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FormFactor.c
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FormFactor.c
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#include "TF1.h"
#include "TF2.h"
#include "Math/WrappedTF1.h"
#include "Math/WrappedMultiTF1.h"
#include "Math/GaussLegendreIntegrator.h"
#include "Math/AdaptiveIntegratorMultiDim.h"
#include "TMath.h"
//#include "/media/storage/home/davidp/git/units/units/units.hpp"
using namespace std;
/*using namespace units;
using namespace units::domains;
using namespace units::precise;
using namespace units::constants;
using namespace units::precise::energy;
*/
#include <cstdio>
#include <cstdlib>
#include <string>
Double_t fHelm_f(Double_t T,Int_t A); //Helm nuclear form factor
Double_t fR0(Int_t A); // Nuclear radius parametrization
Double_t fHelm_fq(Double_t q,Int_t A); // In q units (fm^-1)(?)
Double_t fHelm_fp(Double_t E,Int_t A);
Double_t fBessel1(Double_t x);
void FormFactor() {
//Atomic and mass numbers for the element under study
//Xenon Z=54,N=77;
//Argon Z=20,N=20;
//Neon Z=10,N=10;
//Hidrogen Z=1,N=1
//Carbon Z=6,N=6
//Germanium Z=32,N=32
Int_t Z=54,N=77;
Int_t A=N+Z;
cout << "R0: " << fR0(A) << endl;
double xmin = 10;
double xmax = 10000;
int n = 100000;
double step = (xmax-xmin)/(double)n;
double x[n], y[n], yp[n];
for (int i=0;i<n;i++) {
x[i] = xmin +i*step;
y[i] = fHelm_f(x[i], A);
yp[i] = fHelm_fp(x[i], A);
}
Double_t h = 197.3; //MeV fm (hc)
Double_t nucleon_mass = 0.938; //GeV/c2
Double_t Mn = nucleon_mass * (double)A;
Double_t s = 0.9/h; //Femtometers-Skin thickness of the nucleus
Double_t R = 1.23*pow((double)A,1/3)-0.6;
Double_t R0 = sqrt(pow(R,2)+7.*pow(TMath::Pi(),2)*0.52*0.52/3.-5*h*h*s*s) /h;
/*
// Using units package:
precise_measurement hc = 197.3 *units::precise::mega*eV * units::precise::femto*units::precise::m; //MeV fm (hc)
precise_measurement nucleon_mass = 0.938 *units::precise::giga*eV / (constants::c*constants::c); //GeV/c2
precise_measurement Mn = nucleon_mass * (double)A;
Double_t s = 0.9; //Femtometers-Skin thickness of the nucleus
Double_t R = 1.23*std::cbrt(A)-0.6;
Double_t R0 = sqrt(pow(R,2)+7.*pow(TMath::Pi(),2)*0.52*0.52/3.-5*s*s); // /hc
//R0=sqrt(pow(1.23*std::cbrt(A)-0.60,2)+(7./3.)*pow(TMath::Pi(),2)*0.52*0.52-5*s*s);
*/
cout << s << endl;
cout << std::cbrt(A) << endl;
cout << R << endl;
cout << R0 << endl;
//cout << R0.value();
//cout << to_string(R0.units()) << endl;
//cout << (sqrt(2*Mn*200)).value() << (sqrt(2*Mn*200)).units() << endl;
cout << fHelm_fp(200,A) << endl;
//// FF in energy units. Two different definitions. ////
TCanvas *c=new TCanvas();
c->SetLogx();
c->SetLogy();
auto g = new TGraph(n,x,y);
g->SetLineColor(kMagenta+3);
g->SetLineWidth(4);
g->SetMinimum(pow(10,-10));
g->SetMaximum(10.);
g->Draw("");
auto gp = new TGraph(n,x,yp);
gp->SetLineColor(kGreen+3);
gp->SetLineWidth(4);
//gp->SetMinimum(pow(10,-12));
//gp->SetMaximum(10.);
gp->Draw("same");
double qmin = 0;
double qmax = 5;
int nq = 100;
double qstepsize = (qmax-qmin)/(double)nq;
double xq[nq], yq[nq];
for (int i=0;i<nq;i++) {
xq[i] = qmin +i*qstepsize;
yq[i] = fHelm_fq(xq[i], A);
}
//// FF in q units ////
TCanvas *cq=new TCanvas();
//cq->SetLogx();
cq->SetLogy();
auto gq = new TGraph(nq,xq,yq);
gq->SetLineColor(kBlue+2);
gq->SetLineWidth(4);
gq->SetMinimum(pow(10,-12));
gq->SetMaximum(10.);
gq->Draw("");
cout << "F^2(3000keV): " << fHelm_f(3000, A) << endl;
cout << "sin(30): " << sin(30*TMath::Pi()/180) << endl;
}
///////////// Functions //////////////////
// Nuclear radius parametrization
Double_t fR0(Int_t A){
Double_t s=0.9; //Femtometers-Skin thickness of the nucleus
Double_t R0=sqrt(pow(1.23*std::cbrt(A)-0.60,2)+(7./3.)*pow(TMath::Pi(),2)*0.52*0.52-5*s*s);
return R0;
}
// First Bessel fuction. X in degrees, converted to radians inside this function.
Double_t fBessel1(Double_t x){
Double_t rad = x*TMath::Pi()/180;
//return sin(rad)/(rad*rad)-cos(rad)/rad;
return sin(x)/(x*x)-cos(x)/x;
}
//Helm form factor
Double_t fHelm_f(Double_t E,Int_t A){
// E = recoil energy in keV
//Modulus of the Helm Factor
//Defined as in J.D.LewinP.F.Smith/AstroparticlePhysics6(1996)87-112
//Femtometers-Effective radius of the target nucleus
Double_t s=0.9; //Femtometers-Skin thickness of the nucleus
//Double_t R0=sqrt(pow(1.23*pow(A,1/3)-0.60,2)+(7./3.)*pow(TMath::Pi(),2)*0.52*0.52-5*s*s);
Double_t q=6.927*pow(10,-3)*sqrt(A*E); //*pow(10,-3) Este factor numerico tiene que venir de dividir entre h barra las distancias en fm y de sqrt(2Mn) -> sqrt(2Mn)sqrt(A*Er)/h (hbar = 197)
//hc = 197 Mev fm = 197*1000 keV fm
// sqrt(2*0.931)/0.197 = 6.927 Juraría que para que todo esté en keV sobra ese 10^-3. Si lo quito queda demasiado pequeña la señal. -> No hay que quitarlo, tiene que ver con poner hbar en Mev en lugar de keV qeu es para lo qeu se introduce ese 10^-3, para pasar de keV a Mev en hbar dividiendo: sqrt(A*T)*sqrt(2*Mn)/hbar(en keV)
Double_t qR_0=q*fR0(A);
//return pow(3*(sin(qR_0)-qR_0*cos(qR_0))/pow(qR_0,3), 2)*exp(-q*q*s*s); // /2. TMath::Pi()/180 para pasar a radianes
return pow(3*fBessel1(qR_0)/qR_0, 2)*exp(-q*q*s*s); // /2. TMath::Pi()/180 para pasar a radianes
}
//Helm form factor squared translating python version. // Jelle Aalbers
Double_t fHelm_fp(Double_t E,Int_t A){
// E = recoil energy in keV
//precise_measurement E_keV = E *units::precise::kilo*eV;
//precise_measurement hc = 197327 *units::precise::kilo*eV * units::precise::femto*units::precise::m; //keV fm (hc)
Double_t hc = 197327; //keV fm (hc)
//Double_t nucleon_mass = 0.938; // GeV/c2
Double_t nucleon_mass_keV = 0.938*pow(10,6); // keV/c2
//precise_measurement nucleon_mass = 0.938 *units::precise::giga*eV / (constants::c*constants::c);
Double_t Mn = nucleon_mass_keV * (double)A; //keV/c2
//precise_measurement Mn = nucleon_mass * A; //keV/c2
Double_t s = 0.9; //Femtometers-Skin thickness of the nucleus
//Double_t R = 1.23*std::cbrt(A)-0.6; // Problems with cubic root, use this std::cbrt() function instead
//Double_t R0 = sqrt(pow(R,2)+7.*pow(TMath::Pi(),2)*0.52*0.52/3.-5*h*h*s*s);
Double_t q = sqrt(2*Mn*E);
//return exp(-q*q*s*s/(hc*hc))*pow(3*(sin(q*R0/ (hc*hc))-q*R0*cos(q*R0))/pow(q*R0,3), 2);
return exp(-q*q*s*s/(hc*hc))*9*fBessel1(q*fR0(A)/hc)*fBessel1(q*fR0(A)/hc)/pow(q*fR0(A)/hc, 2);
//return exp(-(q*q*s*s/(hc*hc)).value())*9*fBessel1((q*fR0(A)/hc).value())*fBessel1((q*fR0(A)/hc).value())/pow((q*fR0(A)/hc).value(), 2);
}
/*
/// Version python
def F2(E,A): #Squared form factor. Radius formula Ciaran's thesis
# Esta expresión del factor de forma está sacada de J.Gracia Garza, pero los parámetros R1, R, s provienen del trabajo de C. O`Hare.
h=197.3 #MeV fm (hc)
Mn = nucleon_mass * A
s = 0.9/h #*10**(-15)
R = ((1.23 * A**(1/3))-0.6) #*10**(-15)
R1 = math.sqrt(R**2 +(7*pi**2*0.52**2)/3- 5*h*h*s**2)/h ### Esta es la representación que coincide con la gráfica de Ciaran
q=math.sqrt(2*Mn*E)
return exp(-(q*s)**2)*(3*(sin(q*R1)-q*R1*cos(q*R1))/(q*R1)**3)**2 #(exp(-(q**2)*(s**2)))*(3*(sin(q*R1)/((q**2)*(R1**2))-(cos(q*R1)/(q*R1)))/(q*R1))**2
*/
//Helm form factor in q units
Double_t fHelm_fq(Double_t q,Int_t A){
// T = recoil energy in keV
//Modulus of the Helm Factor
//Defined as in J.D.LewinP.F.Smith/AstroparticlePhysics6(1996)87-112
//Femtometers-Effective radius of the target nucleus
Double_t s=0.9; //Femtometers-Skin thickness of the nucleus
//Double_t R0=sqrt(pow(1.23*pow(A,1/3)-0.60,2)+(7./3.)*pow(TMath::Pi(),2)*0.52*0.52-5*s*s);
//Double_t q=6.927*pow(10,-3)*sqrt(A*T); //*pow(10,-3) Este factor numerico tiene que venir de dividir entre h barra las distancias en fm y de sqrt(2Mn) -> sqrt(2Mn)sqrt(A*Er)/h (hbar = 197)
//hc = 197 Mev fm = 197*1000 keV fm
// sqrt(2*0.931)/0.197 = 6.927 Juraría que para que todo esté en keV sobra ese 10^-3. Si lo quito queda demasiado pequeña la señal
Double_t qR_0=q*fR0(A);
return pow(3*(sin(qR_0)-qR_0*cos(qR_0))/pow(qR_0,3), 2)*exp(-q*q*s*s); // /2.
}