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Update KSIntCalculatorMott.cxx
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@juniorpena
juniorpena authored May 6, 2024
1 parent 26034d4 commit 341c15c
Showing 1 changed file with 107 additions and 71 deletions.
178 changes: 107 additions & 71 deletions Kassiopeia/Interactions/Source/KSIntCalculatorMott.cxx
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Original file line number Diff line number Diff line change
@@ -1,4 +1,6 @@
#include "KSIntCalculatorMott.h"
#include <vector>
#include <random>

#include "KRandom.h"
using katrin::KRandom;
Expand All @@ -10,13 +12,12 @@ using KGeoBag::KThreeVector;
namespace Kassiopeia
{

KSIntCalculatorMott::KSIntCalculatorMott() : fThetaMin(0.), fThetaMax(0.), fMDCS(nullptr), fMTCS(nullptr) {}
KSIntCalculatorMott::KSIntCalculatorMott() : fThetaMin(0.), fThetaMax(0.), fNucleus("") {}
KSIntCalculatorMott::KSIntCalculatorMott(const KSIntCalculatorMott& aCopy) :
KSComponent(aCopy),
fThetaMin(aCopy.fThetaMin),
fThetaMax(aCopy.fThetaMax),
fMDCS(nullptr),
fMTCS(nullptr)
fNucleus(aCopy.fNucleus)
{}
KSIntCalculatorMott* KSIntCalculatorMott::Clone() const
{
Expand All @@ -28,14 +29,10 @@ void KSIntCalculatorMott::CalculateCrossSection(const KSParticle& anInitialParti
{

double tInitialKineticEnergy = anInitialParticle.GetKineticEnergy_eV();
InitializeMDCS(tInitialKineticEnergy);

double fCrossSection = (fMTCS->Eval(fThetaMax) - fMTCS->Eval(fThetaMin)) * pow(10, -30);

DeinitializeMDCS();
double fCrossSection = (MTCS(fThetaMax, tInitialKineticEnergy) - MTCS(fThetaMin, tInitialKineticEnergy));

aCrossSection = fCrossSection;

return;
}
void KSIntCalculatorMott::ExecuteInteraction(const KSParticle& anInitialParticle, KSParticle& aFinalParticle,
Expand All @@ -51,7 +48,7 @@ void KSIntCalculatorMott::ExecuteInteraction(const KSParticle& anInitialParticle


double tPhi = KRandom::GetInstance().Uniform(0., 2. * katrin::KConst::Pi());
tMomentum.SetPolarAngle(tTheta);
tMomentum.SetPolarAngle(tTheta * katrin::KConst::Pi() / 180);
tMomentum.SetAzimuthalAngle(tPhi);

aFinalParticle.SetTime(tTime);
Expand All @@ -60,7 +57,7 @@ void KSIntCalculatorMott::ExecuteInteraction(const KSParticle& anInitialParticle
aFinalParticle.SetKineticEnergy_eV(tInitialKineticEnergy - tLostKineticEnergy);
aFinalParticle.SetLabel(GetName());

fStepAngularChange = tTheta * 180. / katrin::KConst::Pi();
fStepAngularChange = tTheta;

return;
}
Expand All @@ -69,11 +66,36 @@ double KSIntCalculatorMott::GetTheta(const double& anEnergy){

double tTheta;

InitializeMDCS(anEnergy);
std::vector<double> theta_arr;

tTheta = fMDCS->GetRandom(fThetaMin, fThetaMax);
// Populate theta_arr
for (int i = 0; i <= 1000; ++i) {
theta_arr.push_back(fThetaMin + i * (fThetaMax - fThetaMin) / 1000.0);
}

DeinitializeMDCS();
double k = 0.0;

// Calculating rescaling factor for rejection sampling
for (double theta : theta_arr) {
double MDCS_val = MDCS(theta, anEnergy);
double PDF_val = Normalized_RDCS(theta);
double ratio = MDCS_val / PDF_val;
if (ratio > k) {
k = MDCS_val / PDF_val;
} else {
break;
}
}

// Rejection sampling taking initial sample from Rutherford Diff. X-Sec
while (true) {
double sample = Normalized_RTCSInverse(KRandom::GetInstance().Uniform(0.0, 1.0, false, true));
double uniform_sample = KRandom::GetInstance().Uniform(0.0, 1.0, false, true);
if (MDCS(sample, anEnergy) / (k * Normalized_RDCS(sample)) > uniform_sample) {
tTheta = sample;
break;
}
}

return tTheta;

Expand All @@ -82,94 +104,108 @@ double KSIntCalculatorMott::GetTheta(const double& anEnergy){
double KSIntCalculatorMott::GetEnergyLoss(const double& anEnergy, const double& aTheta){
double M, me, p, anELoss;

M = 4.0026 * katrin::KConst::AtomicMassUnit_eV(); // eV/c^2
double amu = 0.0;

if (fNucleus == "He") {
amu = 4.0026;
} else if (fNucleus == "Ne") {
amu = 20.1797;
}

M = amu * katrin::KConst::AtomicMassUnit_eV(); // eV/c^2
me = katrin::KConst::M_el_eV(); // electron mass eV/c^2

p = sqrt(anEnergy * (anEnergy + 2 * me * pow(katrin::KConst::C(), 2))) / katrin::KConst::C();

anELoss = 2 * pow(p, 2) * M / (pow(me, 2) + pow(M, 2) + 2 * M * sqrt( pow((p/katrin::KConst::C()), 2) + pow(me, 2))) * (1 - cos(aTheta));
anELoss = 2 * pow(p, 2) * M / (pow(me, 2) + pow(M, 2) + 2 * M * sqrt( pow((p/katrin::KConst::C()), 2) + pow(me, 2))) * (1 - cos(aTheta * katrin::KConst::Pi() / 180));

return anELoss;
}

void KSIntCalculatorMott::InitializeMDCS(const double E0)
{

double beta = TMath::Sqrt( pow(E0, 2) + 2 * E0 * katrin::KConst::M_el_eV()) / (E0 + katrin::KConst::M_el_eV());

/* Constants given in publication in header file. These are the constants for scattering off of Helium */
static double b[5][6] = {{ 1. , 3.76476 * pow(10, -8), -3.05313 * pow(10, -7), -3.27422 * pow(10, -7), 2.44235 * pow(10, -6), 4.08754 * pow(10, -6)},
{ 2.35767 * pow(10, -2), 3.24642 * pow(10, -2), -6.37269 * pow(10, -4), -7.69160 * pow(10, -4), 5.28004 * pow(10, -3), 9.45642 * pow(10, -3)},
{ -2.73743 * pow(10, -1), -7.40767 * pow(10, -1), -4.98195 * pow(10, -1), 1.74337 * pow(10, -3), -1.25798 * pow(10, -2), -2.24046 * pow(10, -2)},
{ -7.79128 * pow(10, -4), -4.14495 * pow(10, -4), -1.62657 * pow(10, -3), -1.37286 * pow(10, -3), 1.04319 * pow(10, -2), 1.83488 * pow(10, -2)},
{ 2.02855 * pow(10, -4), 1.94598 * pow(10, -6), 4.30102 * pow(10, -4), 4.32180 * pow(10, -4), -3.31526 * pow(10, -3), -5.81788 * pow(10, -3)}};

double a[6] = {0, 0, 0, 0, 0, 0};
double KSIntCalculatorMott::Beta(double const E0) {
return sqrt( pow(E0, 2) + 2 * E0 * katrin::KConst::M_el_eV()) / (E0 + katrin::KConst::M_el_eV());
}

for (int j = 0; j < 5; j++){
for (int k = 0; k < 6; k++){
a[j] += b[j][k] * pow((beta - 0.7181287), k);
std::vector<double> KSIntCalculatorMott::RMott_coeffs(double const E0) {

std::vector<double> a(6, 0.0); // Initialize a with 6 zeros, the last entry is not related to coefficient calculation it is Z for the nucleus of choice
std::vector<std::vector<double>> b(5, std::vector<double>(6));

if (fNucleus == "He") {
a[5] = 2; // Charge Z
b = {{ 1.0 , 3.76476e-8, -3.05313e-7, -3.27422e-7, 2.44235e-6, 4.08754e-6},
{ 2.35767e-2, 3.24642e-2, -6.37269e-4, -7.69160e-4, 5.28004e-3, 9.45642e-3},
{-2.73743e-1, -7.40767e-1, -4.98195e-1, 1.74337e-3, -1.25798e-2, -2.24046e-2},
{-7.79128e-4, -4.14495e-4, -1.62657e-3, -1.37286e-3, 1.04319e-2, 1.83488e-2},
{ 2.02855e-4, 1.94598e-6, 4.30102e-4, 4.32180e-4, -3.31526e-3, -5.81788e-3}};
} else if (fNucleus == "Ne") {
a[5] = 10;
b = {{ 9.99997e-1, -1.87404e-7, 3.10276e-5, 5.20000e-5, 2.98132e-4, -5.19259e-4},
{ 1.20783e-1, 1.66407e-1, 1.06608e-2, 6.48772e-3, -1.53031e-3, -7.59354e-2},
{-3.15222e-1, -8.28793e-1, -6.05740e-1, -1.47812e-1, 1.15760 , 1.58565 },
{-2.89055e-2, -9.08096e-4, 1.21467e-1, -1.77575e-1, -1.29110 , -1.90333 },
{ 7.65342e-3, -8.85417e-4, -3.89092e-2, -5.44040e-2, 3.93087e-1, 5.79439e-1}};
}

for (int j = 0; j < 5; ++j) {
a[j] = 0.0;
for (int k = 0; k < 6; ++k) {
a[j] += b[j][k] * pow(Beta(E0) - 0.7181287, k);
}
}

/* ROOT TF1 takes in analytical formulas as strings. This is the conversion into strings */
std::string Rmott;
std::ostringstream RmottStream;

RmottStream << std::fixed;
RmottStream << std::setprecision(12);

RmottStream << a[0] << " + " << a[1] << " * pow( ( 1 - cos(x) ) , 0.5) + " << a[2] << " * ( 1 - cos(x) ) + " << a[3] << " * pow( ( 1 - cos(x) ) , 1.5) + " << a[4] << " * pow( ( 1 - cos(x) ) , 2)";
Rmott = RmottStream.str();
return a;
}

double KSIntCalculatorMott::MDCS(double theta, const double E0) {

double r_e = 2.8179403227 * pow(10, -15);

std::string RutherfordDCS;
std::ostringstream RutherfordDCSStream;
std::vector<double> a = RMott_coeffs(E0);

RutherfordDCSStream << std::fixed;
RutherfordDCSStream << std::setprecision(12);
double Z = a[5];

RutherfordDCSStream << "pow((2 * 2.8179403227 ), 2) * ( (1 - pow(" << beta << ", 2) ) / ( pow(" << beta << ", 4) )) * (1 / pow( (1 - cos(x)), 2))";
RutherfordDCS = RutherfordDCSStream.str();
return pow(Z, 2) * pow(r_e, 2) * ( (1 - pow(Beta(E0), 2))/(pow(Beta(E0), 4)) ) * ((a[0] * pow(1 - cos(theta), -2)) + (a[1] * pow((1 - cos(theta)), ((1 / 2) - 2))) + (a[2] * pow((1 - cos(theta)), (-1))) + (a[3] * pow((1 - cos(theta)), ((3 / 2) - 2))) + a[4] );
}

double KSIntCalculatorMott::MTCS(double theta, const double E0) {

double r_e = 2.8179403227 * pow(10, -15);

std::string MottDCS = "(" + RutherfordDCS + ") * (" + Rmott + ")";
std::vector<double> a = RMott_coeffs(E0);

double Z = a[5];

std::string MottTCS;
std::ostringstream MottTCSStream;
std::ostringstream MottTCSStreamThetaIndepPrefactor;

MottTCSStream << std::fixed;
MottTCSStream << std::setprecision(12);

MottTCSStreamThetaIndepPrefactor << std::fixed;
MottTCSStreamThetaIndepPrefactor << std::setprecision(12);
return 2 * katrin::KConst::Pi() * pow(Z, 2) * pow(r_e, 2) *
((1 - pow(Beta(E0), 2)) / pow(Beta(E0), 4)) *
((a[0] * pow((1 - cos(theta * katrin::KConst::Pi() / 180)), -1) / (-1)) +
(a[1] * pow((1 - cos(theta * katrin::KConst::Pi() / 180)), (1.0 / 2) - 1) / ((1.0 / 2) - 1)) +
(a[2] * log(1 - cos(theta * katrin::KConst::Pi() / 180))) +
(a[3] * pow((1 - cos(theta * katrin::KConst::Pi() / 180)), (3.0 / 2) - 1) / ((3.0 / 2) - 1)) +
(a[4] * -1 * cos(theta * katrin::KConst::Pi() / 180)))
- 2 * katrin::KConst::Pi() * pow(Z, 2) * pow(r_e, 2) *
((1 - pow(Beta(E0), 2)) / pow(Beta(E0), 4)) *
((a[0] * pow((1 - cos(fThetaMin * katrin::KConst::Pi() / 180)), -1) / (-1)) +
(a[1] * pow((1 - cos(fThetaMin * katrin::KConst::Pi() / 180)), (1.0 / 2) - 1) / ((1.0 / 2) - 1)) +
(a[2] * log(1 - cos(fThetaMin * katrin::KConst::Pi() / 180))) +
(a[3] * pow((1 - cos(fThetaMin * katrin::KConst::Pi() / 180)), (3.0 / 2) - 1) / ((3.0 / 2) - 1)) +
(a[4] * -1 * cos(fThetaMin * katrin::KConst::Pi() / 180)));
}

MottTCSStreamThetaIndepPrefactor << "pow((2 * 2.8179403227 ), 2) * ( (1 - pow(" << beta << ", 2) ) / ( pow(" << beta << ", 4) )) * ";
double KSIntCalculatorMott::Normalized_RDCS(double theta) {

MottTCSStream << "(2 * " << katrin::KConst::Pi() << " * (-4 * sqrt(2) * ( (" << a[1] << ") + (-1) * (" << a[2]
<< ") * sqrt(( 1 - cos(x) )) * log( sin(x / 2) )) * pow(sin(x / 2), 4) + 4 * sqrt(2) * (2 * ("
<< a[3] << ") + (" << a[4] << ") * sqrt( (1 - cos(x))) ) * pow(sin(x / 2), 6) - 2 * (" << a[0]
<< ") * pow(sin( x / 2 ), 3) ) ) / ( pow((-1 + cos(x)), 2) * sin( x / 2 ))";
double C = 1 / ((1 / (1 - cos(fThetaMin* katrin::KConst::Pi() / 180))) - (1 / (1 - cos(fThetaMax* katrin::KConst::Pi() / 180))));

MottTCS = MottTCSStreamThetaIndepPrefactor.str() + MottTCSStream.str();
return C / pow((1 - cos(theta* katrin::KConst::Pi() / 180)), 2);
}

fMDCS = new TF1("function", MottDCS.c_str(), fThetaMin, fThetaMax);
fMTCS = new TF1("function", MottTCS.c_str(), fThetaMin, fThetaMax);
double KSIntCalculatorMott::Normalized_RTCSInverse(double x) {

return;
}
double C = 1 / ((1 / (1 - cos(fThetaMin * katrin::KConst::Pi() / 180))) - (1 / (1 - cos(fThetaMax * katrin::KConst::Pi() / 180))));

void KSIntCalculatorMott::DeinitializeMDCS()
{
delete fMDCS;
fMDCS = nullptr;
delete fMTCS;
fMTCS = nullptr;
return;
return acos( 1 - (1 / ((1 / (1 - cos(fThetaMin * katrin::KConst::Pi() / 180))) - x / C)) ) * 180 / katrin::KConst::Pi();
}

} // namespace Kassiopeia

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