G4AtimaFluctuations.cc

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//
// GEANT4 Class header file
//
//
// File name:     G4AtimaFluctuations
//
// Author:        Jose Luis Rodriguez Sanchez on base of ATIMA code
//
// Creation date: 16.01.2018
//
// Modifications:
// 09/10/2018: Deleted Titeica's correction at high energies
//
//
// Class Description:
//
// This model calculates the energy-loss fluctuations according to the ATIMA code
// developed at GSI, Darmstadt, Germany.
// For details: http://web-docs.gsi.de/~weick/atima/
//
// Helmut Weick, GSI (responsible for fortran version)
// Andrej Prochazka, GSI (responsible for C version)
// Christoph Scheidenberger, GSI (project coordination)
//
// -------------------------------------------------------------------
//
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#include "G4AtimaFluctuations.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "Randomize.hh"
#include "G4Poisson.hh"
#include "G4MaterialCutsCouple.hh"
#include "G4Material.hh"
#include "G4NistManager.hh"
#include "G4DynamicParticle.hh"
#include "G4Log.hh"
#include "G4Exp.hh"
#include "G4Pow.hh"

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using namespace std;

G4double G4AtimaFluctuations::stepE = 0.0;
G4double G4AtimaFluctuations::tableE[] = {0.0};

G4AtimaFluctuations::G4AtimaFluctuations(const G4String& nam)
  : G4VEmFluctuationModel(nam),
    particle(0),
    particleMass(CLHEP::proton_mass_c2),
    charge(1.0),
    chargeSquare(1.0),
    effChargeSquare(1.0),
    minLoss(0.001*CLHEP::eV)
{
  g4calc = G4Pow::GetInstance();
  kineticEnergy = 0.0;
  beta2 = 0.0;
  MLN10 = 2.30258509299;
  atomic_mass_unit = 931.4940954; // MeV/c^2
  dedx_constant = 0.3070749187;  //4*pi*Na*me*c^2*r_e^2  //MeV cm^2
  electron_mass = 0.510998928;   // MeV/c^2
  fine_structure = 1.0/137.035999139;
  domega2dx_constant = dedx_constant*electron_mass;  //4*pi*Na*me*c^2*r_e^2  //MeV^2 cm^2
  if(tableE[0] == 0.0) {
    G4double logmin = 0.;
    G4double logmax = 5.;
    stepE = (logmax-logmin)/(G4double)(199);
    for(G4int i=0; i<200; ++i){
      tableE[i] = G4Exp(MLN10*(logmin + ((G4double)i)*stepE));
    }
  }
}

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G4AtimaFluctuations::~G4AtimaFluctuations()
{}

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void G4AtimaFluctuations::InitialiseMe(const G4ParticleDefinition* part)
{
  particle       = part;
  particleMass   = part->GetPDGMass();
  charge         = part->GetPDGCharge()/eplus;
  chargeSquare   = charge*charge;
  effChargeSquare= chargeSquare;
  uniFluct.InitialiseMe(part);
}

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G4double 
G4AtimaFluctuations::SampleFluctuations(const G4MaterialCutsCouple* couple,
                                      const G4DynamicParticle* dp,
                                      G4double tmax,
                                      G4double length,
                                      G4double meanLoss)
{
  //  G4cout << "### meanLoss= " << meanLoss << G4endl;
  if(meanLoss <= minLoss) return meanLoss;

 // G4cout << "G4AtimaFluctuations::SampleFluctuations E(MeV)= " 
 //    << dp->GetKineticEnergy()
 //    << "  Elim(MeV)= " << parameter*charge*particleMass 
 //    << " " << parameter << " " << charge << " " << particleMass << G4endl; 

  const G4Material* material = couple->GetMaterial();
  G4double siga = Dispersion(material,dp,tmax,length);
  
  CLHEP::HepRandomEngine* rndmEngine = G4Random::getTheEngine();
  //G4cout << "meanLoss= " << meanLoss << " loss= " << siga << G4endl;
  return G4RandGauss::shoot(rndmEngine,meanLoss,std::sqrt(siga));
}

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G4double G4AtimaFluctuations::Dispersion(const G4Material* mat,
                                       const G4DynamicParticle* dp,
                                       G4double,
                                       G4double length)
{
  kineticEnergy = dp->GetKineticEnergy();
  const G4ParticleDefinition* p = dp->GetDefinition();

  G4double ap = p->GetPDGMass()/atomic_mass_unit;
  G4double zp = p->GetPDGCharge();
  G4double ep = kineticEnergy/ap;// ep in MeV/u
  G4double zt = mat->GetIonisation()->GetZeffective();
  G4double at = G4NistManager::Instance()->GetAtomicMassAmu(G4lrint(zt));

  G4int z = G4lrint(zp);
  if(z > 109) { z = 109; }

  G4double gamma=1.0 + ep/atomic_mass_unit;
  beta2=1.0-1.0/(gamma*gamma);
  G4double beta = std::sqrt(beta2);
  //z_eff_Pierce_Blann(Z, beta);
  G4double zp_eff = zp*(1.0-G4Exp(-0.95*137.035999139*beta/g4calc->Z23(z)));
  //
  G4double f = domega2dx_constant*zp_eff*zp_eff*zt/at;
  //
  G4double cor =
    24.89 * g4calc->powA(zt,1.2324)/(electron_mass*1e6 * beta2)*
    G4Log( 2.0*electron_mass*1e6*beta2/(33.05*g4calc->powA(zt,1.6364)));
  cor = std::max(cor, 0.0 );

  //Lindhard corrections
  if(ep<tableE[0])ep = tableE[0];
  G4double da = (ap - element_atomic_weights[z])/element_atomic_weights[z];

  G4double v3 = EnergyTable_interpolate(tableE,ep,ls_X_coefficients_a[z-1]);
  G4double v4 = EnergyTable_interpolate(tableE,ep,ls_X_coefficients_ahi[z-1]);
  G4double dif = v4 - v3;
  G4double X = v3+(dif*da/0.05);
  X *= gamma*gamma;
  //
  G4double sse = 0.;
  if(ep<30.0){
    //Energy straggling Firsov
    G4double factor = 4.8184e-3*g4calc->powA(zp+zt,8.0/3.0)/at;
    sse = std::min(f*(X+cor), factor*beta2/fine_structure/fine_structure);
  }else{
   // sse = f*(X+cor); 
    sse = f*X;//09/10/2018
  }
  //
  return sse*length/(cm)*mat->GetDensity()/(g/cm3);
}

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void G4AtimaFluctuations::SetParticleAndCharge(const G4ParticleDefinition* part,
                                             G4double q2)
{
  if(part != particle) {
    particle       = part;
    particleMass   = part->GetPDGMass();
    charge         = part->GetPDGCharge()/eplus;
    chargeSquare   = charge*charge;
  }
  effChargeSquare  = q2;
  uniFluct.SetParticleAndCharge(part, q2);
}

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G4double G4AtimaFluctuations::EnergyTable_interpolate(const G4double* table, G4double xval,const G4double* y){
  G4double r;
  G4int num=200;
  G4double lxval = G4Log(xval)/MLN10;
  if(xval<table[0] || xval>table[num-1])return 0.0;
  if(xval==table[num-1])return y[num-1];
  G4int i = (G4int)(lxval/stepE);
  i = std::min(std::max(i, 0), num-2);
  G4double linstep = table[i+1] - table[i];
  G4double x = 1.0 - ((xval - table[i])/linstep);
  r = (x*y[i]) + ((1-x)*y[i+1]);
  return r;
}

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const G4double G4AtimaFluctuations::element_atomic_weights[110]={
 0.0,
 1.00794, //H
 4.0026, //He
 6.941, //Li
 9.01218, //Be
 10.811, //B
 12.0107, //C
 14.0067, //N
 15.9994, //O
 18.9984, //F
 20.1797, //Ne
 22.9898, //Na
 24.305, //Mg
 26.9815, //Al
 28.0855, //Si
 30.9738, //P
 32.065, //S
 35.453, //Cl
 39.948, //Ar
 39.0983, //K
 40.078, //Ca
 44.9559, //Sc
 47.867, //Ti
 50.9415, //V
 51.9961, //Cr
 54.938, //Mn
 55.845, //Fe
 58.9332, //Co
 58.6934, //Ni
 63.546, //Cu
 65.409, //Zn
 69.723, //Ga
 72.64, //Ge
 74.9216, //As
 78.96, //Se
 79.904, //Br
 83.798, //Kr
 85.4678, //Rb
 87.62, //Sr
 88.9059, //Y
 91.224, //Zr
 92.9064, //Nb
 95.94, //Mo
 97.9072, //Tc
 101.07, //Ru
 102.906, //Rh
 106.42, //Pd
 107.868, //Ag
 112.411, //Cd
 114.818, //In
 118.71, //Sn
 121.76, //Sb
 127.6, //Te
 126.904, //I
 131.293, //Xe
 132.905, //Cs
 137.327, //Ba
 138.905, //La
 140.116, //Ce
 140.908, //Pr
 144.24, //Nd
 144.913, //Pm
 150.36, //Sm
 151.964, //Eu
 157.25, //Gd
 158.925, //Tb
 162.5, //Dy
 164.93, //Ho
 167.259, //Er
 168.934, //Tm
 173.04, //Yb
 174.967, //Lu
 178.49, //Hf
 180.948, //Ta
 183.84, //W
 186.207, //Re
 190.23, //Os
 192.217, //Ir
 195.078, //Pt
 196.967, //Au
 200.59, //Hg
 204.383, //Tl
 207.2, //Pb
 208.98, //Bi
 208.982, //Po
 209.987, //At
 222.018, //Rn
 223.02, //Fr
 226.025, //Ra
 227.028, //Ac
 232.038, //Th
 231.036, //Pa
 238.029, //U
 237.048, //Np
 244.064, //Pu
 243.061, //Am
 247.07, //Cm
 247.07, //Bk
 251.08, //Cf
 252.083, //Es
 257.095, //Fm
 258.098, //Md
 259.101, //No
 262.11, //Lr
 261.109, //Rf
 262.114, //Db
 266.122, //Sg
 264.125, //Bh
 269.134, //Hs
 268.139 //Mt
};

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//arrays dimensions are [z][energy], z=1 starts from index=0

//LS X coefficient (dE straggling) for A=atomic weight
const G4double G4AtimaFluctuations::ls_X_coefficients_a[110][200]=
{
  {0.999182,0.999124,0.999062,0.998995,0.998925,0.998851,0.998772,0.998688,0.998598,0.998504,0.998404,0.998297,0.998184,0.998064,0.997937,0.997802,0.997659,0.997507,0.997346,0.997175,0.996994,0.996802,0.996598,0.996382,0.996153,0.99591,0.995653,0.995381,0.995092,0.994785,0.994461,0.994117,0.993753,0.993367,0.992958,0.992526,0.992067,0.991582,0.991068,0.990524,0.989948,0.989338,0.988693,0.988011,0.987289,0.986525,0.985717,0.984863,0.98396,0.983005,0.981996,0.98093,0.979804,0.978614,0.977358,0.976032,0.974632,0.973155,0.971597,0.969955,0.968223,0.966397,0.964474,0.962449,0.960317,0.958074,0.955714,0.953233,0.950626,0.947887,0.945012,0.941995,0.938832,0.935516,0.932044,0.928409,0.924608,0.920635,0.916485,0.912155,0.90764,0.902937,0.898042,0.892953,0.887666,0.88218,0.876495,0.870608,0.864522,0.858236,0.851752,0.845074,0.838206,0.831151,0.823917,0.81651,0.808938,0.801211,0.79334,0.785335,0.77721,0.768979,0.760656,0.752258,0.7438,0.735302,0.72678,0.718255,0.709744,0.701267,0.692844,0.684494,0.676236,0.668089,0.660071,0.6522,0.644492,0.636962,0.629625,0.622494,0.61558,0.608894,0.602443,0.596236,0.590278,0.584573,0.579123,0.573929,0.568991,0.564308,0.559877,0.555692,0.55175,0.548044,0.544568,0.541314,0.538274,0.535439,0.532801,0.53035,0.528078,0.525974,0.52403,0.522236,0.520584,0.519064,0.517667,0.516386,0.515211,0.514137,0.513154,0.512256,0.511437,0.510689,0.510008,0.509387,0.508822,0.508306,0.507837,0.507408,0.507018,0.50666,0.506333,0.506032,0.505756,0.5055,0.505262,0.50504,0.504831,0.504632,0.504442,0.504258,0.504078,0.503901,0.503723,0.503542,0.503357,0.503165,0.502964,0.50275,0.502522,0.502277,0.502011,0.501721,0.501403,0.501053,0.500667,0.500239,0.499764,0.499237,0.49865,0.497996,0.497267,0.496453,0.495544,0.494529,0.493396,0.492131,0.490717,0.489139},
  {0.999599,0.999546,0.999489,0.999428,0.999363,0.999294,0.999221,0.999143,0.99906,0.998971,0.998877,0.998778,0.998671,0.998558,0.998438,0.998311,0.998175,0.998031,0.997878,0.997716,0.997543,0.99736,0.997165,0.996959,0.99674,0.996507,0.99626,0.995998,0.99572,0.995425,0.995112,0.99478,0.994428,0.994054,0.993659,0.993239,0.992795,0.992323,0.991824,0.991295,0.990734,0.990141,0.989512,0.988846,0.988141,0.987395,0.986606,0.98577,0.984886,0.983951,0.982962,0.981917,0.980812,0.979645,0.978411,0.977108,0.975732,0.974279,0.972746,0.971129,0.969423,0.967625,0.965729,0.963732,0.961629,0.959416,0.957086,0.954636,0.952061,0.949354,0.946512,0.943529,0.940401,0.93712,0.933684,0.930086,0.926322,0.922387,0.918276,0.913985,0.90951,0.904848,0.899994,0.894946,0.889702,0.884259,0.878617,0.872775,0.866733,0.860491,0.854053,0.847421,0.840598,0.833589,0.826401,0.81904,0.811515,0.803834,0.796008,0.78805,0.779971,0.771785,0.763507,0.755154,0.746741,0.738286,0.729807,0.721324,0.712855,0.704419,0.696036,0.687725,0.679505,0.671396,0.663414,0.655578,0.647903,0.640406,0.6331,0.625999,0.619114,0.612455,0.606031,0.599849,0.593915,0.588232,0.582803,0.577629,0.57271,0.568044,0.563629,0.559459,0.555531,0.551838,0.548373,0.54513,0.542099,0.539272,0.536641,0.534197,0.531929,0.52983,0.527889,0.526097,0.524445,0.522924,0.521526,0.520242,0.519064,0.517984,0.516995,0.516089,0.51526,0.514501,0.513807,0.513171,0.512587,0.512052,0.511559,0.511105,0.510685,0.510295,0.509931,0.509589,0.509265,0.508957,0.508661,0.508372,0.508089,0.507808,0.507525,0.507238,0.506942,0.506634,0.50631,0.505967,0.505599,0.505203,0.504773,0.504304,0.503789,0.503224,0.502599,0.501908,0.501142,0.500292,0.499346,0.498293,0.497121,0.495814,0.494358,0.492735,0.490925,0.488909,0.486663,0.484161,0.481378,0.478282,0.474842,0.471024},
  {1.00017,1.00012,1.00007,1.00002,0.999959,0.999897,0.99983,0.999759,0.999682,0.999601,0.999514,0.999421,0.999322,0.999217,0.999104,0.998984,0.998857,0.998721,0.998576,0.998422,0.998258,0.998083,0.997898,0.997701,0.997491,0.997268,0.997031,0.996779,0.996512,0.996228,0.995926,0.995606,0.995266,0.994905,0.994522,0.994115,0.993684,0.993226,0.992741,0.992226,0.991681,0.991103,0.99049,0.98984,0.989152,0.988424,0.987652,0.986834,0.985969,0.985054,0.984085,0.98306,0.981976,0.98083,0.979618,0.978338,0.976985,0.975557,0.974048,0.972456,0.970776,0.969004,0.967136,0.965167,0.963092,0.960908,0.958608,0.956188,0.953644,0.95097,0.94816,0.945211,0.942116,0.938871,0.93547,0.931908,0.928181,0.924283,0.92021,0.915958,0.911523,0.9069,0.902087,0.897081,0.891878,0.886478,0.880878,0.875079,0.869081,0.862884,0.85649,0.849902,0.843124,0.836161,0.829018,0.821702,0.814222,0.806587,0.798807,0.790894,0.782859,0.774718,0.766485,0.758175,0.749806,0.741394,0.732958,0.724516,0.716088,0.707692,0.699348,0.691076,0.682894,0.67482,0.666874,0.659072,0.651431,0.643965,0.63669,0.629619,0.622762,0.61613,0.609732,0.603574,0.597663,0.592002,0.586594,0.58144,0.576539,0.571891,0.567491,0.563337,0.559422,0.555742,0.552289,0.549056,0.546034,0.543216,0.540593,0.538155,0.535893,0.533798,0.531861,0.530072,0.528422,0.526902,0.525504,0.524218,0.523038,0.521955,0.520961,0.520049,0.519213,0.518446,0.517741,0.517093,0.516496,0.515945,0.515435,0.514961,0.514518,0.514102,0.513709,0.513335,0.512974,0.512625,0.512282,0.511942,0.511601,0.511255,0.5109,0.510531,0.510144,0.509734,0.509296,0.508825,0.508314,0.507759,0.50715,0.506482,0.505745,0.504931,0.504029,0.503028,0.501917,0.50068,0.499305,0.497774,0.49607,0.494172,0.492059,0.489707,0.487089,0.484179,0.480945,0.477355,0.473372,0.468959,0.464076,0.458682},
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  {1.01181,1.01255,1.01332,1.01414,1.015,1.01591,1.01686,1.01787,1.01893,1.02005,1.02123,1.02247,1.02379,1.02517,1.02663,1.02817,1.0298,1.03151,1.03332,1.03523,1.03724,1.03936,1.0416,1.04396,1.04646,1.04908,1.05186,1.05478,1.05786,1.0611,1.06452,1.06813,1.07193,1.07592,1.08014,1.08457,1.08924,1.09415,1.09931,1.10474,1.11045,1.11644,1.12274,1.12935,1.13629,1.14356,1.15119,1.15918,1.16754,1.1763,1.18545,1.19502,1.20501,1.21543,1.2263,1.23762,1.24941,1.26166,1.2744,1.28762,1.30132,1.31552,1.33021,1.34539,1.36106,1.37722,1.39386,1.41098,1.42855,1.44658,1.46504,1.48393,1.50321,1.52286,1.54287,1.56321,1.58384,1.60473,1.62585,1.64715,1.66861,1.69018,1.71181,1.73346,1.75508,1.77663,1.79805,1.81929,1.84031,1.86106,1.88147,1.90151,1.92113,1.94027,1.9589,1.97697,1.99444,2.01127,2.02743,2.04288,2.05761,2.07159,2.08479,2.09722,2.10884,2.11967,2.1297,2.13893,2.14738,2.15504,2.16194,2.1681,2.17353,2.17826,2.18232,2.18573,2.18852,2.19072,2.19236,2.19346,2.19407,2.19419,2.19387,2.19312,2.19198,2.19045,2.18855,2.18631,2.18374,2.18084,2.17763,2.1741,2.17027,2.16612,2.16166,2.15688,2.15178,2.14633,2.14053,2.13435,2.12779,2.12082,2.11341,2.10555,2.09719,2.08832,2.07891,2.06891,2.05829,2.04701,2.03505,2.02234,2.00886,1.99455,1.97938,1.96329,1.94623,1.92816,1.90903,1.88877,1.86736,1.84472,1.82082,1.79559,1.76901,1.74101,1.71157,1.68063,1.64817,1.61417,1.5786,1.54146,1.50275,1.46248,1.42069,1.3774,1.3327,1.28666,1.23938,1.191,1.14165,1.09151,1.04079,0.989695,0.938475,0.887385,0.836697,0.786688,0.737636,0.689807,0.643452,0.598791,0.556011,0.515254,0.476615,0.440142,0.405835,0.373654,0.343529,0.315373},
  {1.01163,1.01236,1.01312,1.01393,1.01478,1.01567,1.01662,1.01761,1.01866,1.01976,1.02093,1.02215,1.02345,1.02481,1.02626,1.02778,1.02938,1.03107,1.03286,1.03474,1.03673,1.03882,1.04104,1.04337,1.04583,1.04843,1.05116,1.05405,1.0571,1.0603,1.06369,1.06725,1.07101,1.07497,1.07914,1.08353,1.08815,1.09301,1.09813,1.10352,1.10918,1.11513,1.12138,1.12795,1.13484,1.14207,1.14966,1.15761,1.16594,1.17466,1.18379,1.19333,1.2033,1.21371,1.22457,1.2359,1.24769,1.25997,1.27273,1.28599,1.29975,1.31401,1.32878,1.34405,1.35984,1.37612,1.39291,1.41019,1.42795,1.44619,1.46488,1.48401,1.50357,1.52353,1.54387,1.56456,1.58556,1.60686,1.62841,1.65018,1.67212,1.69421,1.71638,1.7386,1.76081,1.78298,1.80504,1.82695,1.84866,1.87011,1.89126,1.91205,1.93242,1.95234,1.97176,1.99062,2.00889,2.02653,2.0435,2.05977,2.0753,2.09008,2.10409,2.1173,2.1297,2.14129,2.15207,2.16203,2.17118,2.17954,2.1871,2.1939,2.19995,2.20527,2.2099,2.21384,2.21714,2.21981,2.2219,2.22342,2.22441,2.2249,2.22491,2.22446,2.22358,2.22229,2.22061,2.21856,2.21614,2.21337,2.21026,2.20681,2.20303,2.19891,2.19445,2.18965,2.1845,2.17898,2.17308,2.1668,2.1601,2.15296,2.14537,2.1373,2.12873,2.11961,2.10992,2.09963,2.0887,2.0771,2.06478,2.0517,2.03782,2.0231,2.00749,1.99094,1.9734,1.95483,1.93517,1.91438,1.8924,1.86918,1.84467,1.81883,1.7916,1.76294,1.73281,1.70117,1.668,1.63326,1.59695,1.55905,1.51956,1.47851,1.43593,1.39186,1.34636,1.29953,1.25147,1.20231,1.15221,1.10134,1.0499,0.998117,0.946241,0.89453,0.843259,0.792708,0.743155,0.694867,0.648094,0.603053,0.559929,0.518859,0.479935,0.443201,0.40865,0.376241,0.345902,0.317543},
  {1.01145,1.01216,1.01292,1.01372,1.01455,1.01544,1.01637,1.01735,1.01838,1.01947,1.02062,1.02183,1.0231,1.02445,1.02587,1.02737,1.02895,1.03062,1.03238,1.03424,1.0362,1.03827,1.04045,1.04275,1.04518,1.04775,1.05045,1.0533,1.05631,1.05948,1.06282,1.06634,1.07006,1.07397,1.07809,1.08244,1.08701,1.09183,1.0969,1.10223,1.10784,1.11374,1.11994,1.12646,1.1333,1.14048,1.14802,1.15593,1.16421,1.1729,1.18198,1.19149,1.20144,1.21182,1.22267,1.23398,1.24578,1.25806,1.27084,1.28412,1.29792,1.31223,1.32707,1.34242,1.3583,1.3747,1.39162,1.40905,1.42698,1.4454,1.46431,1.48368,1.5035,1.52374,1.54439,1.56542,1.58679,1.60848,1.63045,1.65266,1.67508,1.69767,1.72037,1.74315,1.76595,1.78872,1.81142,1.834,1.85639,1.87854,1.90041,1.92194,1.94308,1.96378,1.98398,2.00364,2.02272,2.04117,2.05896,2.07604,2.0924,2.10799,2.1228,2.13681,2.15,2.16237,2.17391,2.18461,2.19449,2.20354,2.21179,2.21924,2.22592,2.23185,2.23704,2.24153,2.24535,2.24851,2.25105,2.253,2.25439,2.25524,2.25558,2.25543,2.25482,2.25378,2.25231,2.25044,2.24817,2.24553,2.24251,2.23913,2.23539,2.23128,2.22681,2.22197,2.21675,2.21115,2.20513,2.19871,2.19184,2.18452,2.17672,2.16841,2.15957,2.15017,2.14017,2.12955,2.11827,2.10628,2.09356,2.08006,2.06573,2.05053,2.03442,2.01735,1.99927,1.98013,1.95987,1.93846,1.91584,1.89195,1.86675,1.84019,1.81223,1.78281,1.7519,1.71947,1.68547,1.6499,1.61274,1.57397,1.53362,1.49169,1.44822,1.40327,1.35689,1.30919,1.26028,1.21028,1.15937,1.10772,1.05554,1.00307,0.950546,0.898241,0.846433,0.795403,0.745431,0.696782,0.649704,0.604409,0.561076,0.519837,0.480774,0.443923,0.409272,0.376775,0.346354,0.317918},
  {1.01126,1.01197,1.01271,1.0135,1.01432,1.01519,1.01611,1.01707,1.01809,1.01916,1.0203,1.02149,1.02275,1.02407,1.02547,1.02695,1.02851,1.03016,1.03189,1.03372,1.03565,1.03769,1.03985,1.04212,1.04451,1.04704,1.0497,1.05252,1.05548,1.05861,1.06191,1.06539,1.06906,1.07292,1.077,1.08129,1.08581,1.09058,1.09559,1.10087,1.10642,1.11227,1.11841,1.12487,1.13166,1.13879,1.14627,1.15412,1.16236,1.17099,1.18003,1.1895,1.19941,1.20976,1.22058,1.23187,1.24365,1.25593,1.26871,1.28201,1.29583,1.31018,1.32507,1.34049,1.35645,1.37294,1.38998,1.40754,1.42563,1.44423,1.46333,1.48293,1.50299,1.52351,1.54445,1.5658,1.58752,1.60959,1.63197,1.65462,1.67751,1.70059,1.72382,1.74714,1.77053,1.79391,1.81725,1.84048,1.86356,1.88642,1.90902,1.9313,1.95321,1.97469,1.9957,2.01617,2.03607,2.05535,2.07398,2.0919,2.10909,2.12552,2.14117,2.156,2.17001,2.18318,2.1955,2.20698,2.21761,2.2274,2.23636,2.2445,2.25184,2.2584,2.26421,2.26928,2.27365,2.27733,2.28037,2.28278,2.28459,2.28584,2.28655,2.28675,2.28645,2.28568,2.28446,2.28281,2.28074,2.27826,2.27538,2.27211,2.26845,2.26441,2.25997,2.25514,2.24991,2.24426,2.23819,2.23168,2.22472,2.21727,2.20932,2.20085,2.19183,2.18222,2.172,2.16113,2.14959,2.13732,2.1243,2.11048,2.09581,2.08026,2.06378,2.04632,2.02783,2.00826,1.98756,1.96569,1.94259,1.91821,1.89249,1.8654,1.83689,1.8069,1.77541,1.74238,1.70778,1.67158,1.63377,1.59435,1.55332,1.51071,1.46656,1.4209,1.37383,1.32542,1.27579,1.22509,1.17347,1.12112,1.06825,1.01509,0.961903,0.90895,0.856513,0.804876,0.75432,0.705112,0.6575,0.611697,0.56788,0.526181,0.486681,0.449415,0.41437,0.381498,0.350721,0.321949},
  {1.01107,1.01176,1.0125,1.01327,1.01409,1.01494,1.01585,1.0168,1.0178,1.01886,1.01997,1.02115,1.02238,1.02369,1.02507,1.02653,1.02806,1.02968,1.03139,1.03319,1.0351,1.03711,1.03922,1.04146,1.04382,1.04631,1.04894,1.05171,1.05464,1.05772,1.06098,1.06441,1.06803,1.07184,1.07586,1.0801,1.08457,1.08928,1.09423,1.09945,1.10495,1.11073,1.11681,1.12321,1.12993,1.137,1.14442,1.15221,1.16039,1.16896,1.17795,1.18736,1.19722,1.20753,1.21831,1.22957,1.24132,1.25358,1.26635,1.27965,1.29348,1.30785,1.32277,1.33824,1.35426,1.37084,1.38797,1.40565,1.42387,1.44263,1.46191,1.48171,1.502,1.52277,1.54399,1.56564,1.5877,1.61012,1.63289,1.65596,1.6793,1.70285,1.72658,1.75045,1.7744,1.79837,1.82233,1.84621,1.86996,1.89352,1.91684,1.93986,1.96253,1.98479,2.00659,2.02787,2.04859,2.0687,2.08816,2.10692,2.12495,2.14222,2.15869,2.17435,2.18918,2.20315,2.21627,2.22852,2.23991,2.25043,2.26011,2.26894,2.27695,2.28415,2.29056,2.29622,2.30113,2.30534,2.30886,2.31173,2.31397,2.31561,2.31668,2.3172,2.3172,2.3167,2.31571,2.31426,2.31235,2.31001,2.30724,2.30405,2.30044,2.29642,2.29198,2.28711,2.28182,2.27608,2.2699,2.26325,2.25611,2.24847,2.24031,2.23159,2.2223,2.2124,2.20186,2.19065,2.17874,2.16609,2.15265,2.13838,2.12325,2.10721,2.09022,2.07222,2.05316,2.033,2.01169,1.98918,1.96541,1.94034,1.91391,1.88608,1.8568,1.82603,1.79374,1.75988,1.72442,1.68736,1.64867,1.60835,1.56642,1.5229,1.47783,1.43126,1.38328,1.33398,1.28348,1.23192,1.17948,1.12635,1.07273,1.01888,0.965058,0.911526,0.858573,0.806486,0.755544,0.706013,0.658139,0.612127,0.568149,0.526327,0.486735,0.449399,0.414298,0.38138,0.350562,0.321751}
};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

//LS X coefficient for A=atomic weight * 1.05
const G4double G4AtimaFluctuations::ls_X_coefficients_ahi[110][200]=
{
  {0.999182,0.999124,0.999062,0.998995,0.998925,0.998851,0.998772,0.998688,0.998598,0.998504,0.998404,0.998297,0.998184,0.998064,0.997937,0.997802,0.997659,0.997507,0.997346,0.997175,0.996994,0.996802,0.996598,0.996382,0.996153,0.99591,0.995653,0.995381,0.995092,0.994785,0.994461,0.994117,0.993753,0.993367,0.992958,0.992526,0.992067,0.991582,0.991068,0.990524,0.989948,0.989338,0.988693,0.988011,0.987289,0.986525,0.985717,0.984863,0.98396,0.983005,0.981996,0.98093,0.979804,0.978614,0.977358,0.976032,0.974632,0.973155,0.971597,0.969955,0.968223,0.966397,0.964474,0.962449,0.960317,0.958074,0.955714,0.953233,0.950626,0.947887,0.945012,0.941995,0.938832,0.935516,0.932044,0.928409,0.924608,0.920635,0.916485,0.912155,0.90764,0.902937,0.898042,0.892952,0.887666,0.88218,0.876495,0.870608,0.864522,0.858236,0.851752,0.845074,0.838206,0.831151,0.823917,0.81651,0.808938,0.801211,0.79334,0.785335,0.77721,0.768979,0.760656,0.752258,0.7438,0.735302,0.72678,0.718255,0.709743,0.701267,0.692844,0.684494,0.676236,0.668089,0.660071,0.6522,0.644492,0.636962,0.629625,0.622494,0.61558,0.608893,0.602443,0.596236,0.590278,0.584572,0.579122,0.573929,0.568991,0.564308,0.559876,0.555692,0.55175,0.548044,0.544568,0.541314,0.538273,0.535438,0.5328,0.53035,0.528077,0.525973,0.524029,0.522235,0.520583,0.519062,0.517665,0.516384,0.515209,0.514135,0.513152,0.512254,0.511434,0.510686,0.510005,0.509383,0.508817,0.508302,0.507831,0.507403,0.507011,0.506653,0.506325,0.506024,0.505746,0.505489,0.50525,0.505026,0.504815,0.504615,0.504423,0.504237,0.504055,0.503874,0.503693,0.503509,0.50332,0.503124,0.502918,0.502699,0.502465,0.502213,0.501939,0.501641,0.501313,0.500953,0.500554,0.500113,0.499624,0.49908,0.498474,0.4978,0.497047,0.496207,0.495269,0.494222,0.493052,0.491747,0.490288,0.48866},
  {0.999599,0.999546,0.999489,0.999428,0.999363,0.999294,0.999221,0.999143,0.99906,0.998971,0.998877,0.998778,0.998671,0.998558,0.998438,0.998311,0.998175,0.998031,0.997878,0.997716,0.997543,0.99736,0.997165,0.996959,0.99674,0.996507,0.99626,0.995998,0.99572,0.995425,0.995112,0.99478,0.994428,0.994054,0.993659,0.993239,0.992795,0.992323,0.991824,0.991295,0.990734,0.990141,0.989512,0.988846,0.988141,0.987395,0.986605,0.98577,0.984886,0.983951,0.982962,0.981917,0.980812,0.979644,0.978411,0.977108,0.975732,0.974279,0.972746,0.971129,0.969423,0.967625,0.965729,0.963732,0.961629,0.959416,0.957086,0.954636,0.95206,0.949354,0.946512,0.943529,0.9404,0.93712,0.933684,0.930086,0.926322,0.922387,0.918276,0.913985,0.90951,0.904848,0.899994,0.894946,0.889702,0.884259,0.878617,0.872775,0.866732,0.860491,0.854053,0.847421,0.840598,0.833589,0.826401,0.81904,0.811514,0.803834,0.796008,0.78805,0.77997,0.771785,0.763507,0.755153,0.74674,0.738286,0.729807,0.721324,0.712855,0.704419,0.696036,0.687725,0.679505,0.671395,0.663414,0.655577,0.647903,0.640406,0.6331,0.625999,0.619114,0.612455,0.606031,0.599848,0.593914,0.588231,0.582802,0.577628,0.572709,0.568043,0.563628,0.559458,0.55553,0.551837,0.548372,0.545128,0.542097,0.539271,0.536639,0.534195,0.531927,0.529827,0.527886,0.526094,0.524442,0.522921,0.521522,0.520238,0.519059,0.517979,0.516989,0.516083,0.515253,0.514493,0.513798,0.513161,0.512576,0.51204,0.511546,0.51109,0.510669,0.510277,0.50991,0.509566,0.50924,0.508929,0.508629,0.508337,0.50805,0.507765,0.507477,0.507184,0.506881,0.506566,0.506235,0.505883,0.505505,0.505098,0.504656,0.504173,0.503643,0.50306,0.502417,0.501704,0.500915,0.500037,0.499061,0.497975,0.496766,0.495418,0.493916,0.492242,0.490376,0.488297,0.485981,0.483402,0.480533,0.477343,0.4738,0.469868},
  {1.00017,1.00012,1.00007,1.00002,0.999959,0.999897,0.99983,0.999759,0.999682,0.999601,0.999514,0.999421,0.999322,0.999217,0.999104,0.998984,0.998857,0.998721,0.998576,0.998422,0.998258,0.998083,0.997898,0.997701,0.997491,0.997268,0.997031,0.996779,0.996512,0.996228,0.995926,0.995606,0.995266,0.994905,0.994522,0.994115,0.993684,0.993226,0.992741,0.992226,0.991681,0.991103,0.99049,0.98984,0.989152,0.988423,0.987652,0.986834,0.985969,0.985054,0.984085,0.98306,0.981976,0.98083,0.979618,0.978338,0.976985,0.975557,0.974048,0.972456,0.970776,0.969004,0.967136,0.965167,0.963092,0.960907,0.958608,0.956188,0.953644,0.95097,0.94816,0.945211,0.942116,0.938871,0.935469,0.931908,0.92818,0.924283,0.92021,0.915958,0.911523,0.9069,0.902087,0.897081,0.891878,0.886478,0.880878,0.875079,0.869081,0.862884,0.85649,0.849902,0.843124,0.836161,0.829018,0.821702,0.814222,0.806587,0.798807,0.790893,0.782859,0.774718,0.766485,0.758175,0.749806,0.741394,0.732958,0.724516,0.716087,0.707692,0.699348,0.691075,0.682893,0.67482,0.666873,0.659071,0.65143,0.643965,0.63669,0.629618,0.622761,0.616129,0.609731,0.603573,0.597662,0.592001,0.586593,0.581439,0.576538,0.571889,0.56749,0.563335,0.559421,0.55574,0.552287,0.549053,0.546032,0.543214,0.54059,0.538152,0.53589,0.533794,0.531857,0.530067,0.528417,0.526896,0.525498,0.524212,0.523031,0.521947,0.520952,0.520039,0.519202,0.518434,0.517728,0.517079,0.51648,0.515928,0.515415,0.514939,0.514494,0.514075,0.513679,0.513301,0.512937,0.512583,0.512236,0.511891,0.511544,0.511191,0.510828,0.510451,0.510054,0.509634,0.509185,0.508701,0.508176,0.507604,0.506978,0.506289,0.50553,0.50469,0.50376,0.502728,0.501582,0.500307,0.498889,0.49731,0.495552,0.493595,0.491416,0.488992,0.486294,0.483295,0.479964,0.476266,0.472165,0.467623,0.4626,0.457054},
  {1.00086,1.00082,1.00078,1.00073,1.00069,1.00063,1.00058,1.00051,1.00045,1.00038,1.0003,1.00021,1.00012,1.00003,0.999924,0.999813,0.999695,0.999568,0.999433,0.999288,0.999134,0.998969,0.998793,0.998606,0.998406,0.998193,0.997967,0.997726,0.997469,0.997196,0.996906,0.996598,0.996269,0.995921,0.99555,0.995157,0.994739,0.994295,0.993823,0.993323,0.992793,0.99223,0.991632,0.990999,0.990327,0.989615,0.988861,0.988062,0.987215,0.986318,0.985369,0.984364,0.983301,0.982176,0.980986,0.979728,0.978398,0.976993,0.975508,0.973941,0.972286,0.97054,0.968699,0.966757,0.96471,0.962554,0.960284,0.957895,0.955381,0.952738,0.949961,0.947044,0.943983,0.940771,0.937405,0.933879,0.930188,0.926327,0.922292,0.918078,0.913682,0.909099,0.904325,0.899359,0.894198,0.888839,0.883282,0.877525,0.87157,0.865416,0.859066,0.852522,0.845788,0.838869,0.831771,0.8245,0.817065,0.809474,0.801738,0.793869,0.785879,0.777782,0.769592,0.761326,0.752999,0.744629,0.736235,0.727834,0.719445,0.711089,0.702784,0.694549,0.686403,0.678365,0.670453,0.662685,0.655076,0.647642,0.640397,0.633354,0.626525,0.61992,0.613547,0.607413,0.601525,0.595886,0.590498,0.585363,0.580481,0.575849,0.571465,0.567325,0.563425,0.559757,0.556315,0.553093,0.550081,0.547272,0.544656,0.542225,0.539969,0.537879,0.535946,0.53416,0.532512,0.530994,0.529596,0.528311,0.527129,0.526044,0.525047,0.524131,0.52329,0.522516,0.521804,0.521147,0.520539,0.519976,0.519452,0.518962,0.518501,0.518064,0.517648,0.517247,0.516857,0.516475,0.516095,0.515713,0.515325,0.514927,0.514513,0.514078,0.513618,0.513126,0.512597,0.512023,0.511399,0.510715,0.509964,0.509136,0.508222,0.507209,0.506086,0.504839,0.503454,0.501913,0.500199,0.498292,0.49617,0.493809,0.491184,0.488265,0.485024,0.481427,0.477438,0.473019,0.468131,0.462732,0.456779,0.450227},
  {1.00162,1.0016,1.00157,1.00154,1.00151,1.00147,1.00143,1.00138,1.00132,1.00127,1.0012,1.00113,1.00105,1.00097,1.00088,1.00078,1.00067,1.00056,1.00043,1.0003,1.00016,1,0.99984,0.999664,0.999476,0.999275,0.99906,0.998831,0.998587,0.998326,0.998048,0.997752,0.997436,0.997101,0.996743,0.996363,0.995959,0.995529,0.995072,0.994586,0.99407,0.993523,0.992941,0.992324,0.991668,0.990973,0.990236,0.989455,0.988626,0.987748,0.986818,0.985833,0.98479,0.983685,0.982517,0.981281,0.979973,0.978591,0.977131,0.975587,0.973958,0.972237,0.970422,0.968507,0.966488,0.96436,0.962118,0.959758,0.957275,0.954663,0.951917,0.949033,0.946004,0.942827,0.939495,0.936003,0.932348,0.928523,0.924525,0.920349,0.91599,0.911446,0.906712,0.901786,0.896665,0.891347,0.885831,0.880116,0.874203,0.868092,0.861784,0.855284,0.848593,0.841718,0.834663,0.827436,0.820045,0.812498,0.804806,0.79698,0.789033,0.780979,0.772832,0.764608,0.756323,0.747994,0.73964,0.731279,0.72293,0.714612,0.706344,0.698146,0.690036,0.682033,0.674155,0.66642,0.658842,0.651439,0.644223,0.637209,0.630407,0.623827,0.617479,0.611369,0.605503,0.599885,0.594517,0.589401,0.584536,0.579921,0.575553,0.571428,0.567541,0.563885,0.560455,0.557243,0.554241,0.551441,0.548833,0.546409,0.544159,0.542074,0.540146,0.538364,0.536719,0.535203,0.533807,0.532522,0.531341,0.530255,0.529256,0.528337,0.527493,0.526714,0.525996,0.525333,0.524718,0.524145,0.52361,0.523108,0.522633,0.522181,0.521747,0.521326,0.520914,0.520506,0.520098,0.519685,0.519261,0.518823,0.518364,0.517879,0.517363,0.516808,0.516209,0.515557,0.514845,0.514064,0.513204,0.512255,0.511206,0.510043,0.508752,0.507319,0.505727,0.503956,0.501987,0.499797,0.497363,0.494656,0.49165,0.488312,0.484609,0.480505,0.475962,0.47094,0.465395,0.459285,0.452567,0.445192},
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