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NEST.cpp
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NEST.cpp
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#include <exception>
#include "NEST.hh"
#include <stdexcept>
#define ZurichEXOW 1.1716263232
#define ZurichEXOQ \
1.08 // Qy Boost Factor to fit EXO-200 Data (error on this quantity is +/-
// 0.03)
//#define InfraredNR 7.
#define ChargeLoss 1.000 // 0.77 is LUX Run03 default (wall BG model)
using namespace std;
using namespace NEST;
static constexpr int podLength = 1100; // roughly 100-1,000 ns for S1
bool kr83m_reported_low_deltaT = false; // to aid in verbosity
NESTresult NESTcalc::FullCalculation(INTERACTION_TYPE species, double energy,
double density, double dfield, double A,
double Z,
const std::vector<double> &NRYieldsParam,
const std::vector<double> &NRERWidthsParam,
const std::vector<double> &ERYieldsParam,
bool do_times /*=true*/) {
if (density < 1.) fdetector->set_inGas(true);
NESTresult result;
result.yields = GetYields(species, energy, density, dfield, A, Z,
NRYieldsParam, ERYieldsParam);
result.quanta =
GetQuanta(result.yields, density, NRERWidthsParam, false, -999.);
if (do_times)
result.photon_times = GetPhotonTimes(
species, result.quanta.photons, result.quanta.excitons, dfield, energy);
else {
result.photon_times = photonstream(result.quanta.photons, 0.0);
}
return result;
}
double NESTcalc::PhotonTime(INTERACTION_TYPE species, bool exciton,
double dfield, double energy) {
double time_ns = 0., SingTripRatio, tauR = 0., tau3 = 23.97,
tau1 =
3.27; // arXiv:1802.06162. NR may need tauR ~0.5-1ns instead of 0
if (fdetector->get_inGas() || energy < W_DEFAULT * 0.001) {
// from G4S1Light.cc in old NEST
tau1 = 5.18; // uncertainty of 1.55 ns from G4S2Light
tau3 = 100.1; // uncertainty of 7.90 ns from G4S2Light
}
// tau1 = 3.5*ns; tau3 = 20.*ns; tauR = 40.*ns for solid Xe from old NEST.
// Here assuming same as in liquid
// if ( dfield > 60. ) dfield = 60. // makes Xed work. 200 for LUX Run04
// instead. A mystery! Why no field dep?
double LET = CalcElectronLET(energy, ATOM_NUM);
if (ValidityTests::nearlyEqual(ATOM_NUM, 18.)) {
// copied from 2013 NEST version for LAr on LBNE
tau1 = RandomGen::rndm()->rand_gauss(6.5, 0.8,
true); // error from weighted average
tau3 = RandomGen::rndm()->rand_gauss(1300, 50, true); // ibid.
tauR = RandomGen::rndm()->rand_gauss(0.8, 0.2, true); // Kubota 1979
if (species <= Cf)
SingTripRatio = 0.22218 * pow(energy, 0.48211);
else if (species == ion) { // really only alphas here
SingTripRatio = (-0.065492 + 1.9996 * exp(-energy / 1e3)) /
(1. + 0.082154 / pow(energy / 1e3, 2.)) +
2.1811; // uses energy in MeV not keV
} else {
SingTripRatio = 0.2701 + 0.003379 * LET - 4.7338e-5 * pow(LET, 2.) +
8.1449e-6 * pow(LET, 3.);
if (LET < 3. && !exciton)
SingTripRatio = RandomGen::rndm()->rand_gauss(0.5, 0.2, true);
if (LET < 3. && exciton)
SingTripRatio = RandomGen::rndm()->rand_gauss(0.36, 0.06, true);
} // lastly is ER for LAr
} else {
if (species <= Cf) // NR
SingTripRatio =
(0.21 - 0.0001 * dfield) *
pow(energy,
0.21 - 0.0001 * dfield); // arXiv:1803.07935. LUX:0.15*E^0.15
else if (species == ion) {
// e.g., alphas
SingTripRatio =
0.065 *
pow(energy,
0.416); // spans 2.3 (alpha) and 7.8 (Cf in Xe) from NEST v1
} else {
// ER
if (!exciton) {
if (energy > 1e3)
energy = 1e3; // MIP above ~1 MeV. Fix thanks to Austin de St. Croix
tauR = exp(-0.00900 * dfield) *
(7.3138 + 3.8431 * log10(energy)); // arXiv:1310.1117
if (tauR < 3.5)
tauR = 3.5; // used to be for gammas only but helpful for matching
// beta data better
if (dfield > 8e2) dfield = 8e2; // to match Kubota's 4,000 V/cm
SingTripRatio =
1.00 *
pow(energy,
-0.45 +
0.0005 *
dfield); // see comment below; also, dfield may need to
// be fixed at ~100-200 V/cm (for NR too)
} else {
SingTripRatio =
0.20 *
pow(energy,
-0.45 +
0.0005 *
dfield); // mixing arXiv:1807.07121 with Kubota 1979
}
}
}
if (fdetector->get_inGas() || energy < W_DEFAULT * 0.001) {
SingTripRatio = 0.1;
if (fdetector->get_inGas() && !exciton)
tauR = 28e3;
else {
tauR = 0.; // 28 microseconds comes from Henrique:
// https://doi.org/10.1016/j.astropartphys.2018.04.006
}
if (ValidityTests::nearlyEqual(ATOM_NUM, 18.)) {
tau3 = 1600.;
tau1 = 6.;
} // from old G4S2Light
}
if (tauR < 0.) tauR = 0.; // in case varied with Gaussian earlier
// the recombination time is non-exponential, but approximates
// to exp at long timescales (see Kubota '79)
time_ns += tauR * (1.0 / RandomGen::rndm()->rand_uniform() - 1.);
if (RandomGen::rndm()->rand_uniform() < SingTripRatio / (1. + SingTripRatio))
time_ns -= tau1 * log(RandomGen::rndm()->rand_uniform());
else {
time_ns -= tau3 * log(RandomGen::rndm()->rand_uniform());
}
return time_ns;
}
// in analytical model, an empirical distribution (Brian Lenardo and Dev A.K.)
photonstream NESTcalc::AddPhotonTransportTime(const photonstream &emitted_times,
double x, double y, double z) {
photonstream return_photons;
for (auto t : emitted_times) {
double newtime = t + fdetector->OptTrans(x, y, z);
return_photons.emplace_back(newtime);
}
return return_photons;
}
photonstream NESTcalc::GetPhotonTimes(INTERACTION_TYPE species,
int total_photons, int excitons,
double dfield, double energy) {
photonstream return_photons;
int total, excit;
for (int ip = 0; ip < total_photons; ++ip) {
bool isExciton = false;
if (ip < excitons) isExciton = true;
// message from Matthew: please stop telling me next line bad. I can't skip
// PhotonTime, it's a func not array
return_photons.emplace_back(PhotonTime(species, isExciton, dfield, energy));
}
return return_photons;
}
double NESTcalc::RecombOmegaNR(double elecFrac,
const std::vector<double> &NRERWidthsParam) {
double omega =
NRERWidthsParam[2] * exp(-0.5 * pow(elecFrac - NRERWidthsParam[3], 2.) /
(NRERWidthsParam[4] * NRERWidthsParam[4]));
if (omega < 0.) omega = 0;
return omega;
}
double NESTcalc::RecombOmegaER(double efield, double elecFrac,
const std::vector<double> &NRERWidthsParam,
bool oldModel) {
double ampl;
if (!oldModel)
ampl = 0.086036 + (NRERWidthsParam[7] - 0.086036) /
pow(1. + pow(efield / 295.2, 251.6),
0.0069114); // NEW(GregR)
// NRERWidthsParam[7] sets the lower-asymptote of field-dependence of ampl
else
ampl = 0.14 + (0.043 - 0.14) / (1. + pow(efield / 1210., 1.25)); // OLD
if (ampl < 0.) ampl = 0.;
double wide = NRERWidthsParam[8]; // Width of omega vs. electron-fraction
// (i.e. recomb. prob.)
double cntr =
NRERWidthsParam[9]; // NEW(GregR) Center of omega vs. elec-frac (OLD
// value of 0.50 for OLD ampl above 0.14...)
if (oldModel) cntr = 0.50;
double skew =
NRERWidthsParam[10]; // Skewness of omega vs. elec-frac distribution
double mode = cntr + 2. * inv_sqrt2_PI * skew * wide / sqrt(1. + skew * skew);
double norm =
1. / (exp(-0.5 * pow(mode - cntr, 2.) / (wide * wide)) *
(1. + erf(skew * (mode - cntr) /
(wide * sqrt2)))); // makes sure omega never exceeds ampl
double omega = norm * ampl *
exp(-0.5 * pow(elecFrac - cntr, 2.) / (wide * wide)) *
(1. + erf(skew * (elecFrac - cntr) / (wide * sqrt2)));
if (omega < 0.) omega = 0;
return omega;
}
double NESTcalc::FanoER(double density, double Nq_mean, double efield,
const std::vector<double> &NRERWidthsParam) {
if (ValidityTests::nearlyEqual(ATOM_NUM, 18.)) // liquid argon
return 0.1115; // T&I. conflicting reports of .107 (Doke) & ~0.1 elsewhere
double Fano =
0.12707 - 0.029623 * density - // Fano factor is << 1
0.0057042 *
pow(density,
2.) + //~0.1 for GXe w/ formula from Bolotnikov et al. 1995
0.0015957 *
pow(density,
3.); // to get it to be ~0.03 for LXe (E Dahl Ph.D. thesis)
if (!fdetector->get_inGas()) {
if (NRERWidthsParam[6] < 0.)
Fano += fabs(NRERWidthsParam[6]) * sqrt(Nq_mean) * pow(efield, 0.5);
else
Fano = NRERWidthsParam[6];
}
return Fano;
}
QuantaResult NESTcalc::GetQuanta(const YieldResult &yields, double density,
const std::vector<double> &NRERWidthsParam,
bool oldModelER, double SkewnessER) {
QuantaResult result{};
bool HighE;
int Nq_actual, Ne, Nph, Ni, Nex;
if (NRERWidthsParam.size() < 11) {
throw std::runtime_error(
"ERROR: You need a minimum of 11 free parameters for the resolution "
"model.");
}
double excitonRatio = yields.ExcitonRatio;
double Nq_mean = yields.PhotonYield + yields.ElectronYield;
double elecFrac = max(0., min(yields.ElectronYield / Nq_mean, 1.));
if (excitonRatio < 0.) {
excitonRatio = 0.;
HighE = true;
} else {
HighE = false;
}
double alf = 1. / (1. + excitonRatio);
double recombProb = 1. - (excitonRatio + 1.) * elecFrac;
if (recombProb < 0.) {
excitonRatio = 1. / elecFrac - 1.;
}
if (ValidityTests::nearlyEqual(yields.Lindhard, 1.)) {
if (ValidityTests::nearlyEqual(Nq_mean, 0.))
Nq_actual = 0;
else {
double Fano =
FanoER(density, Nq_mean, yields.ElectricField, NRERWidthsParam);
Nq_actual = int(floor(
RandomGen::rndm()->rand_gauss(Nq_mean, sqrt(Fano * Nq_mean), true) +
0.5));
}
Ni = RandomGen::rndm()->binom_draw(Nq_actual, alf);
Nex = Nq_actual - Ni;
} else {
double Fano = NRERWidthsParam[0];
Ni = int(floor(RandomGen::rndm()->rand_gauss(
Nq_mean * alf, sqrt(Fano * Nq_mean * alf), true) +
0.5));
Fano = NRERWidthsParam[1];
Nex = int(floor(RandomGen::rndm()->rand_gauss(
Nq_mean * excitonRatio * alf,
sqrt(Fano * Nq_mean * excitonRatio * alf), true) +
0.5));
Nq_actual = Nex + Ni;
}
if (Nq_actual == 0) {
result.ions = 0;
result.excitons = 0;
result.photons = 0;
result.electrons = 0;
result.Variance = 0;
result.recombProb = 0;
return result;
}
if (Nex < 0) Nex = 0;
if (Ni < 0) Ni = 0;
if (Nex > Nq_actual) Nex = Nq_actual;
if (Ni > Nq_actual) Ni = Nq_actual;
result.ions = Ni;
result.excitons = Nex;
if (Nex <= 0 && HighE) recombProb = yields.PhotonYield / double(Ni);
recombProb = max(0., min(recombProb, 1.));
if (std::isnan(recombProb) || std::isnan(elecFrac) || Ni == 0 ||
ValidityTests::nearlyEqual(recombProb, 0.0)) {
result.photons = Nex;
result.electrons = Ni;
elecFrac = 1.0;
result.recombProb = 0.;
result.Variance = 0.;
return result;
}
// set omega (non-binomial recombination fluctuations parameter) according to
// whether the Lindhard <1, i.e. this is NR.
double omega = yields.Lindhard < 1
? RecombOmegaNR(elecFrac, NRERWidthsParam)
: RecombOmegaER(yields.ElectricField, elecFrac,
NRERWidthsParam, oldModelER);
if (ValidityTests::nearlyEqual(ATOM_NUM, 18.))
omega = 0.0; // Ar has no non-binom sauce
double Variance =
recombProb * (1. - recombProb) * Ni + omega * omega * Ni * Ni;
// if ( !fdetector->get_OldW13eV() ) Variance /= sqrt ( ZurichEXOQ );
double skewness;
if ((yields.PhotonYield + yields.ElectronYield) > 1e4 ||
yields.ElectricField > 4e3 || yields.ElectricField < 50.) {
skewness = 0.00; // make it a constant 0 when outside the range of Vetri
// Velan's Run04 models.
} else {
// LUX Skewness Model
Wvalue wvalue = WorkFunction(density, fdetector->get_molarMass(),
fdetector->get_OldW13eV());
double Wq_eV = wvalue.Wq_eV;
double engy = 1e-3 * Wq_eV * (yields.PhotonYield + yields.ElectronYield);
double fld = yields.ElectricField;
double alpha0 = 1.39;
double cc0 = 4.0, cc1 = 22.1;
double E0 = 7.7, E1 = 54., E2 = 26.7, E3 = 6.4;
double F0 = 225., F1 = 71.;
skewness = 0.;
if (ValidityTests::nearlyEqual(yields.Lindhard, 1.)) {
if (SkewnessER != -999.) {
skewness = SkewnessER;
} else {
skewness = 1. / (1. + exp((engy - E2) / E3)) *
(alpha0 + cc0 * exp(-1. * fld / F0) *
(1. - exp(-1. * engy / E0))) +
1. / (1. + exp(-1. * (engy - E2) / E3)) * cc1 *
exp(-1. * engy / E1) * exp(-1. * sqrt(fld) / sqrt(F1));
}
// if ( std::abs(skewness) <= DBL_MIN ) skewness = DBL_MIN;
} else {
skewness = NRERWidthsParam[5]; // 2.25 but ~5-20 also good (for NR). All
// better than zero, but 0 is OK too
} // note to self: find way to make 0 for ion (wall BG) incl. alphas?
}
double widthCorrection =
sqrt(1. - (2. / M_PI) * skewness * skewness / (1. + skewness * skewness));
double muCorrection = (sqrt(Variance) / widthCorrection) *
(skewness / sqrt(1. + skewness * skewness)) * 2. *
inv_sqrt2_PI;
if (std::abs(skewness) > DBL_MIN &&
ValidityTests::nearlyEqual(ATOM_NUM,
54.)) // skewness model only for Xenon!
Ne = int(floor(RandomGen::rndm()->rand_skewGauss(
(1. - recombProb) * Ni - muCorrection,
sqrt(Variance) / widthCorrection, skewness) +
0.5));
else {
Ne = int(floor(RandomGen::rndm()->rand_gauss((1. - recombProb) * Ni,
sqrt(Variance), true) +
0.5));
}
Ne = NESTcalc::clamp(Ne, 0, Ni);
Nph = Nq_actual - Ne;
if (Nph > Nq_actual) Nph = Nq_actual;
if (Nph < Nex) Nph = Nex;
if ((Nph + Ne) != (Nex + Ni)) {
throw std::runtime_error(
"ERROR: Quanta not conserved. Tell Matthew Immediately!");
}
result.Variance = Variance;
result.recombProb = recombProb;
result.photons = Nph;
result.electrons = Ne;
return result; // quanta returned with recomb fluctuations
}
YieldResult NESTcalc::GetYieldGamma(double energy, double density,
double dfield) {
Wvalue wvalue = WorkFunction(density, fdetector->get_molarMass(),
fdetector->get_OldW13eV());
double Wq_eV = wvalue.Wq_eV;
double alpha = wvalue.alpha;
constexpr double m3 = 2., m4 = 2., m6 = 0.;
const double m1 =
33.951 + (3.3284 - 33.951) / (1. + pow(dfield / 165.34, .72665));
double m2 = 1000 / Wq_eV;
double m5 = 23.156 + (10.737 - 23.156) / (1. + pow(dfield / 34.195, .87459));
double densCorr = 240720. / pow(density, 8.2076);
double m7 =
66.825 + (829.25 - 66.825) / (1. + pow(dfield / densCorr, .83344));
double Nq = energy * 1000. / Wq_eV;
double m8 = 2.;
if (fdetector->get_inGas()) m8 = -2.;
double Qy = m1 + (m2 - m1) / (1. + pow(energy / m3, m4)) + m5 +
(m6 - m5) / (1. + pow(energy / m7, m8));
if (!fdetector->get_OldW13eV()) Qy *= ZurichEXOQ;
double Ly = Nq / energy - Qy;
YieldResult result{};
result.PhotonYield = Ly * energy;
result.ElectronYield = Qy * energy;
result.ExcitonRatio = NexONi(energy, density);
result.Lindhard = 1;
result.ElectricField = dfield;
result.DeltaT_Scint = -999;
return YieldResultValidity(result, energy, Wq_eV);
}
YieldResult NESTcalc::GetYieldERWeighted(
double energy, double density, double dfield,
const std::vector<double> &ERYieldsParam) {
Wvalue wvalue = WorkFunction(density, fdetector->get_molarMass(),
fdetector->get_OldW13eV());
double Wq_eV = wvalue.Wq_eV;
const std::vector<double> EnergyParams = {0.23, 0.77, 2.95, -1.44};
const std::vector<double> FieldParams = {421.15, 3.27};
YieldResult yieldsB = GetYieldBetaGR(energy, density, dfield, ERYieldsParam);
YieldResult yieldsG = GetYieldGamma(energy, density, dfield);
double weightG =
EnergyParams[0] +
EnergyParams[1] * erf(EnergyParams[2] * (log(energy) + EnergyParams[3])) *
(1. - (1. / (1. + pow(dfield / FieldParams[0], FieldParams[1]))));
// field weighting added to match dependence reported by XELDA and LUX Run3.
// Not validated beyond of fields on the order of a few hundred V/cm
double weightB = 1. - weightG;
YieldResult result{};
result.PhotonYield =
weightG * yieldsG.PhotonYield + weightB * yieldsB.PhotonYield;
result.ElectronYield =
weightG * yieldsG.ElectronYield + weightB * yieldsB.ElectronYield;
result.ExcitonRatio =
weightG * yieldsG.ExcitonRatio + weightB * yieldsB.ExcitonRatio;
result.Lindhard = weightG * yieldsG.Lindhard + weightB * yieldsB.Lindhard;
result.ElectricField =
weightG * yieldsG.ElectricField + weightB * yieldsB.ElectricField;
result.DeltaT_Scint =
weightG * yieldsG.DeltaT_Scint + weightB * yieldsB.DeltaT_Scint;
return YieldResultValidity(result, energy, Wq_eV);
}
NESTresult NESTcalc::GetYieldERdEOdxBasis(
const std::vector<double> &dEOdxParam, string muonInitPos,
vector<double> vTable, const std::vector<double> &NRERWidthsParam) {
Wvalue wvalue = WorkFunction(dEOdxParam[8], fdetector->get_molarMass(),
fdetector->get_OldW13eV());
double Wq_eV = wvalue.Wq_eV;
double rho = dEOdxParam[8];
double xi = -999., yi = -999., zi = fdetector->get_TopDrift();
double xf, yf, zf, pos_x, pos_y, pos_z, r, phi, field,
eMin = dEOdxParam[4], z_step = dEOdxParam[5], inField = dEOdxParam[6];
if (ValidityTests::nearlyEqual(eMin, 0.) || std::isnan(eMin))
throw std::runtime_error("Energy cannot be zero or undefined");
NESTresult result{};
xf = dEOdxParam[0];
yf = dEOdxParam[1];
zf = dEOdxParam[2];
if (ValidityTests::nearlyEqual(dEOdxParam[3], -1.)) {
if (NRERWidthsParam[0] < 0. && eMin < 0.) {
xi = xf - 10.;
yi = yf;
zi = zf;
} else {
r = fdetector->get_radmax() * sqrt(RandomGen::rndm()->rand_uniform());
phi = 2. * M_PI * RandomGen::rndm()->rand_uniform();
xi = r * cos(phi);
yi = r * sin(phi);
}
} else {
string position = muonInitPos;
string delimiter = ",";
size_t loc = 0;
int ii = 0;
while ((loc = position.find(delimiter)) != string::npos) {
string token = position.substr(0, loc);
if (ii == 0)
xi = stof(token);
else
yi = stof(token);
position.erase(0, loc + delimiter.length());
++ii;
}
zi = stof(position);
}
if (zi <= 0.) zi = fdetector->get_TopDrift();
double dEOdx, eStep, refEnergy;
if (eMin < 0.) {
refEnergy = -eMin;
if (dEOdxParam[10] > 0. && dEOdxParam[11] != 0.) {
dEOdx = dEOdxParam[10] * pow(-eMin, dEOdxParam[11]);
if (dEOdxParam[12] > 0.)
dEOdx =
RandomGen::rndm()->rand_gauss(dEOdx, dEOdxParam[12] * dEOdx, true);
} else
dEOdx = CalcElectronLET(-eMin, ATOM_NUM, dEOdxParam[10]);
eStep = dEOdx * rho * z_step * 1e2;
} else {
refEnergy = dEOdxParam[9];
eStep = eMin * rho * z_step * 1e2;
}
double driftTime, vD, keV = 0., Nq_mean;
int Nph = 0, Ne = 0, Nq = 0;
double xx = xi, yy = yi, zz = zi;
if (zf < 0.) zf = 0.;
double distance = sqrt((xf - xi) * (xf - xi) + (yf - yi) * (yf - yi) +
(zf - zi) * (zf - zi));
double norm[3];
double xi_tib;
norm[0] = (xf - xi) / distance;
norm[1] = (yf - yi) / distance;
norm[2] = (zf - zi) / distance;
bool stopCond = false;
while (!stopCond &&
(xx * xx + yy * yy) <
fdetector->get_radmax() * fdetector->get_radmax() &&
std::abs(refEnergy) > PHE_MIN) {
if (((zf < zi && zz <= zf) || (zf > zi && zz >= zf)) &&
((xx - xf) * (xx - xf) + (yy - yf) * (yy - yf)) <
4. * z_step * z_step) {
stopCond = true;
break;
}
// stop making S1 and S2 if particle exits Xe volume, OR runs out of
// energy (in case of beta)
if (inField == -1.)
field = fdetector->FitEF(xx, yy, zz);
else
field = inField;
if (eMin < 0.) {
if ((keV + eStep) > -eMin) eStep = -eMin - keV;
if (NRERWidthsParam[0] < 0.) {
YieldResult yields{};
Nq_mean = -NRERWidthsParam[0] * eStep;
double Ni_mean = Nq_mean / (1. + NRERWidthsParam[1]);
xi_tib = Ni_mean * (NRERWidthsParam[3] / 4.) *
pow(eStep, NRERWidthsParam[4] - 1.);
yields.PhotonYield =
Ni_mean * (1. + NRERWidthsParam[1] -
log(NRERWidthsParam[2] + xi_tib) / xi_tib);
yields.ElectronYield = Nq_mean - yields.PhotonYield;
yields.ExcitonRatio = NRERWidthsParam[1];
yields.Lindhard = 1.;
yields.ElectricField = field;
yields.DeltaT_Scint = -999;
result.yields = yields;
} else
result.yields = GetYieldBetaGR(eStep, rho, field);
} else
result.yields = GetYieldBetaGR(refEnergy, rho, field);
if (eMin < 0. && NRERWidthsParam[0] < 0.) {
QuantaResult quanta{};
if (Nq_mean < 1.)
Nq = 0;
else
Nq = int(ceil(RandomGen::rndm()->rand_gauss(
Nq_mean, sqrt(NRERWidthsParam[5] * Nq_mean), true) -
0.5));
if (result.yields.PhotonYield < 1. || Nq <= 0)
quanta.photons = 0;
else
quanta.photons = int(ceil(
RandomGen::rndm()->rand_gauss(
result.yields.PhotonYield,
sqrt(NRERWidthsParam[6] * result.yields.PhotonYield), true) -
0.5));
quanta.electrons = Nq - quanta.photons;
quanta.ions = int(ceil(double(Nq) / (1. + NRERWidthsParam[1]) - 0.5));
quanta.excitons = Nq - quanta.ions;
quanta.recombProb = 1. - log(NRERWidthsParam[2] + xi_tib) / xi_tib;
quanta.Variance = NRERWidthsParam[6] * result.yields.PhotonYield;
result.quanta = quanta;
Ne += result.quanta.electrons;
} else
result.quanta =
GetQuanta(result.yields, rho, default_NRERWidthsParam, false, -999.);
if (eMin > 0.)
Nph += result.quanta.photons * (eStep / refEnergy);
else {
if (NRERWidthsParam[0] >= 0.) {
Nq = result.quanta.photons + result.quanta.electrons;
double FanoOverall =
1.; // use 6 for ~0.7% energy resolution at 2.6 MeV and 190 V/cm
double FanoScint =
200.; // standin for recombination fluctuations in this approach
Nq = int(floor(
RandomGen::rndm()->rand_gauss(Nq, sqrt(FanoOverall * Nq), false) +
0.5));
result.quanta.photons =
int(floor(RandomGen::rndm()->rand_gauss(
result.quanta.photons,
sqrt(FanoScint * result.quanta.photons), false) +
0.5));
result.quanta.electrons = Nq - result.quanta.photons;
}
Nph += result.quanta.photons;
}
int index = int(floor(zz / z_step + 0.5));
if (index >= vTable.size()) index = vTable.size() - 1;
if (vTable.size() == 0)
vD = dEOdxParam[7];
else
vD = vTable[index];
driftTime = (fdetector->get_TopDrift() - zz) / vD;
if (zz >= fdetector->get_cathode() && NRERWidthsParam[0] >= 0.) {
if (eMin > 0.)
Ne += result.quanta.electrons *
exp(-driftTime / fdetector->get_eLife_us()) * (eStep / refEnergy);
else
Ne += result.quanta.electrons *
exp(-driftTime / fdetector->get_eLife_us());
}
keV += eStep;
xx += norm[0] * z_step;
yy += norm[1] * z_step;
zz += norm[2] * z_step;
if (eMin < 0.) {
refEnergy -= eStep;
if (dEOdxParam[10] > 0. && dEOdxParam[11] != 0.) {
dEOdx = dEOdxParam[10] * pow(refEnergy, dEOdxParam[11]);
if (dEOdxParam[12] > 0.)
dEOdx = RandomGen::rndm()->rand_gauss(dEOdx, dEOdxParam[12] * dEOdx,
true);
} else
dEOdx = CalcElectronLET(refEnergy, ATOM_NUM, dEOdxParam[10]);
eStep = dEOdx * rho * z_step * 1e2;
}
// cerr << keV << "\t\t" << xx << "\t" << yy << "\t" << zz << "\t" << Nph <<
// "\t" << Ne << endl;
}
if (Nph < 0) Nph = 0;
if (Ne < 0) Ne = 0;
result.quanta.photons = Nph;
result.quanta.electrons = Ne;
pos_x =
0.5 * (xi + xx); // approximate things not already done right in loop as
// middle of detector since muon traverses whole length
pos_y = 0.5 * (yi + yy);
pos_z = 0.5 * (zi + zz);
if (inField == -1.)
field = fdetector->FitEF(pos_x, pos_y, pos_z);
else
field = inField;
result.yields.DeltaT_Scint = pos_z;
result.yields.ElectricField = field;
return result;
}
YieldResult NESTcalc::GetYieldNROld(
double energy,
int option) { // possible anti-correlation in NR ignored totally
double Ne, Nph, FakeField;
if (option == 0) {
// with old-school L_eff*S_nr conversion, and more explicit Thomas-Imel box
// model formulae but approximation where Qy can sail off as energy to 0
FakeField = 1.00;
Nph = 0.95 * 64. * energy *
(0.050295 * pow(energy, 1.3483) *
(log(1. + (0.84074 * pow(energy, 1.3875))) /
(0.84074 *
pow(energy,
1.3875)))); // NESTv0.97beta (2011) ~0 V/cm arXiv:1106.1613
Ne = energy * (10.661 * pow(energy, 0.16199) *
(log(1. + (0.745330 * pow(energy, 1.0880))) /
(0.745330 * pow(energy, 1.0880))) +
0.93739); // essentially Lindhard with k of 0.166
} else if (option == 1) {
FakeField = 200.;
Ne = energy *
(4.1395 * pow(energy, 0.13816) *
(log(1. + (0.040945 * pow(energy, 1.1388))) /
(0.040945 *
pow(energy,
1.1388)))); // conservative: k < or ~ to 0.110 (Hitachi-like)
Nph = energy * 3.35 *
pow(energy,
0.29222); // NESTv0.98 (2013) model for legacy comparisons
// (arXiv:1307.6601) using simple power law (optional
// constant; optional for Nph)
} else if (option == 2) {
FakeField = 730.;
Nph = 7582.3 +
(-1.3728 - 7582.3) /
(1. + pow(energy / 385.46,
1.2669)); // NEST v1.0 (2015) arXiv:1412.4417, with
// ability to cut off yield at either low or
// high energy. Fit to Nph
Ne = (60.914 * pow(energy, 0.32220)) *
(1. -
exp(-0.12684 * pow(energy,
0.65729))); // middle of road: k = 0.14. By Brian
// Lenardo, still pre-LUX-DD. With
// explicit bi-Exc quenching
} else {
// simplest by far, but not 1st principles: based on work of M. Wyman
// UAlbany
FakeField = 180.; // fit to LUX Run03 D-D alone
Ne = (-3.8780 + 12.372 * pow(energy, 0.73502)) *
exp(-0.0034329 *
energy); // slide 68 of Matthew's private Google Slides mega-deck
Nph = 0.81704 + 3.8584 * pow(energy, 1.30180); // ditto
}
YieldResult result{};
if (Nph < 0.) Nph = 0.;
if (Ne < 0.) Ne = 0.;
result.PhotonYield = Nph;
result.ElectronYield = Ne;
result.ExcitonRatio = 1.;
result.Lindhard = ((Nph + Ne) / energy) * W_DEFAULT * 1e-3;
result.ElectricField = FakeField;
result.DeltaT_Scint = -999.;
return YieldResultValidity(result, energy, W_DEFAULT);
}
YieldResult NESTcalc::GetYieldNR(double energy, double density, double dfield,
double massNum,
const std::vector<double> &NRYieldsParam) {
if (ValidityTests::nearlyEqual(ATOM_NUM, 18.))
massNum = fdetector->get_molarMass();
if (NRYieldsParam.size() < 12) {
throw std::runtime_error(
"ERROR: You need a minimum of 12 nuisance parameters for the mean "
"yields.");
}
if (energy > HIGH_E_NR)
cerr << "\nWARNING: No data out here, you are beyond the AmBe endpoint of "
"about 300 keV.\n";
int massNumber;
double ScaleFactor[2] = {1., 1.};
if (ValidityTests::nearlyEqual(massNum, 0.))
massNumber = RandomGen::rndm()->SelectRanXeAtom();
else {
massNumber = int(massNum);
}
ScaleFactor[0] = sqrt(fdetector->get_molarMass() / (double)massNumber);
ScaleFactor[1] = ScaleFactor[0];
double Nq = NRYieldsParam[0] * pow(energy, NRYieldsParam[1]);
if (!fdetector->get_OldW13eV()) Nq *= ZurichEXOW;
double ThomasImel = NRYieldsParam[2] * pow(dfield, NRYieldsParam[3]) *
pow(density / DENSITY, 0.3);
double Qy =
1. / (ThomasImel * pow(energy + NRYieldsParam[4], NRYieldsParam[9]));
Qy *= 1. - 1. / pow(1. + pow((energy / NRYieldsParam[5]), NRYieldsParam[6]),
NRYieldsParam[10]);
if (!fdetector->get_OldW13eV()) Qy *= ZurichEXOQ;
double Ly = Nq / energy - Qy;
if (Qy < 0.0) Qy = 0.0;
if (Ly < 0.0) Ly = 0.0;
double Ne = Qy * energy * ScaleFactor[1];
double Nph =
Ly * energy * ScaleFactor[0] *
(1. - 1. / pow(1. + pow((energy / NRYieldsParam[7]), NRYieldsParam[8]),
NRYieldsParam[11]));
Nq = Nph + Ne;
double Ni = (4. / ThomasImel) * (exp(Ne * ThomasImel / 4.) - 1.);
double Nex = (-1. / ThomasImel) *
(4. * exp(Ne * ThomasImel / 4.) - (Ne + Nph) * ThomasImel - 4.);
double NexONi = Nex / Ni;
Wvalue wvalue = WorkFunction(density, fdetector->get_molarMass(),
fdetector->get_OldW13eV());
if (NexONi < wvalue.alpha && energy > 1e2) {
NexONi = wvalue.alpha;
Ni = Nq / (1. + NexONi);
Nex = Nq - Ni;
}
if (NexONi > 1.0 && energy < 1.) {
NexONi = 1.00;
Ni = Nq / (1. + NexONi);
Nex = Nq - Ni;
}
if (Nex < 0. && density >= 1.)
cerr << "\nCAUTION: You are approaching the border of NEST's validity for "
"high-energy (OR, for LOW) NR, or are beyond it, at "
<< energy << " keV." << endl;
if (std::abs(Nex + Ni - Nq) > 2. * PHE_MIN) {
throw std::runtime_error(
"ERROR: Quanta not conserved. Tell Matthew Immediately!");
}
double Wq_eV = wvalue.Wq_eV;
double L = (Nq / energy) * Wq_eV * 1e-3;
YieldResult result{};
result.PhotonYield = Nph;
result.ElectronYield = Ne;
result.ExcitonRatio = NexONi;
result.Lindhard = L;
result.ElectricField = dfield;
result.DeltaT_Scint = -999;
return YieldResultValidity(
result, energy, Wq_eV); // everything needed to calculate fluctuations
}
YieldResult NESTcalc::GetYieldIon(
double energy, double density, double dfield, double massNum,
double atomNum,
const std::vector<double>
&NRYieldsParam) { // simply uses the original Lindhard model, but as
// cited by Hitachi in:
// https://indico.cern.ch/event/573069/sessions/230063/attachments/1439101/2214448/Hitachi_XeSAT2017_DM.pdf
double A1 = massNum, A2 = RandomGen::rndm()->SelectRanXeAtom();
double Z1 = atomNum, Z2 = ATOM_NUM;
double Z_mean = pow(pow(Z1, (2. / 3.)) + pow(Z2, (2. / 3.)), 1.5);
double E1c = pow(A1, 3.) * pow(A1 + A2, -2.) * pow(Z_mean, (4. / 3.)) *
pow(Z1, (-1. / 3.)) * 500.;
double E2c = pow(A1 + A2, 2.) * pow(A1, -1.) * Z2 * 125.;
double gamma = 4. * A1 * A2 / pow(A1 + A2, 2.);
double Ec_eV = gamma * E2c;
double Constant = (2. / 3.) * (1. / sqrt(E1c) + 0.5 * sqrt(gamma / Ec_eV));
double L = Constant * sqrt(energy * 1e3);
double L_max = 0.96446 / (1. + pow(massNum * massNum / 19227., 0.99199));
if (ValidityTests::nearlyEqual(atomNum, 2.) &&
ValidityTests::nearlyEqual(massNum, 4.))
L = 0.56136 * pow(energy, 0.056972);
if (L > L_max) L = L_max;
double densDep = pow(density / 0.2679, -2.3245);
double massDep =
0.02966094 * exp(0.17687876 * (massNum / 4. - 1.)) + 1. - 0.02966094;
double fieldDep = pow(1. + pow(dfield / 95., 8.7), 0.0592);
if (fdetector->get_inGas()) fieldDep = sqrt(dfield);
double ThomasImel = 0.00625 * massDep / (1. + densDep) / fieldDep;
double alpha = 0.64 / pow(1. + pow(density / 10., 2.), 449.61);
double NexONi = alpha + 0.00178 * pow(atomNum, 1.587);
if (ValidityTests::nearlyEqual(A1, 206.) &&
ValidityTests::nearlyEqual(Z1,
82.)) { // Pb-206 (from Po-210 alpha decay).
ThomasImel =
exp(-1.28683 - 1.42053e-03 * dfield); // updated by Nishat Parveen
NexONi = 1.1; // updated by Nishat Parveen
}
const double logden = log10(density);
double Wq_eV = 28.259 + 25.667 * logden - 33.611 * pow(logden, 2.) -
123.73 * pow(logden, 3.) - 136.47 * pow(logden, 4.) -
74.194 * pow(logden, 5.) - 20.276 * pow(logden, 6.) -
2.2352 * pow(logden, 7.);
double Nq = 1e3 * L * energy / Wq_eV;
if (!fdetector->get_OldW13eV()) Nq *= ZurichEXOW;
double Ni = Nq / (1. + NexONi);
double recombProb;
if (Ni > 0. && ThomasImel > 0.)
recombProb =
1. - log(1. + (ThomasImel / 4.) * Ni) / ((ThomasImel / 4.) * Ni);
else {
recombProb = 0.0;
}
double Nph = Nq * NexONi / (1. + NexONi) + recombProb * Ni;
double Ne = Nq - Nph;
if (ValidityTests::nearlyEqual(A1, 206.) &&
ValidityTests::nearlyEqual(Z1, 82.))
Ne = RandomGen::rndm()->binom_draw(Ne, ChargeLoss);
// some electrons from lead recoils get absorbed by the Teflon wall
if (ValidityTests::nearlyEqual(Z2, 18.) &&
ValidityTests::nearlyEqual(Z1, 2.) &&
ValidityTests::nearlyEqual(A1, 4.)) { // alphas in argon
double factorE = pow((4.71598 + pow(dfield, 7.72848)), 0.109802);
double Qy = (1. / 6200.) *
(64478398.7663 -
(64478398.7663 * 0.173553719 +
(64478398.7663 / 1.21) *
(1. - (0.02852 * log(1. + (64478398.7663 / 1.21) *
((0.01 / factorE) / 3.))) /
((64478398.7663 / 1.21) * (0.01 / factorE)))));
double qu = 1. / (1.16 * pow(dfield, -0.012));
factorE = pow(4.98483 + pow(dfield / 10.0822, 1.2076), 0.97977);
double Ly =
qu * (1. / 6500.) *
(278037.250283 * 0.173553719 +
(278037.250283 / 1.21) *
(1. - (2. * log(1. + (278037.250283 / 1.21) *
((0.653503 / factorE) / 3.))) /
((278037.250283 / 1.21) * (0.653503 / factorE))));
Ne = Qy * energy;
Nph = Ly * energy;
L = 0.0;
NexONi = 0.21;
Wq_eV = 19.5;
}
YieldResult result{};
result.PhotonYield = Nph;
result.ElectronYield = Ne;
result.ExcitonRatio = NexONi;
result.Lindhard = L;
result.ElectricField = dfield;
result.DeltaT_Scint = -999;
return YieldResultValidity(
result, energy, Wq_eV); // everything needed to calculate fluctuations
}
YieldResult NESTcalc::GetYieldKr83m(double energy, double density,
double dfield, double maxTimeSeparation,
double minTimeSeparation) {
if (minTimeSeparation > maxTimeSeparation &&
(energy < 32.0 || energy >= 32.2))
throw std::runtime_error("ERROR: min greater than max");
double Nq = -999;
double Nph = -999;
double Ne = -999;
Wvalue wvalue = WorkFunction(density, fdetector->get_molarMass(),
fdetector->get_OldW13eV());
double Wq_eV = wvalue.Wq_eV;
double alpha = wvalue.alpha;
constexpr double deltaT_ns_halflife = 154.4;
double deltaT_ns = -999.;
if (ValidityTests::nearlyEqual(minTimeSeparation, maxTimeSeparation))
deltaT_ns = maxTimeSeparation;
if (minTimeSeparation < 100. && energy < 32. &&
kr83m_reported_low_deltaT == false) {
kr83m_reported_low_deltaT = true;
cerr << "\tWARNING! Outside of Kr83m model fit validity region. Details:"
<< " minTimeSeparation is < 100 ns and your input E is 9.4 keV."
<< " Data for separated Kr83m decays do not yet exist for deltaT_ns "
"<100 ns."
<< " 9.4 & 32.1 keV yields are still summed to physically accurate "
"result, but individually will be nonsensical."
<< endl;
}
if (energy > 9.35 && energy < 9.45) {
if (!ValidityTests::nearlyEqual(minTimeSeparation, maxTimeSeparation))
deltaT_ns = RandomGen::rndm()->rand_exponential(
deltaT_ns_halflife, minTimeSeparation, maxTimeSeparation);
Nq = energy * 1e3 / Wq_eV;
double medTlevel =
57.462 + (69.201 - 57.462) / pow(1. + pow(dfield / 250.13, 0.9), 1.);
double lowTdrop = 35. + (75. - 35.) / pow(1. + pow(dfield / 60, 1), 1);
double lowTpeak =
6.2831e4 - (6.2831e4 - 5.949e4) / pow(1. + pow(dfield / 60, 1.), 1);
Nph = energy * (lowTpeak * pow(2. * deltaT_ns + 10., -1.5) + medTlevel) /
(1. + pow(deltaT_ns / lowTdrop, -1. * lowTdrop / 5.));
Ne = Nq - Nph;
if (Ne < 0) Ne = 0.;
alpha = 0.;
} else {
if (energy >= 32.0 && energy < 32.2) {
Nq = energy * 1e3 / Wq_eV;
Nph = energy * (6. + (66.742 - 6.) /
pow(1. + pow(dfield / 115.037, 0.6409), 0.3215));
Ne = Nq - Nph;
if (Ne < 0.) Ne = 0.;
} else { // merged 41.5 keV decay
if (!ValidityTests::nearlyEqual(minTimeSeparation, maxTimeSeparation))
deltaT_ns = RandomGen::rndm()->rand_exponential(
deltaT_ns_halflife, minTimeSeparation, maxTimeSeparation);
double medTlevel =
57.462 + (69.201 - 57.462) / pow(1. + pow(dfield / 250.13, 0.9), 1.);
double lowTdrop = 35. + (75. - 35.) / pow(1. + pow(dfield / 60, 1), 1);
double lowTpeak =
6.2831e4 - (6.2831e4 - 5.949e4) / pow(1. + pow(dfield / 60, 1.), 1);
// 9.4 keV model
Nph = 9.4 * (lowTpeak * pow(2. * deltaT_ns + 10., -1.5) + medTlevel) /
(1. + pow(deltaT_ns / lowTdrop, -1. * lowTdrop / 5.));
Ne = (9.4 * 1e3 / Wq_eV) - Nph;
if (Ne < 0.) Ne = 0.; // can't have negative charge from either decay
// Add in 32.1 keV yields