catima/srim.cpp

#include "srim.h"
#include <cmath>
#include <algorithm>
namespace catima{
/**
  * return SRIM proton stopping power
  * @param Z - proton number of material
  * @param energy - energy per nuclein in MeV/u
  */
 
double p_se(int Z, double energy){
    double sp = -1;
    double e = 1000*energy; //e in keV/u
    int i = Z - 1;
    if(Z>92){  // dealing with trans-U where no Srim data
        i = 91;
        }
    if(e<=25)e=25;
    double sl = (pse_95[i][0]*std::pow(e,pse_95[i][1])) + (pse_95[i][2]*std::pow(e,pse_95[i][3]));
    double sh = pse_95[i][4]/std::pow(e,pse_95[i][5]) * std::log( (pse_95[i][6]/e) + (pse_95[i][7]*e));
    sp = sl*sh/(sl+sh);
    e=1000*energy;
    if(e<=25){
        sp *=(Z>6)?std::pow(e/25.0,0.45):std::pow(e/25.0,0.25);
    }
    
    return sp;
};
/**
  * return SRIM proton stopping power
  * @param Z - proton number of material
  * @param energy - energy per nuclein in MeV/u
  */
double p_se85(int Z, double energy){
    double sp = -1;
    double e = 1000*energy; //e in keV/u
    int i = Z - 1;
    if(Z>92){  // dealing with trans-U where no Srim data
        i = 91;
        }
    if(e<=25)e=25;
    double sl = (proton_stopping_coef[i][0]*std::pow(e,proton_stopping_coef[i][1])) + (proton_stopping_coef[i][2]*std::pow(e,proton_stopping_coef[i][3]));
    double sh = proton_stopping_coef[i][4]/std::pow(e,proton_stopping_coef[i][5]) * std::log( (proton_stopping_coef[i][6]/e) + (proton_stopping_coef[i][7]*e));
    sp = sl*sh/(sl+sh);
    e=1000*energy;
    if(e<=25){
        sp *=(Z>6)?std::pow(e/25.0,0.45):std::pow(e/25.0,0.25);
    }
    
    return sp;
};

/**
  * return srim stopping power 
  * @param pZ - projectile Z
  * @param pZ - material Z
  * @param energy - projectile energy in MeV/u unit
  */
double srim_dedx_e(int pZ, int tZ, double energy, bool use_new){
    double e=energy*1000; // e in keV/u
    double se = 0;
    double (*const fp_se)(int, double) = (use_new)?p_se:p_se85;
//    double (*const fp_se)(int, double) = p_se85;
    if(pZ==1){
        return (*fp_se)(tZ, energy);
    }
    else if(pZ == 2){
        double a=0;
        double b=0;
        
        if(e<=1)e=1;
        // He Zeff
        b = log(e);
        a = 0.2865 + b*(0.1266+ b*(-0.001429+ b*(0.02402 + b*(-0.01135 + b*0.001475))));
        double heh = 1.0 - exp(-std::min(30.,a));
        b = 7.6 - std::max(0., b);
        a = (1.0 + (0.007 + 0.00005*tZ)*exp(- b*b ));
        heh *= a*a;
        //zeta = sqrt(heh);
        se = (*fp_se)(tZ, energy)*heh*4.0; //scale proton stopping
        if(e==1)se*= sqrt(e);  //vel proportional
        return se;
    }
    else{ // heavy ion
        double h1,h4;
        double a,q,b;
        double l1,l0,l;
        double YRmin = 0.130; //  YRmin = VR / ZP**0.67 <= 0.13 OR VR <= 1.0
        double VRmin = 1.0;
        double v=0;
        double vfermi;
        double yr=0;
        double zeta = 0;
        double se;
        int i;
        
        i = tZ - 1;
        if(tZ>92){
            i = 91;
            }
        vfermi = atima_vfermi[i];
        
        v = sqrt(e/25.0)/vfermi;
        double v2=v*v;
        
        double vr = (v >= 1)? v*vfermi*(1.+ 1./(5.*v2)) : 3.0*vfermi/4.0*(1.0+v2*(2.0/3.0-v2/15.0));
        
        h1= 1./std::pow(pZ,0.6667);
        yr = std::max(YRmin,vr*h1);
        yr = std::max(yr, VRmin*h1);
        
        //--  CALCULATE ZEFF
        a = -0.803*std::pow(yr,0.3) + 1.3167*std::pow(yr,0.6) + 0.38157*yr + 0.008983*yr*yr;
        q = std::min(1.0, std::max(0.0 , (1.0 - exp(-std::min(a, 50.0))))); //-- Q = IONIZATION LEVEL OF THE ION AT RELATIVE VELOCITY YR
        
        //-- IONIZATION LEVEL TO EFFECTIVE CHARGE
        h1 = 1./ std::pow(pZ,0.3333);
        
        b = (std::min(0.43, std::max(0.32,0.12 + 0.025*pZ)))*h1;
        l0 = (.8 - q * std::min(1.2,0.6 +pZ/30.0))*h1;
        if(q < 0.2){
            l1 = 0;
            }
        else{
            if (q < std::max(0.0,0.9-0.025*pZ)){
                l1 = b*(q-0.2)/fabs(std::max(0.0,0.9-0.025*pZ)-0.2000001);
                }
	     	 else{
             	if(q < std::max(0.0,1.0 - 0.025*std::min(16.,(double)pZ))) l1 = b;
                else l1 = b*(1.0 - q)/(0.025*std::min(16.,(double)pZ));
                }
        }
        // calculate screening
        i = (pZ>92)?91:pZ-1;
        l = std::max(l1,l0*atima_lambda_screening[i]);
        h1 =4.0*l*vfermi/1.919;
        zeta = q + (1./(2.*(vfermi*vfermi)))*(1. - q)* log(1. + h1*h1); 
         // ZP**3 EFFECT AS IN REF. 779?
        a = 7.6 - std::max(0.0, log(e));
        zeta = zeta*(1. + (1./(pZ*pZ))*(0.18 + .0015*tZ)*exp(-a*a));
        h1= 1./std::pow(pZ,0.6667);
        if (yr <= ( std::max(YRmin, VRmin*h1))){
            VRmin=std::max(VRmin, YRmin/h1);
            //--C        ..CALCULATE VELOCITY STOPPING FOR YR < YRmin
            double vmin =.5*(VRmin + sqrt(std::max(0.0,VRmin*VRmin - .8*vfermi*vfermi)));
            double eee = 25.0*vmin*vmin;
            double eval = 1;
//              if((tZ == 6) || (((tZ == 14) || (tZ == 32)) &&  (pZ <= 19))) eval = 0.375;
            if((tZ == 6) || (((tZ == 14) || (tZ == 32)) &&  (pZ <= 19))) eval = 0.35;
            else eval = 0.5;
            
            h1 = zeta *pZ;
            h4 = std::pow(e / eee,eval);
            se = (*fp_se)(tZ, eee*0.001) * h1*h1*h4;
            return se;
        }
        else {
            return (*fp_se)(tZ,energy)*std::pow(zeta*pZ,2.0);
        }
        return 0;
    }
};

const double pse_95[92][8] = {
//H
{0.0128116,0.00533047,0.651042,0.531902,1959.01,1.1887,598.263,0.00954514},
//He
{0.311787,0.00499529,0.118546,0.920917,984.843,1.08223,554.388,0.0505072},
//Li
{0.644503,0.00500368,0.866544,0.567488,962.9,1.01566,1620.34,0.0237767},
//Be
{0.953561,0.00507406,1.3045,0.5903,1945.12,1.05703,326.951,0.0130441},
//B
{1.53151,0.0048852,2.5676,0.423246,1738.88,1.03208,1829.42,0.0200331},
//C
{2.40289,0.00491497,2.49101,0.414939,1858.36,1.01581,2504.17,0.0181984},
//N
{3.31007,0.00495744,0.540621,0.77994,1104.15,0.967848,2235.35,0.0531612},
//O
{0.972706,0.0050039,1.35102,0.5498,1254.28,0.968356,5093.2,0.0536453},
//F
{0.690408,0.00462723,0.326749,1.1052,1301.9,0.943525,47.0373,0.0280245},
//Ne
{0.281235,0.00459698,0.52563,0.878183,1158.3,0.938564,10.1606,0.0414147},
//Na
{2.15352,0.00440847,2.30923,0.606001,1332.24,0.943478,735.116,0.0577231},
//Mg
{3.42983,0.00436897,2.39377,0.554737,1140.29,0.929844,2107.48,0.0789342},
//Al
{0.0389096,0.00454168,4.27975,0.478838,1316.42,0.934106,565.574,0.052722},
//Si
{1.33101,0.00443533,1.52262,0.775843,1227.02,0.914146,1091.17,0.0444972},
//P
{5.78119,0.00398281,0.324072,1.22769,673.459,0.865731,123.619,0.182036},
//S
{0.611741,0.00446376,3.38101,0.542907,1160.67,0.912049,14031.2,0.087705},
//Cl
{1.15307,0.00447333,4.20464,0.538231,1301.13,0.902702,4923.01,0.0525717},
//Ar
{1.70408,0.00447609,2.75072,0.583835,2713.93,0.953183,2035.79,0.0146897},
//K
{2.60265,0.00432185,1.56811,0.864656,556.393,0.84475,120.01,0.962648},
//Ca
{0.536555,0.00440846,3.22706,0.602927,500.851,0.83345,1766.39,2.02699},
//Sc
{1.7187,0.00436934,4.60285,0.516212,1601.6,0.914664,6341.68,0.0629243},
//Ti
{0.146403,0.00484558,5.54014,0.455903,1763.46,0.919014,3951.93,0.0550341},
//V
{4.21238,0.0040013,3.79858,0.482892,2416.97,0.936204,7735.96,0.0289635},
//Cr
{0.697881,0.00430794,2.2863,0.784069,967.872,0.857874,17.8526,0.111149},
//Mn
{0.592743,0.00431334,1.40625,0.968261,1426.42,0.881488,14.4002,0.0424183},
//Fe
{0.0283155,0.00354506,0.564961,1.24111,1527.81,0.881848,25.9497,0.0354067},
//Co
{0.269545,0.00432088,2.24249,0.764706,1243.91,0.867051,23.4911,0.0604457},
//Ni
{3.68234,0.00437139,1.52146,0.736656,1470.86,0.874909,251.685,0.0428115},
//Cu
{2.15403,0.00432278,2.6939,0.523003,1717.27,0.893617,2099.38,0.0525222},
//Zn
{0.531847,0.00382833,0.675606,1.06647,1008.48,0.826099,35.8939,0.0419818},
//Ga
{6.91973,0.00401198,0.522284,0.974708,899.033,0.821636,371.581,0.0738361},
//Ge
{1.80976,0.00448896,5.6612,0.418493,1558.21,0.870542,1756.05,0.0605859},
//As
{1.64641,0.00430255,5.12108,0.516356,1020.24,0.832723,2202.77,0.0846531},
//Se
{4.0715,0.00429051,3.33803,0.543517,2606.26,0.903072,1089.74,0.0181133},
//Br
{1.99798,0.00429503,3.23907,0.593111,4645.72,0.947444,640.841,0.0096946},
//Kr
{5.08884,0.0042563,1.43,0.722156,7087.78,0.979865,762.818,0.00604351},
//Rb
{0.62637,0.00413189,0.0666229,2.65318,1074.6,0.814706,8.69523,0.0504427},
//Sr
{5.04987,0.00393427,4.95613,0.527062,1886.17,0.868672,4817.65,0.0349423},
//Y
{1.17376,0.00421587,5.93823,0.49052,1556.91,0.849851,7821.93,0.0434207},
//Zr
{7.26083,0.00419413,5.93121,0.447579,4687.69,0.939722,2446.36,0.0101526},
//Nb
{0.351621,0.00412551,1.33637,1.28649,1495.35,0.850544,12.7864,0.0471084},
//Mo
{0.0179112,0.00417066,1.16601,1.18837,1260.27,0.825733,12.9721,0.0482827},
//Tc
{3.72287,0.00417681,4.6286,0.567689,1678.02,0.86202,3093.95,0.0624402},
//Ru
{0.0179112,0.00417066,1.16601,1.18837,1260.27,0.825733,12.9721,0.0482827},
//Rh
{0.307959,0.00414183,0.545099,1.36766,1499.06,0.836456,26.5156,0.0382323},
//Pd
{0.813324,0.00421976,5.48878,0.621228,1491.47,0.843298,17.0197,0.0633415},
//Ag
{2.89508,0.00420494,5.30021,0.458632,1380.77,0.835929,13156.5,0.07682},
//Cd
{3.47169,0.0041344,3.23372,0.637885,1116.36,0.819589,4766.03,0.117895},
//In
{2.28576,0.00422582,3.48478,0.625713,804.033,0.79599,8953.57,0.302479},
//Sn
{4.70915,0.00409414,3.88322,0.582491,1031.4,0.815544,13300.4,0.167355},
//Sb
{7.35883,0.00438746,3.2273,0.693616,1364.65,0.832171,1512.36,0.0787703},
//Te
{1.20379,0.00421476,4.65732,0.615557,857.568,0.794208,5814.37,0.255765},
//I
{4.21323,0.00420978,4.67533,0.579451,3503.93,0.892614,1468.87,0.014359},
//Xe
{10.0615,0.00391035,0.364002,1.20347,1539.97,0.821892,1424.28,0.0402424},
//Cs
{0.373157,0.00364035,2.26519,1.151,1675.29,0.837764,13.0656,0.0516993},
//Ba
{4.82483,0.00414578,6.09343,0.570256,2300.11,0.863588,2980.72,0.0386788},
//La
{0.574872,0.00410857,2.76314,0.878406,654.727,0.777081,460.584,0.963426},
//Ce
{3.27544,0.00421774,5.76803,0.54054,6631.29,0.942817,744.066,0.00830259},
//Pr
{2.99783,0.00409014,4.52986,0.620247,2161.15,0.856688,1268.59,0.0430305},
//Nd
{3.02248,0.00410313,3.16182,0.750444,687.321,0.765038,363.38,0.389438},
//Pm
{3.5655,0.00411367,6.01196,0.521709,1830.02,0.838996,3661.99,0.0575667},
//Sm
{3.64072,0.0041782,4.87424,0.578614,1267.7,0.822111,3508.17,0.241737},
//Eu
{0.542525,0.00412806,4.33656,0.639323,1107.85,0.788122,352.321,0.0946601},
//Gd
{7.54702,0.00408134,4.92913,0.507107,2565.83,0.861877,3299.96,0.031273},
//Tb
{4.43006,0.00419028,5.3921,0.508608,3605.27,0.885038,1687.86,0.0164866},
//Dy
{4.31706,0.00406269,3.55237,0.572971,2138.74,0.839174,3204.35,0.029471},
//Ho
{2.73097,0.00402842,3.1059,0.645438,1802.36,0.820889,691.941,0.0306839},
//Er
{1.27982,0.00405535,4.63018,0.573846,1595.12,0.816419,1067.28,0.0552321},
//Tm
{5.75613,0.00404905,4.357,0.524956,2207.32,0.837956,1579.51,0.027165},
//Yb
{9.2061,0.00403636,3.37689,0.572174,3660.35,0.868034,1191.14,0.00953995},
//Lu
{8.23962,0.00404348,3.83028,0.534511,4357.71,0.882431,1524.26,0.00786437},
//Hf
{3.06189,0.00405111,3.5803,0.59082,2346.1,0.837132,1221.99,0.0200717},
//Ta
{7.99485,0.00329576,1.26335,0.777934,1804.13,0.8124,1266.3,0.0263526},
//W
{6.48326,0.00414609,0.776185,1.08393,250.557,0.643106,177.277,0.898821},
//Re
{0.620494,0.00403017,2.53792,0.677642,727.918,0.74834,117.069,0.201369},
//Os
{0.551045,0.00402571,2.70928,0.68387,1089.46,0.777755,1088.3,0.0810305},
//Ir
{1.26011,0.00404797,3.57127,0.525416,2613.09,0.853001,2155.71,0.0282139},
//Pt
{3.20857,0.00405101,3.66577,0.536178,3091.16,0.856024,1508.12,0.0154014},
//Au
{1.04066,0.00405071,5.61035,0.439133,3646.13,0.869259,2878.4,0.0139437},
//Hg
{1.04586,0.00405038,5.38433,0.445067,3717.15,0.87031,2907.28,0.0132933},
//Tl
{3.15124,0.00405235,4.09956,0.542499,3246.31,0.857723,1691.77,0.0150581},
//Pb
{3.06995,0.00405334,6.62045,0.452822,3380.58,0.860267,2638.56,0.0153938},
//Bi
{3.84541,0.00406028,8.7792,0.442301,2721.99,0.843866,2513.15,0.0228962},
//Po
{4.36117,0.00405648,8.18512,0.43626,3113.58,0.852235,3001.79,0.0172051},
//At
{4.36117,0.00405648,8.18512,0.43626,3113.58,0.852235,3001.79,0.0172051},
//Rn
{3.222,0.00400409,5.90236,0.526779,4040.15,0.868037,1658.35,0.0117469},
//Fr
{9.34124,0.00396606,7.92099,0.429769,5180.9,0.887726,2173.16,0.0092007},
//Ra
{6.28686,0.00396735,5.81778,0.535859,4866.43,0.884427,2257.34,0.0105815},
//Ac
{5.92839,0.00396948,6.40824,0.521225,4619.51,0.880827,2323.52,0.0116274},
//Th
{5.24536,0.0039744,6.79689,0.485424,4586.31,0.877944,2481.5,0.0112824},
//Pa
{2.77047,0.00398192,3.55107,0.638231,2516.88,0.829309,2155.59,0.0231207},
//U
{2.78483,0.00398116,3.32988,0.647983,2662.77,0.83678,2337.43,0.024074}
};

//constexpr double hps[92][4] = {
//skipHPS_COEFFICIENTS//
//}

//constexpr double v_fermi[92] = {
//skipV_FERMI//
//}

//constexpr double v_fermi_correction[92][15] = {
//skipV_FERMI_CORRECTIONS//
//}

//constexpr double lambda_screening[92][19] = {
//skipLAMBDA_SCREENING//
//}

const double atima_lambda_screening[92]= {
 1.00,
 1.00,
 1.10,
 1.06,
 1.01,
 1.03,
 1.04,
 0.99,
 0.95,
 0.90,
 0.82,
 0.81,
 0.83,
 0.88,
 1.00,
 0.95,
 0.97,
 0.99,
 0.98,
 0.97,
 0.98,
 0.97,
 0.96,
 0.93,
 0.91,
 0.9, 
 0.88,
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.85,
 0.9, 
 0.9, 
 0.91,
 0.92,
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.88,
 0.9, 
 0.88,
 0.88,
 0.9, 
 0.9, 
 0.88,
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.96,
 1.2, 
 0.9, 
 0.88,
 0.88,
 0.85,
 0.90,
 0.90,
 0.92,
 0.95,
 0.99,
 1.03,
 1.05,
 1.07,
 1.08,
 1.10,
 1.08,
 1.08,
 1.08,
 1.08,
 1.09,
 1.09,
 1.10,
 1.11,
 1.12,
 1.13,
 1.14,
 1.15,
 1.17,
 1.20,
 1.18,
 1.17,
 1.17,
 1.16,
 1.16,
 1.16,
 1.16,
 1.16,
 1.16,
 1.16};


// this is take from atima
const double proton_stopping_coef[92][8] = { // proton in material stopping coefficient
{  .0091827, .0053496, .69741, .48493, 316.07,1.0143, 9329.3, .0539890}, //H
{  .11393, .0051984, 1.0822, .39252,  1081.0, 1.0645, 4068.5, .0176990}, //He
{  .85837, .0050147, 1.6044, .38844,  1337.3, 1.0470, 2659.2, .01898},
{  .8781,  .0051049, 5.4232, .2032,   1200.6, 1.0211, 1401.8, .0385290},
{ 1.4608,  .0048836, 2.338,  .44249, 1801.3, 1.0352, 1784.1, .02024},
{ 3.2579,  .0049148, 2.7156, .36473, 2092.2, 1.0291, 2643.6, .0182370}, //C
{  .59674, .0050837, 4.2073, .30612,  2394.2, 1.0255, 4892.1, .0160060},
{  .75253, .0050314, 4.0824, .30067, 2455.8, 1.0181, 5069.7, .0174260}, //O
{ 1.226,   .0051385, 3.2246, .32703, 2525.0, 1.0142, 7563.6, .0194690},
{ 1.0332,  .0051645, 3.004,  .33889, 2338.6, .99997, 6991.2, .0217990}, //Ne
{ 6.0972,  .0044292, 3.1929, .45763, 1363.3, .95182, 2380.6, .0818350},
{14.013,   .0043646, 2.2641, .36326, 2187.4, .99098, 6264.8, .0462},
{ .039001, .0045415, 5.5463, .39562, 1589.2, .95316, 816.16, .0474840},
{ 2.072,   .0044516, 3.5585, .53933, 1515.2, .93161, 1790.3, .0351980},
{17.575,   .0038346, .078694, 1.2388,2806.0, .97284, 1037.6, .0128790},
{16.126,   .0038315, .054164, 1.3104,2813.3, .96587, 1251.4, .0118470},
{ 3.217,   .0044579, 3.6696, .5091,  2734.6, .96253, 2187.5, .0169070},
{ 2.0379,  .0044775, 3.0743, .54773, 3505.0, .97575, 1714.00, .0117010},
{ .74171, .0043051, 1.1515, .95083,   917.21, .8782, 389.93, .18926},
{ 9.1316,  .0043809, 5.4611, .31327, 3891.8, .97933, 6267.9, .0151960}, //Ca
{ 7.2247,  .0043718, 6.1017, .37511, 2829.2, .95218, 6376.1, .0203980},
{  .147,   .0048456, 6.3485, .41057, 2164.1, .94028, 5292.6, .0502630},
{ 5.0611,  .0039867, 2.6174, .57957, 2218.9, .92361, 6323.00, .0256690},
{  .53267, .0042968, .39005, 1.2725, 1872.7, .90776, 64.166, .0301070},
{  .47697, .0043038, .31452, 1.3289, 1920.5, .90649, 45.576, .0274690},
{  .027426, .0035443, .031563, 2.1755,  1919.5, .90099, 23.902, .0253630},
{  .16383, .0043042, .073454, 1.8592, 1918.4, .89678, 27.61, .0231840},
{ 4.2562,  .0043737, 1.5606, .72067, 1546.8, .87958, 302.02, .0409440}, //Ni
{ 2.3508,  .0043237, 2.882,  .50113, 1837.7, .89992, 2377.00, .04965},
{ 3.1095,  .0038455, .11477, 1.5037, 2184.7, .89309, 67.306, .0165880},
{15.322,   .0040306, .65391, .67668, 3001.7, .92484, 3344.2, .0163660},
{ 3.6932,  .0044813, 8.608,  .27638,  2982.7, .9276, 3166.6, .0308740},
{ 7.1373,  .0043134, 9.4247, .27937,  2725.8, .91597, 3166.1, .0250080},
{ 4.8979,  .0042937, 3.7793, .50004,  2824.5, .91028, 1282.4, .0170610},
{ 1.3683,  .0043024, 2.5679, .60822,  6907.8, .9817, 628.01, .0068055},
{ 1.8301,  .0042983, 2.9057, .6038,   4744.6, .94722, 936.64, .0092242},
{  .42056, .0041169, .01695, 2.3616, 2252.7, .89192, 39.752, .0277570},
{30.78,    .0037736, .55813, .76816, 7113.2, .97697, 1604.4, .0065268},
{11.576,   .0042119, 7.0244, .37764, 4713.5, .94264, 2493.2, .01127},
{ 6.2406,  .0041916, 5.2701, .49453, 4234.6, .93232, 2063.9, .0118440},
{  .33073, .0041243, 1.7246, 1.1062, 1930.2, .86907, 27.416, .0382080},
{  .017747, .0041715, .14586, 1.7305,1803.6, .86315, 29.669, .0321230},
{ 3.7229,  .0041768, 4.6286, .56769, 1678.0, .86202, 3094.00, .06244},
{  .13998, .0041329, .25573, 1.4241, 1919.3, .86326, 72.797, .0322350},
{  .2859,  .0041386, .31301, 1.3424, 1954.8, .86175, 115.18, .0293420},
{ .76,    .0042179, 3.386,  .76285,  1867.4, .85805, 69.994, .0364480},
{ 6.3957,  .0041935, 5.4689, .41378, 1712.6, .85397,18493.00, .0564710},
{ 3.4717,  .0041344, 3.2337, .63788, 1116.4, .81959, 4766.0, .1179},
{ 2.5265,  .0042282, 4.532,  .53562, 1030.8, .81652,16252.0, .19722},
{ 7.3683,  .0041007, 4.6791, .51428, 1160.0, .82454,17965.0, .13316},
{ 7.7197,  .004388, 3.242,   .68434, 1428.1, .83398, 1786.7, .0665120},
{16.78,    .0041918, 9.3198, .29568, 3370.9, .90289, 7431.7, .02616},
{ 4.2132,  .0042098, 4.6753, .57945, 3503.9, .89261, 1468.9, .0143590},
{ 4.0818,  .004214, 4.4425,  .58393, 3945.3, .90281, 1340.5, .0134140}, //Xe
{.18517, .0036215, .00058788,3.5315, 2931.3, .88936, 26.18, .0263930},
{ 4.8248,  .0041458, 6.0934, .57026, 2300.1, .86359, 2980.7, .0386790},
{  .49857, .0041054, 1.9775, .95877, 786.55, .78509, 806.6, .40882},
{ 3.2754,  .0042177, 5.768,  .54054, 6631.3, .94282, 744.07, .0083026},
{ 2.9978,  .0040901, 4.5299, .62025, 2161.2, .85669, 1268.6, .0430310},
{ 2.8701,  .004096, 4.2568,  .6138,  2130.4, .85235, 1704.1, .0393850},
{10.853,   .0041149, 5.8907, .46834, 2857.2, .8755, 3654.2, .0299550},
{ 3.6407,  .0041782, 4.8742, .57861, 1267.7, .82211, 3508.2, .24174},
{17.645,   .0040992, 6.5855, .32734, 3931.3, .90754, 5156.7, .0362780},
{ 7.5309,  .0040814, 4.9389, .50679, 2519.7, .85819, 3314.6, .0305140},
{ 5.4742,  .0040829, 4.897,  .51113, 2340.1, .85296, 2342.7, .0356620},
{ 4.2661,  .0040667, 4.5032, .55257, 2076.4, .84151, 1666.6, .0408010},
{ 6.8313,  .0040486, 4.3987, .51675, 2003.0, .83437, 1410.4, .03478},
{ 1.2707,  .0040553, 4.6295, .57428, 1626.3, .81858, 995.68, .0553190},
{ 5.7561,  .0040491, 4.357,  .52496, 2207.3, .83796, 1579.5, .0271650},
{14.127,   .0040596, 5.8304, .37755, 3645.9, .87823, 3411.8, .0163920},
{ 6.6948,  .0040603, 4.9361, .47961, 2719.0, .85249, 1885.8, .0197130},
{ 3.0619,  .0040511, 3.5803, .59082, 2346.1, .83713, 1222.0, .0200720},
{10.811,   .0033008, 1.3767, .76512, 2003.7, .82269, 1110.6, .0249580},
{ 2.7101,  .0040961, 1.2289, .98598, 1232.4, .79066, 155.42, .0472940},
{  .52345, .0040244, 1.4038, .8551,  1461.4, .79677, 503.34, .0367890},
{  .4616,  .0040203, 1.3014, .87043, 1473.5, .79687, 443.09, .0363010},
{  .97814, .0040374, 2.0127, .7225,  1890.8, .81747, 930.7, .02769},
{ 3.2086,  .004051, 3.6658,  .53618, 3091.2, .85602, 1508.1, .0154010},
{ 2.0035,  .0040431, 7.4882, .3561,  4464.3, .88836, 3966.5, .0128390},
{15.43,    .0039432, 1.1237, .70703, 4595.7, .88437, 1576.5, .0088534},
{ 3.1512,  .0040524, 4.0996, .5425,  3246.3, .85772, 1691.8, .0150580},
{ 7.1896,  .0040588, 8.6927, .35842, 4760.6, .88833, 2888.3, .0110290}, //Pb
{ 9.3209,  .004054, 11.543,  .32027, 4866.2, .89124, 3213.4, .0119350},
{29.242,   .0036195, .16864, 1.1226, 5688.0, .89812, 1033.3, .0071303},
{ 1.8522,  .0039973, 3.1556, .65096, 3755.0, .86383, 1602.0, .0120420},
{ 3.222,   .0040041, 5.9024, .52678, 4040.2, .86804, 1658.4, .0117470},
{ 9.3412,  .0039661, 7.921,  .42977, 5180.9, .88773, 2173.2, .0092007},
{36.183,   .0036003, .58341, .86747, 6990.2, .91082, 1417.1, .0062187},
{ 5.9284,  .0039695, 6.4082, .52122, 4619.5, .88083, 2323.5, .0116270},
{ 5.2454,  .0039744, 6.7969, .48542, 4586.3, .87794, 2481.5, .0112820},
{33.702,   .0036901, .47257, .89235, 5295.7, .8893, 2053.3, .0091908},
{2.7589,  .0039806, 3.2092, .66122,  2505.4, .82863, 2065.1, .0228160} //U
};

const double  atima_vfermi[92] = {
1.0309, 
0.15976,
0.59782,
1.0781, 
1.0486, 
1.00,   
1.058,  
0.93942,
0.74562,
0.3424, 
0.45259,
0.71074,
0.90519,
0.97411,
0.97184,
0.89852,
0.70827,
0.39816,
0.36552,
0.62712,
0.81707,
0.9943, 
1.1423, 
1.2381, 
1.1222, 
0.92705,
1.0047, 
1.2,    
1.0661, 
0.97411,
0.84912,
0.95,   
1.0903, 
1.0429, 
0.49715,
0.37755,
0.35211,
0.57801,
0.77773,
1.0207, 
1.029,  
1.2542, 
1.122,  
1.1241, 
1.0882, 
1.2709, 
1.2542, 
0.90094,
0.74093,
0.86054,
0.93155,
1.0047, 
0.55379,
0.43289,
0.32636,
0.5131, 
0.6950, 
0.72591,
0.71202,
0.67413,
0.71418,
0.71453,
0.5911, 
0.70263,
0.68049,
0.68203,
0.68121,
0.68532,
0.68715,
0.61884,
0.71801,
0.83048,
1.1222, 
1.2381, 
1.045,  
1.0733, 
1.0953, 
1.2381, 
1.2879, 
0.78654,
0.66401,
0.84912,
0.88433,
0.80746,
0.43357,
0.41923,
0.43638,
0.51464,
0.73087,
0.81065,
1.9578, 
1.0257};

}  // namespace catima