genie::alvarezruso::AREikonalSolution Class Reference

Eikonal wavefunction solution for Alvarez-Ruso Coherent Pion Production xsec. More...

#include <AREikonalSolution.h>

Inheritance diagram for genie::alvarezruso::AREikonalSolution:

Collaboration diagram for genie::alvarezruso::AREikonalSolution:

Public Member Functions
	AREikonalSolution (bool debug, AlvarezRusoCOHPiPDXSec *parent)
	AREikonalSolution (bool debug, ARSampledNucleus *nucl)
virtual	~AREikonalSolution ()
virtual std::complex< double >	Element (const double radius, const double cosine_rz, const double e_pion)
void	Solve ()
Public Member Functions inherited from genie::alvarezruso::ARWFSolution
	ARWFSolution (bool debug=false)
virtual	~ARWFSolution ()

Private Member Functions
AlvarezRusoCOHPiPDXSec *	Parent ()
ARSampledNucleus *	Nucleus ()
ARConstants *	Con ()
std::complex< double >	PionSelfEnergy (const double rhop_cent, const double rhon_cent, const double omepi, const double ppim)
void	Deltamed (const double sdel, const double pf, const double rat, double &gamdpb, double &imsig, const double ppim, const double omepi)
double	Cc (const double a, const double b, const double c, const double ome)
double	Gamd (const double s)
double	Qcm (const double s)

Private Attributes
AlvarezRusoCOHPiPDXSec *	parent_
ARSampledNucleus *	fNucleus
ARConstants *	constants_
bool	owns_constants

Additional Inherited Members
Public Attributes inherited from genie::alvarezruso::ARWFSolution
bool	debug_

Detailed Description

Eikonal wavefunction solution for Alvarez-Ruso Coherent Pion Production xsec.

References:

Author

Steve Dennis University of Warwick, Rutherford Appleton Laboratory

Created:

05/12/2013

License:

Copyright (c) 2003-2024, The GENIE Collaboration For the full text of the license visit http://copyright.genie-mc.org

Definition at line 34 of file AREikonalSolution.h.

Constructor & Destructor Documentation

genie::alvarezruso::AREikonalSolution::AREikonalSolution	(	bool	debug,
		AlvarezRusoCOHPiPDXSec *	parent
	)

Definition at line 255 of file AREikonalSolution.cxx.

References constants_, genie::alvarezruso::ARWFSolution::debug_, fNucleus, genie::alvarezruso::AlvarezRusoCOHPiPDXSec::GetConstants(), genie::alvarezruso::AlvarezRusoCOHPiPDXSec::GetNucleus(), owns_constants, and Parent().

                                                                              : ARWFSolution(debug), parent_(parent)
{
  if( debug_ ) std::cerr << "AREikonalSolution::AREikonalSolution" << std::endl;
  this->fNucleus   = &(this->Parent()->GetNucleus());
  this->constants_ = &(this->Parent()->GetConstants());
  owns_constants = false;
}

genie::alvarezruso::AREikonalSolution::AREikonalSolution	(	bool	debug,
		ARSampledNucleus *	nucl
	)

Definition at line 263 of file AREikonalSolution.cxx.

References constants_, genie::alvarezruso::ARWFSolution::debug_, and owns_constants.

                                                                      : ARWFSolution(debug), fNucleus(nucl)
{
  if( debug_ ) std::cerr << "AREikonalSolution::AREikonalSolution" << std::endl;
  this->constants_ = new ARConstants();
  owns_constants = true;
}

genie::alvarezruso::AREikonalSolution::~AREikonalSolution ( )

virtual

Definition at line 270 of file AREikonalSolution.cxx.

References constants_, and owns_constants.

                                     {
  if (owns_constants) delete constants_;
}

Member Function Documentation

double genie::alvarezruso::AREikonalSolution::Cc ( const double  a, const double  b, const double  c, const double  ome  )

private

Definition at line 219 of file AREikonalSolution.cxx.

References genie::alvarezruso::AlvarezRusoCOHPiPDXSec::GetPiMass(), and Parent().

Referenced by Deltamed().

{
  double mpi = this->Parent()->GetPiMass();
  const double x = ome / mpi - 1.0;
  return (a*x*x + b*x + c);
}

ARConstants* genie::alvarezruso::AREikonalSolution::Con ( )

inlineprivate

Definition at line 50 of file AREikonalSolution.h.

References constants_.

Referenced by Deltamed(), Element(), Gamd(), PionSelfEnergy(), and Qcm().

{ return this->constants_; }

void genie::alvarezruso::AREikonalSolution::Deltamed ( const double  sdel, const double  pf, const double  rat, double &  gamdpb, double &  imsig, const double  ppim, const double  omepi  )

private

Definition at line 137 of file AREikonalSolution.cxx.

References Cc(), Con(), Gamd(), genie::alvarezruso::AlvarezRusoCOHPiPDXSec::GetPiMass(), genie::alvarezruso::ARConstants::HBar(), genie::alvarezruso::ARConstants::NucleonMass(), Parent(), and Qcm().

Referenced by PionSelfEnergy().

{
  unsigned int iapr = 1; // approximation chosen to calculate gamdpb

  // Calculation of the pauli-blocked width
  double gamdfree = this->Gamd(sdel);

  if( gamdfree == 0.0)
  {
    gamdpb = 0.0;
  }
  else
  {
    double f;
    if( iapr == 1 )
    {
      // Approximation from Nieves et al. NPA 554(93)554
      const double r = this->Qcm(sdel) / pf;
      if( r > 1.0 )
      {
                                // f=1.+(-2./5./r**2+9./35./r**4-2./21./r**6)
        f = 1.0 + ( -2.0 / 5.0 / (r*r) + 9.0 / 35.0 / (r*r*r*r) - 2.0 / 21.0 / (r*r*r*r*r*r) );
      }
      else
      {
        //f=34./35.*r-22./105*r**3
        f = 34.0 / 35.0 * r - 22.0 / 105 * (r*r*r);
      }
    }
    else
    {
      //Approximation from Garcia-Recio, NPA 526(91)685

      const double mn = this->Con()->NucleonMass();
      const double wd = TMath::Sqrt(sdel); // Delta inv. mass
      const double ef = TMath::Sqrt(mn*mn + pf*pf); // Fermi energy
      const double kd = ppim; // modulus of the Delta 3-momentum in Lab.
      const double pn = this->Qcm(sdel); // nucleon(and pion) momentum in C.M.
      const double en = TMath::Sqrt(mn*mn + pn*pn);

      f = ( kd * pn + TMath::Sqrt(sdel+kd*kd) * en - ef * wd ) / (2.0 * kd * pn);
      if (f < 0.0) f = 0.0;
      if (f > 1.0) f = 1.0;
    }
    gamdpb = gamdfree * f;
  }

  //Calculation of the delta selfenergy

  // Imaginary part: using Oset, Salcedo, NPA 468(87)631
  // Using eq. (3.5) to relate the energy of the delta with the pion energy used
  // in the parametrization

  // Prescriptions for the effective pion energy
  // nucleon at rest
  // ! ome=p(0)-mn
  // ! ome=(sdel-mn**2-mpi**2)/2./mn
  // nucleon with an average momentum
  // ! ekp=3./5.*pf**2/2./mn
  // ! ome=p(0)-mn-ekp
  // ! ome=(sdel-mn**2-mpi**2-ekp**2)/2./(mn+ekp)
  double ome = omepi;
  double mpi = this->Parent()->GetPiMass();

  // The parameterization is valid for 85 MeV < tpi < 315. outside  we take a contant values
  const double hb = this->Con()->HBar() * 1000.0;
  if( ome <= (mpi + 85.0 / hb) ) ome = mpi + 85.0 / hb;
  if( ome >= (mpi + 315.0 / hb) ) ome = mpi + 315.0 / hb;

  // The parameterization of Oset, Salcedo, with ca3 extrapolated to zero at low kin. energies
  const double cq   = this->Cc(-5.19,15.35,2.06,ome)/hb;
  const double ca2  = this->Cc(1.06,-6.64,22.66,ome)/hb;
  double ca3  = this->Cc(-13.46,46.17,-20.34,ome)/hb;
  const double alpha= this->Cc(0.382,-1.322,1.466,ome);
  const double beta = this->Cc(-0.038,0.204,0.613,ome);
  const double gamma=2.*beta;
  if( ome <= (mpi + 85.0/hb) ) ca3 = this->Cc(-13.46,46.17,-20.34,(mpi+85./hb))/85.*(ome-mpi);

  imsig = - ( cq*TMath::Power(rat,alpha) + ca2*TMath::Power(rat, beta) + ca3*TMath::Power(rat,gamma) );
}

cdouble genie::alvarezruso::AREikonalSolution::Element ( const double  radius, const double  cosine_rz, const double  e_pion  )

virtual

Implements genie::alvarezruso::ARWFSolution.

Definition at line 25 of file AREikonalSolution.cxx.

References genie::alvarezruso::ARSampledNucleus::A(), genie::units::A, genie::alvarezruso::ARSampledNucleus::CalcNumberDensity(), Con(), fNucleus, genie::alvarezruso::AlvarezRusoCOHPiPDXSec::GetPiMass(), genie::alvarezruso::ARConstants::HBar(), Nucleus(), Parent(), PionSelfEnergy(), genie::alvarezruso::ARConstants::PiPMass(), genie::alvarezruso::ARSampledNucleus::RadiusMax(), genie::alvarezruso::integrationtools::RGN1D(), genie::alvarezruso::integrationtools::SGNR(), and genie::alvarezruso::ARSampledNucleus::Z().

{

  const double mpik = this->Parent()->GetPiMass();
  const double mpi = this->Con()->PiPMass();
  const double hb = this->Con()->HBar() * 1000.0;

  const double r = (radius);

  const double ekin = (e_pion - mpik) * hb;

  const double cosa = cosine_rz;

  const double rmax = this->Nucleus()->RadiusMax();

  const unsigned int nz = 1;

  const double za = r * cosa;
  const double be = r * TMath::Sqrt(1.0 - cosa*cosa);
  const double omepi = ekin / hb + mpi;
  const double ppim = TMath::Sqrt(omepi*omepi - mpi*mpi);
  unsigned int sampling = (this->Nucleus())->GetSampling();

  double absiz[sampling];
  double decoy[sampling];

  unsigned int junk;

  integrationtools::SGNR(za, rmax, nz, sampling, absiz, junk, decoy);

  //do i=1,nzs
//  cdouble ordez[sampling];
  cdouble * ordez = new cdouble[sampling]; // CA
  double zp, rp;
  cdouble piself;

  unsigned int A = fNucleus->A();
  unsigned int Z = fNucleus->Z();

  for(unsigned int i = 0; i != sampling; ++i)
  {
    // Sample point in nucleus
    zp = absiz[i];

    // Radius in nucleus
    rp = TMath::Sqrt( be*be + zp*zp );

    // Get nuclear densities
    double dens_cent = fNucleus->CalcNumberDensity(rp);
    double dens_p_cent = dens_cent * Z / A ;
    double dens_n_cent = dens_cent * (A-Z)/A;

    // Calculate pion self energy
    piself = this->PionSelfEnergy(dens_p_cent, dens_n_cent, omepi, ppim);

    // Optical potential at each point in the nucleus
    ordez[i] = piself / 2.0 / ppim;

  }

  //Integrate the optical potential through the nucleus
  cdouble resu = integrationtools::RGN1D(za, rmax, nz, sampling, ordez);

  // Eikonal approximation to the wave function
  cdouble uwaveik = exp( - cdouble(0,1) * ( ppim*za + resu ) );

  delete [] ordez; // CA

  return uwaveik;
}

double genie::alvarezruso::AREikonalSolution::Gamd ( const double  s )

private

Definition at line 227 of file AREikonalSolution.cxx.

References Con(), genie::alvarezruso::ARConstants::DeltaNCoupling(), genie::constants::kPi, genie::alvarezruso::ARConstants::NucleonMass(), genie::alvarezruso::ARConstants::PiPMass(), and Qcm().

Referenced by Deltamed().

{
  // Delta -> N pi
  const double mpi = this->Con()->PiPMass();
  const double mn = this->Con()->NucleonMass();
  if( s <= (mn+mpi)*(mn+mpi) )
  {
    return 0.0;
  }
  else
  {
    double fs_mpi2 = this->Con()->DeltaNCoupling()/mpi;
    fs_mpi2 *= fs_mpi2;
    const double qcm = this->Qcm(s);
    return 1.0 / (6.0*constants::kPi)*fs_mpi2*mn*(qcm*qcm*qcm)/TMath::Sqrt(s);
  }
}

ARSampledNucleus* genie::alvarezruso::AREikonalSolution::Nucleus ( )

inlineprivate

Definition at line 49 of file AREikonalSolution.h.

References fNucleus.

Referenced by Element().

{ return fNucleus; }

AlvarezRusoCOHPiPDXSec* genie::alvarezruso::AREikonalSolution::Parent ( )

inlineprivate

Definition at line 48 of file AREikonalSolution.h.

References parent_.

Referenced by AREikonalSolution(), Cc(), Deltamed(), and Element().

{ return this->parent_; }

cdouble genie::alvarezruso::AREikonalSolution::PionSelfEnergy ( const double  rhop_cent, const double  rhon_cent, const double  omepi, const double  ppim  )

private

Definition at line 98 of file AREikonalSolution.cxx.

References Con(), Deltamed(), genie::alvarezruso::ARConstants::DeltaNCoupling(), genie::alvarezruso::ARConstants::DeltaPMass(), genie::units::fs, genie::alvarezruso::ARConstants::HBar(), genie::constants::kPi, genie::alvarezruso::ARConstants::NucleonMass(), genie::alvarezruso::ARConstants::PiPMass(), and genie::alvarezruso::ARConstants::Rho0().

Referenced by Element().

{
  const double rho0 = this->Con()->Rho0();
  const double mn = this->Con()->NucleonMass();
  const double hb = this->Con()->HBar() * 1000.0;
  const double pi = constants::kPi;
  const double fs = this->Con()->DeltaNCoupling();
  const double mdel = this->Con()->DeltaPMass();
  const double mpi = this->Con()->PiPMass();
  const double fs_mpi2 = fs*fs/(mpi*mpi);


  const cdouble ui(0,1);

  const double resig = -53.0/hb;
  const double rho = rhop_cent + rhon_cent;
  const double rat = rho / rho0;
  const double pf = TMath::Power( (3.*pi*pi/2.*rho), (1.0/3.0) );

  const double sdel = mn*mn + mpi*mpi + 2.*omepi*(mn+3./5.*pf*pf/2./mn);
  const double sqsdel = TMath::Sqrt(sdel);

  double gamdpb, imsig;
  this->Deltamed(sdel, pf, rat, gamdpb, imsig, ppim, omepi);

  const cdouble pe = -1./6./pi*fs_mpi2*
    ( rhop_cent/(sqsdel-mdel-resig*(2.*rhon_cent/rho0)+ui*(gamdpb/2.-imsig)) +
    1./3.*rhon_cent/(sqsdel-mdel-resig*2./3.*(2.*rhon_cent+rhop_cent)/rho0+ui*(gamdpb/2.-imsig)) +
    rhon_cent/(-sqsdel-mdel+2.*mn-resig*(2.*rhop_cent/rho0))+
    1./3.*rhop_cent/(-sqsdel-mdel+2.*mn-resig*2./3.*(2.*rhop_cent+rhon_cent)/rho0) );

  const cdouble efe = 4.*pi*mn*mn/sdel*pe/(1.+4.*pi*0.63*pe);

  const cdouble piself = -1.0*efe*(1.-1./2.*omepi/mn)*ppim*ppim/(1.+efe*(1.-1./2.*omepi/mn));

  return piself;
}

double genie::alvarezruso::AREikonalSolution::Qcm ( const double  s )

private

Definition at line 246 of file AREikonalSolution.cxx.

References Con(), genie::alvarezruso::ARConstants::NucleonMass(), and genie::alvarezruso::ARConstants::PiPMass().

Referenced by Deltamed(), and Gamd().

{
  // Returns the 3-momentum of the pion formed after the decay of a
  // resonance (R->N pi) of inv. mass s in the rest frame of the resonance
  const double mpi = this->Con()->PiPMass();;
  const double mn = this->Con()->NucleonMass();
  return TMath::Sqrt((s-mpi*mpi-mn*mn)*(s-mpi*mpi-mn*mn) - 4.*mpi*mpi*mn*mn)/2.0/TMath::Sqrt(s);
}

void genie::alvarezruso::AREikonalSolution::Solve ( )

virtual

Implements genie::alvarezruso::ARWFSolution.

Definition at line 274 of file AREikonalSolution.cxx.

{
  if(false) std::cout << "Hi!" << std::endl;
}

Member Data Documentation

ARConstants* genie::alvarezruso::AREikonalSolution::constants_

private

Definition at line 62 of file AREikonalSolution.h.

Referenced by AREikonalSolution(), Con(), and ~AREikonalSolution().

ARSampledNucleus* genie::alvarezruso::AREikonalSolution::fNucleus

private

Definition at line 61 of file AREikonalSolution.h.

Referenced by AREikonalSolution(), Element(), and Nucleus().

bool genie::alvarezruso::AREikonalSolution::owns_constants

private

Definition at line 64 of file AREikonalSolution.h.

Referenced by AREikonalSolution(), and ~AREikonalSolution().

AlvarezRusoCOHPiPDXSec* genie::alvarezruso::AREikonalSolution::parent_

private

Definition at line 60 of file AREikonalSolution.h.

Referenced by Parent().

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The documentation for this class was generated from the following files:

• AREikonalSolution.h
• AREikonalSolution.cxx