagneticIon Cr1((std::string) "Cr", (uint16_t)1, j_Cr1[0],
                               j_Cr1[1], j_Cr1[2], j_Cr1[3]);
  ion_map["Cr1"] = Cr1;
  static const MagneticIon Cr2((std::string) "Cr", (uint16_t)2, j_Cr2[0],
                               j_Cr2[1], j_Cr2[2], j_Cr2[3]);
  ion_map["Cr2"] = Cr2;
  static const MagneticIon Cr3((std::string) "Cr", (uint16_t)3, j_Cr3[0],
                               j_Cr3[1], j_Cr3[2], j_Cr3[3]);
  ion_map["Cr3"] = Cr3;
  static const MagneticIon Cr4((std::string) "Cr", (uint16_t)4, j_Cr4[0],
                               j_Cr4[1], j_Cr4[2], j_Cr4[3]);
  ion_map["Cr4"] = Cr4;
  static const MagneticIon Mn0((std::string) "Mn", (uint16_t)0, j_Mn0[0],
                               j_Mn0[1], j_Mn0[2], j_Mn0[3]);
  ion_map["Mn0"] = Mn0;
  static const MagneticIon Mn1((std::string) "Mn", (uint16_t)1, j_Mn1[0],
                               j_Mn1[1], j_Mn1[2], j_Mn1[3]);
  ion_map["Mn1"] = Mn1;
  static const MagneticIon Mn2((std::string) "Mn", (uint16_t)2, j_Mn2[0],
                               j_Mn2[1], j_Mn2[2], j_Mn2[3]);
  ion_map["Mn2"] = Mn2;
  static const MagneticIon Mn3((std::string) "Mn", (uint16_t)3, j_Mn3[0],
                               j_Mn3[1], j_Mn3[2], j_Mn3[3]);
  ion_map["Mn3"] = Mn3;
  static const MagneticIon Mn4((std::string) "Mn", (uint16_t)4, j_Mn4[0],
                               j_Mn4[1], j_Mn4[2], j_Mn4[3]);
  ion_map["Mn4"] = Mn4;
  static const MagneticIon Fe0((std::string) "Fe", (uint16_t)0, j_Fe0[0],
                               j_Fe0[1], j_Fe0[2], j_Fe0[3]);
  ion_map["Fe0"] = Fe0;
  static const MagneticIon Fe1((std::string) "Fe", (uint16_t)1, j_Fe1[0],
                               j_Fe1[1], j_Fe1[2], j_Fe1[3]);
  ion_map["Fe1"] = Fe1;
  static const MagneticIon Fe2((std::string) "Fe", (uint16_t)2, j_Fe2[0],
                               j_Fe2[1], j_Fe2[2], j_Fe2[3]);
  ion_map["Fe2"] = Fe2;
  static const MagneticIon Fe3((std::string) "Fe", (uint16_t)3, j_Fe3[0],
                               j_Fe3[1], j_Fe3[2], j_Fe3[3]);
  ion_map["Fe3"] = Fe3;
  static const MagneticIon Fe4((std::string) "Fe", (uint16_t)4, j_Fe4[0],
                               j_Fe4[1], j_Fe4[2], j_Fe4[3]);
  ion_map["Fe4"] = Fe4;
  static const MagneticIon Co0((std::string) "Co", (uint16_t)0, j_Co0[0],
                               j_Co0[1], j_Co0[2], j_Co0[3]);
  ion_map["Co0"] = Co0;
  static const MagneticIon Co1((std::string) "Co", (uint16_t)1, j_Co1[0],
                               j_Co1[1], j_Co1[2], j_Co1[3]);
  ion_map["Co1"] = Co1;
  static const MagneticIon Co2((std::string) "Co", (uint16_t)2, j_Co2[0],
                               j_Co2[1], j_Co2[2], j_Co2[3]);
  ion_map["Co2"] = Co2;
  static const MagneticIon Co3((std::string) "Co", (uint16_t)3, j_Co3[0],
                               j_Co3[1], j_Co3[2], j_Co3[3]);
  ion_map["Co3"] = Co3;
  static const MagneticIon Co4((std::string) "Co", (uint16_t)4, j_Co4[0],
                               j_Co4[1], j_Co4[2], j_Co4[3]);
  ion_map["Co4"] = Co4;
  static const MagneticIon Ni0((std::string) "Ni", (uint16_t)0, j_Ni0[0],
                               j_Ni0[1], j_Ni0[2], j_Ni0[3]);
  ion_map["Ni0"] = Ni0;
  static const MagneticIon Ni1((std::string) "Ni", (uint16_t)1, j_Ni1[0],
                               j_Ni1[1], j_Ni1[2], j_Ni1[3]);
  ion_map["Ni1"] = Ni1;
  static const MagneticIon Ni2((std::string) "Ni", (uint16_t)2, j_Ni2[0],
                               j_Ni2[1], j_Ni2[2], j_Ni2[3]);
  ion_map["Ni2"] = Ni2;
  static const MagneticIon Ni3((std::string) "Ni", (uint16_t)3, j_Ni3[0],
                               j_Ni3[1], j_Ni3[2], j_Ni3[3]);
  ion_map["Ni3"] = Ni3;
  static const MagneticIon Ni4((std::string) "Ni", (uint16_t)4, j_Ni4[0],
                               j_Ni4[1], j_Ni4[2], j_Ni4[3]);
  ion_map["Ni4"] = Ni4;
  static const MagneticIon Cu0((std::string) "Cu", (uint16_t)0, j_Cu0[0],
                               j_Cu0[1], j_Cu0[2], j_Cu0[3]);
  ion_map["Cu0"] = Cu0;
  static const MagneticIon Cu1((std::string) "Cu", (uint16_t)1, j_Cu1[0],
                               j_Cu1[1], j_Cu1[2], j_Cu1[3]);
  ion_map["Cu1"] = Cu1;
  static const MagneticIon Cu2((std::string) "Cu", (uint16_t)2, j_Cu2[0],
                               j_Cu2[1], j_Cu2[2], j_Cu2[3]);
  ion_map["Cu2"] = Cu2;
  static const MagneticIon Cu3((std::string) "Cu", (uint16_t)3, j_Cu3[0],
                               j_Cu3[1], j_Cu3[2], j_Cu3[3]);
  ion_map["Cu3"] = Cu3;
  static const MagneticIon Cu4((std::string) "Cu", (uint16_t)4, j_Cu4[0],
                               j_Cu4[1], j_Cu4[2], j_Cu4[3]);
  ion_map["Cu4"] = Cu4;
  static const MagneticIon Y0((std::string) "Y", (uint16_t)0, j_Y0[0], j_Y0[1],
                              j_Y0[2], j_Y0[3]);
  ion_map["Y0"] = Y0;
  static const MagneticIon Zr0((std::string) "Zr", (uint16_t)0, j_Zr0[0],
                               j_Zr0[1], j_Zr0[2], j_Zr0[3]);
  ion_map["Zr0"] = Zr0;
  static const MagneticIon Zr1((std::string) "Zr", (uint16_t)1, j_Zr1[0],
                               j_Zr1[1], j_Zr1[2], j_Zr1[3]);
  ion_map["Zr1"] = Zr1;
  static const MagneticIon Nb0((std::string) "Nb", (uint16_t)0, j_Nb0[0],
                               j_Nb0[1], j_Nb0[2], j_Nb0[3]);
  ion_map["Nb0"] = Nb0;
  static const MagneticIon Nb1((std::string) "Nb", (uint16_t)1, j_Nb1[0],
                               j_Nb1[1], j_Nb1[2], j_Nb1[3]);
  ion_map["Nb1"] = Nb1;
  static const MagneticIon Mo0((std::string) "Mo", (uint16_t)0, j_Mo0[0],
                               j_Mo0[1], j_Mo0[2], j_Mo0[3]);
  ion_map["Mo0"] = Mo0;
  static const MagneticIon Mo1((std::string) "Mo", (uint16_t)1, j_Mo1[0],
                               j_Mo1[1], j_Mo1[2], j_Mo1[3]);
  ion_map["Mo1"] = Mo1;
  static const MagneticIon Tc0((std::string) "Tc", (uint16_t)0, j_Tc0[0],
                               j_Tc0[1], j_Tc0[2], j_Tc0[3]);
  ion_map["Tc0"] = Tc0;
  static const MagneticIon Tc1((std::string) "Tc", (uint16_t)1, j_Tc1[0],
                               j_Tc1[1], j_Tc1[2], j_Tc1[3]);
  ion_map["Tc1"] = Tc1;
  static const MagneticIon Ru0((std::string) "Ru", (uint16_t)0, j_Ru0[0],
                               j_Ru0[1], j_Ru0[2], j_Ru0[3]);
  ion_map["Ru0"] = Ru0;
  static const MagneticIon Ru1((std::string) "Ru", (uint16_t)1, j_Ru1[0],
                               j_Ru1[1], j_Ru1[2], j_Ru1[3]);
  ion_map["Ru1"] = Ru1;
  static const MagneticIon Rh0((std::string) "Rh", (uint16_t)0, j_Rh0[0],
                               j_Rh0[1], j_Rh0[2], j_Rh0[3]);
  ion_map["Rh0"] = Rh0;
  static const MagneticIon Rh1((std::string) "Rh", (uint16_t)1, j_Rh1[0],
                               j_Rh1[1], j_Rh1[2], j_Rh1[3]);
  ion_map["Rh1"] = Rh1;
  static const MagneticIon Pd0((std::string) "Pd", (uint16_t)0, j_Pd0[0],
                               j_Pd0[1], j_Pd0[2], j_Pd0[3]);
  ion_map["Pd0"] = Pd0;
  static const MagneticIon Pd1((std::string) "Pd", (uint16_t)1, j_Pd1[0],
                               j_Pd1[1], j_Pd1[2], j_Pd1[3]);
  ion_map["Pd1"] = Pd1;
  static const MagneticIon Ce2((std::string) "Ce", (uint16_t)2, j_Ce2[0],
                               j_Ce2[1], j_Ce2[2], j_Ce2[3]);
  ion_map["Ce2"] = Ce2;
  static const MagneticIon Nd2((std::string) "Nd", (uint16_t)2, j_Nd2[0],
                               j_Nd2[1], j_Nd2[2], j_Nd2[3]);
  ion_map["Nd2"] = Nd2;
  static const MagneticIon Nd3((std::string) "Nd", (uint16_t)3, j_Nd3[0],
                               j_Nd3[1], j_Nd3[2], j_Nd3[3]);
  ion_map["Nd3"] = Nd3;
  static const MagneticIon Sm2((std::string) "Sm", (uint16_t)2, j_Sm2[0],
                               j_Sm2[1], j_Sm2[2], j_Sm2[3]);
  ion_map["Sm2"] = Sm2;
  static const MagneticIon Sm3((std::string) "Sm", (uint16_t)3, j_Sm3[0],
                               j_Sm3[1], j_Sm3[2], j_Sm3[3]);
  ion_map["Sm3"] = Sm3;
  static const MagneticIon Eu2((std::string) "Eu", (uint16_t)2, j_Eu2[0],
                               j_Eu2[1], j_Eu2[2], j_Eu2[3]);
  ion_map["Eu2"] = Eu2;
  static const MagneticIon Eu3((std::string) "Eu", (uint16_t)3, j_Eu3[0],
                               j_Eu3[1], j_Eu3[2], j_Eu3[3]);
  ion_map["Eu3"] = Eu3;
  static const MagneticIon Gd2((std::string) "Gd", (uint16_t)2, j_Gd2[0],
                               j_Gd2[1], j_Gd2[2], j_Gd2[3]);
  ion_map["Gd2"] = Gd2;
  static const MagneticIon Gd3((std::string) "Gd", (uint16_t)3, j_Gd3[0],
                               j_Gd3[1], j_Gd3[2], j_Gd3[3]);
  ion_map["Gd3"] = Gd3;
  static const MagneticIon Tb2((std::string) "Tb", (uint16_t)2, j_Tb2[0],
                               j_Tb2[1], j_Tb2[2], j_Tb2[3]);
  ion_map["Tb2"] = Tb2;
  static const MagneticIon Tb3((std::string) "Tb", (uint16_t)3, j_Tb3[0],
                               j_Tb3[1], j_Tb3[2], j_Tb3[3]);
  ion_map["Tb3"] = Tb3;
  static const MagneticIon Dy2((std::string) "Dy", (uint16_t)2, j_Dy2[0],
                               j_Dy2[1], j_Dy2[2], j_Dy2[3]);
  ion_map["Dy2"] = Dy2;
  static const MagneticIon Dy3((std::string) "Dy", (uint16_t)3, j_Dy3[0],
                               j_Dy3[1], j_Dy3[2], j_Dy3[3]);
  ion_map["Dy3"] = Dy3;
  static const MagneticIon Ho2((std::string) "Ho", (uint16_t)2, j_Ho2[0],
                               j_Ho2[1], j_Ho2[2], j_Ho2[3]);
  ion_map["Ho2"] = Ho2;
  static const MagneticIon Ho3((std::string) "Ho", (uint16_t)3, j_Ho3[0],
                               j_Ho3[1], j_Ho3[2], j_Ho3[3]);
  ion_map["Ho3"] = Ho3;
  static const MagneticIon Er2((std::string) "Er", (uint16_t)2, j_Er2[0],
                               j_Er2[1], j_Er2[2], j_Er2[3]);
  ion_map["Er2"] = Er2;
  static const MagneticIon Er3((std::string) "Er", (uint16_t)3, j_Er3[0],
                               j_Er3[1], j_Er3[2], j_Er3[3]);
  ion_map["Er3"] = Er3;
  static const MagneticIon Tm2((std::string) "Tm", (uint16_t)2, j_Tm2[0],
                               j_Tm2[1], j_Tm2[2], j_Tm2[3]);
  ion_map["Tm2"] = Tm2;
  static const MagneticIon Tm3((std::string) "Tm", (uint16_t)3, j_Tm3[0],
                               j_Tm3[1], j_Tm3[2], j_Tm3[3]);
  ion_map["Tm3"] = Tm3;
  static const MagneticIon Yb2((std::string) "Yb", (uint16_t)2, j_Yb2[0],
                               j_Yb2[1], j_Yb2[2], j_Yb2[3]);
  ion_map["Yb2"] = Yb2;
  static const MagneticIon Yb3((std::string) "Yb", (uint16_t)3, j_Yb3[0],
                               j_Yb3[1], j_Yb3[2], j_Yb3[3]);
  ion_map["Yb3"] = Yb3;
  static const MagneticIon U3((std::string) "U", (uint16_t)3, j_U3[0], j_U3[1],
                              j_U3[2], j_U3[3]);
  ion_map["U3"] = U3;
  static const MagneticIon U4((std::string) "U", (uint16_t)4, j_U4[0], j_U4[1],
                              j_U4[2], j_U4[3]);
  ion_map["U4"] = U4;
  static const MagneticIon U5((std::string) "U", (uint16_t)5, j_U5[0], j_U5[1],
                              j_U5[2], j_U5[3]);
  ion_map["U5"] = U5;
  static const MagneticIon Np3((std::string) "Np", (uint16_t)3, j_Np3[0],
                               j_Np3[1], j_Np3[2], j_Np3[3]);
  ion_map["Np3"] = Np3;
  static const MagneticIon Np4((std::string) "Np", (uint16_t)4, j_Np4[0],
                               j_Np4[1], j_Np4[2], j_Np4[3]);
  ion_map["Np4"] = Np4;
  static const MagneticIon Np5((std::string) "Np", (uint16_t)5, j_Np5[0],
                               j_Np5[1], j_Np5[2], j_Np5[3]);
  ion_map["Np5"] = Np5;
  static const MagneticIon Np6((std::string) "Np", (uint16_t)6, j_Np6[0],
                               j_Np6[1], j_Np6[2], j_Np6[3]);
  ion_map["Np6"] = Np6;
  static const MagneticIon Pu3((std::string) "Pu", (uint16_t)3, j_Pu3[0],
                               j_Pu3[1], j_Pu3[2], j_Pu3[3]);
  ion_map["Pu3"] = Pu3;
  static const MagneticIon Pu4((std::string) "Pu", (uint16_t)4, j_Pu4[0],
                               j_Pu4[1], j_Pu4[2], j_Pu4[3]);
  ion_map["Pu4"] = Pu4;
  static const MagneticIon Pu5((std::string) "Pu", (uint16_t)5, j_Pu5[0],
                               j_Pu5[1], j_Pu5[2], j_Pu5[3]);
  ion_map["Pu5"] = Pu5;
  static const MagneticIon Pu6((std::string) "Pu", (uint16_t)6, j_Pu6[0],
                               j_Pu6[1], j_Pu6[2], j_Pu6[3]);
  ion_map["Pu6"] = Pu6;
  static const MagneticIon Am2((std::string) "Am", (uint16_t)2, j_Am2[0],
                               j_Am2[1], j_Am2[2], j_Am2[3]);
  ion_map["Am2"] = Am2;
  static const MagneticIon Am3((std::string) "Am", (uint16_t)3, j_Am3[0],
                               j_Am3[1], j_Am3[2], j_Am3[3]);
  ion_map["Am3"] = Am3;
  static const MagneticIon Am4((std::string) "Am", (uint16_t)4, j_Am4[0],
                               j_Am4[1], j_Am4[2], j_Am4[3]);
  ion_map["Am4"] = Am4;
  static const MagneticIon Am5((std::string) "Am", (uint16_t)5, j_Am5[0],
                               j_Am5[1], j_Am5[2], j_Am5[3]);
  ion_map["Am5"] = Am5;
  static const MagneticIon Am6((std::string) "Am", (uint16_t)6, j_Am6[0],
                               j_Am6[1], j_Am6[2], j_Am6[3]);
  ion_map["Am6"] = Am6;
  static const MagneticIon Am7((std::string) "Am", (uint16_t)7, j_Am7[0],
                               j_Am7[1], j_Am7[2], j_Am7[3]);
  ion_map["Am7"] = Am7;
}

/**
 * Returns a MagneticIon corresponding to the given symbol containing the atom &
 * charge
 * Throws std::runtime_error if one cannot be found
 * @param symbol :: The string symbol
 * @return A reference to the required ion
 */
const MagneticIon &getMagneticIon(const std::string &symbol) {
  const IonIndex &ionIndex = ionMap();
  std::map<std::string, MagneticIon>::const_iterator cit =
      ionIndex.find(symbol);

  if (cit == ionIndex.end()) {
    // no such combination
    std::stringstream msg;
    msg << "Failed to find an atom using symbol=" << symbol;
    throw std::runtime_error(msg.str());
  } else {
    return cit->second;
  }
}

/**
 * Returns a MagneticIon corresponding  to the given symbol & charge.
 * Throws std::runtime_error if one cannot be found
 * @param symbol :: The string symbol
 * @param charge :: The charge
 * @return
 */
const MagneticIon &getMagneticIon(const std::string &symbol,
                                  const uint16_t charge) {
  std::stringstream what;
  what << symbol << charge;
  return getMagneticIon(what.str());
}

/**
 * Returns the coffieients for a given angular momentum
 * @param symbol :: The string symbol defining the element
 * @param charge :: The charge
 * @param l :: The angular momentum
 * @return The coefficients or throws if either the ion doesn't exist or the
 * angular momentum is invalid
 */
std::vector<double> getJL(const std::string &symbol, const uint16_t charge,
                          const uint16_t l) {
  MagneticIon ion(getMagneticIon(symbol, charge));
  std::vector<double> v(8, 0.);
  switch (l) {
  case 0:
    v = ion.j0;
    break;
  case 2:
    v = ion.j2;
    break;
  case 4:
    v = ion.j4;
    break;
  case 6:
    v = ion.j6;
    break;
  default:
    // all other <jl> are not defined
    std::stringstream msg;
    msg << "Failed to find <j" << l << ">";
    throw std::runtime_error(msg.str());
  }
  return v;
}

} // namespace PhysicalConstants
} // namespace Mantid