Generalized potential model equation of state. More...
#include <eos_had_potential.h>
Public Member Functions | |
virtual int | calc_e (fermion &ne, fermion &pr, thermo <) |
Equation of state as a function of density. | |
int | set_mu_deriv (deriv_base<> &de) |
Set the derivative object to calculate the chemical potentials. | |
virtual const char * | type () |
Return string denoting type ("eos_had_potential") | |
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virtual int | calc_p (fermion &n, fermion &p, thermo &th) |
Equation of state as a function of the chemical potentials. | |
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virtual double | fcomp (double nb, double delta=0.0) |
Calculate the incompressibility in ![]() | |
virtual double | fcomp_err (double nb, double delta, double &unc) |
Compute the incompressibility and its uncertainty. More... | |
virtual double | feoa (double nb, double delta=0.0) |
Calculate the energy per baryon in ![]() | |
virtual double | fesym (double nb, double delta=0.0) |
Calculate symmetry energy of matter in ![]() | |
virtual double | fesym_err (double nb, double delta, double &unc) |
Calculate symmetry energy of matter and its uncertainty in ![]() | |
virtual double | fesym_slope (double nb, double delta=0.0) |
The symmetry energy slope parameter in ![]() | |
virtual double | fesym_curve (double nb, double delta=0.0) |
The curvature of the symmetry energy in ![]() | |
virtual double | fesym_skew (double nb, double delta=0.0) |
The skewness of the symmetry energy in ![]() | |
virtual double | fesym_diff (double nb) |
Calculate symmetry energy of matter as energy of neutron matter minus the energy of nuclear matter in ![]() | |
virtual double | feta (double nb) |
The strength parameter for quartic terms in the symmetry energy. | |
virtual double | feta_prime (double nb) |
The derivative of the strength parameter for quartic terms in the symmetry energy. | |
virtual double | fkprime (double nb, double delta=0.0) |
Calculate skewness of nuclear matter in ![]() | |
virtual double | fmsom (double nb, double delta=0.0) |
Calculate reduced neutron effective mass using calc_e() More... | |
virtual double | f_effm_neut (double nb, double delta=0.0) |
Neutron (reduced) effective mass. | |
virtual double | f_effm_prot (double nb, double delta=0.0) |
Proton (reduced) effective mass. | |
virtual double | f_effm_scalar (double nb, double delta=0.0) |
Scalar effective mass. More... | |
virtual double | f_effm_vector (double nb, double delta=1.0) |
Vector effective mass. More... | |
virtual double | fn0 (double delta, double &leoa) |
Calculate saturation density using calc_e() More... | |
virtual void | f_number_suscept (double mun, double mup, double &dPdnn, double &dPdnp, double &dPdpp) |
Compute the number susceptibilities as a function of the chemical potentials, ![]() | |
virtual void | f_inv_number_suscept (double mun, double mup, double &dednn, double &dednp, double &dedpp) |
Compute the 'inverse' number susceptibilities as a function of the densities, ![]() | |
virtual void | saturation () |
Calculates some of the EOS properties at the saturation density. More... | |
double | calc_mun_e (double nn, double np) |
Compute the neutron chemical potential at fixed density. More... | |
double | calc_ed (double nn, double np) |
Compute the energy density as a function of the nucleon densities. | |
double | calc_pr (double nn, double np) |
Compute the pressure as a function of the nucleon chemical potentials. | |
double | calc_mup_e (double nn, double np) |
Compute the proton chemical potential at fixed density. More... | |
double | calc_nn_p (double mun, double mup) |
Compute the neutron density at fixed chemical potential. More... | |
double | calc_np_p (double mun, double mup) |
Compute the proton density at fixed chemical potential. More... | |
double | calc_dmu_delta (double delta, double nb) |
Compute the difference between neutron and proton chemical potentials as a function of the isospin asymmetry. More... | |
double | calc_musum_delta (double delta, double nb) |
Compute the sum of the neutron and proton chemical potentials as a function of the isospin asymmetry. More... | |
double | calc_pressure_nb (double nb, double delta=0.0) |
Compute the pressure as a function of baryon density at fixed isospin asymmetry. More... | |
double | calc_edensity_nb (double nb, double delta=0.0) |
Compute the energy density as a function of baryon density at fixed isospin asymmetry. More... | |
void | const_pf_derivs (double nb, double pf, double &dednb_pf, double &dPdnb_pf) |
Compute derivatives at constant proton fraction. | |
double | calc_press_over_den2 (double nb, double delta=0.0) |
Calculate pressure / baryon density squared in nuclear matter as a function of baryon density at fixed isospin asymmetry. More... | |
double | calc_edensity_delta (double delta, double nb) |
Calculate energy density as a function of the isospin asymmetry at fixed baryon density. More... | |
int | nuc_matter_p (size_t nv, const ubvector &x, ubvector &y, double nn0, double np0) |
Solve for the chemical potentials given the densities. More... | |
int | nuc_matter_e (size_t nv, const ubvector &x, ubvector &y, double mun0, double mup0) |
Solve for the densities given the chemical potentials. More... | |
virtual void | set_mroot (mroot<> &mr) |
Set class mroot object for use in calculating chemical potentials from densities. More... | |
virtual void | set_sat_root (root<> &mr) |
Set class mroot object for use calculating saturation density. More... | |
virtual void | set_sat_deriv (deriv_base<> &de) |
Set deriv_base object to use to find saturation properties. | |
virtual void | set_sat_deriv2 (deriv_base<> &de) |
Set the second deriv_base object to use to find saturation properties. More... | |
virtual void | set_n_and_p (fermion &n, fermion &p) |
Set neutron and proton. | |
void | gradient_qij (fermion &n, fermion &p, thermo &th, double &qnn, double &qnp, double &qpp, double &dqnndnn, double &dqnndnp, double &dqnpdnn, double &dqnpdnp, double &dqppdnn, double &dqppdnp) |
Calculate coefficients for gradient part of Hamiltonian. More... | |
void | check_mu (fermion &n, fermion &p, thermo &th, double &mun_deriv, double &mup_deriv, double &mun_err, double &mup_err) |
Check the chemical potentials by computing the derivatives numerically. | |
void | check_den (fermion &n, fermion &p, thermo &th, double &nn_deriv, double &np_deriv, double &nn_err, double &np_err) |
Check the densities by computing the derivatives numerically. | |
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virtual void | set_thermo (thermo &th) |
Set class thermo object. | |
virtual const thermo & | get_thermo () |
Get class thermo object. | |
Public Attributes | |
int | form |
Form of potential. | |
deriv_gsl | def_mu_deriv |
The default derivative object for calculating chemical potentials. | |
The parameters for the various interactions | |
double | x |
double | Au |
double | Al |
double | rho0 |
double | B |
double | sigma |
double | Cl |
double | Cu |
double | Lambda |
double | A |
double | x0 |
double | x3 |
double | Bp |
double | C1 |
double | z1 |
double | Lambda2 |
double | C2 |
double | z2 |
double | bpal_esym |
int | sym_index |
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double | eoa |
Binding energy (without the rest mass) in ![]() | |
double | comp |
Compression modulus in ![]() | |
double | esym |
Symmetry energy in ![]() | |
double | n0 |
Saturation density in ![]() | |
double | msom |
Effective mass (neutron) | |
double | kprime |
Skewness in ![]() | |
fermion | def_neutron |
The defaut neutron. More... | |
fermion | def_proton |
The defaut proton. More... | |
deriv_gsl | def_deriv |
The default object for derivatives. More... | |
deriv_gsl | def_deriv2 |
The second default object for derivatives. More... | |
mroot_hybrids | def_mroot |
The default solver. More... | |
root_cern | def_sat_root |
The default solver for calculating the saturation density. More... | |
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thermo | def_thermo |
The default thermo object. | |
Static Public Attributes | |
static const int | mdi_form =1 |
The "momentum-dependent-interaction" form from Das03. | |
static const int | bgbd_form =2 |
The modifed GBD form. | |
static const int | bpal_form =3 |
The form from Prakash88 as formulated in Bombaci01. | |
static const int | sl_form =4 |
The "SL" form. See Bombaci01. | |
static const int | gbd_form =5 |
The Gale, Bertsch, Das Gupta from Gale87. | |
static const int | pal_form =6 |
The form from Prakash88. | |
Protected Member Functions | |
double | mom_integral (double pft, double pftp) |
Compute the momentum integral for mdi_form. | |
double | energy (double x) |
Compute the energy. | |
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double | t1_fun (double barn) |
Compute t1 for gradient_qij(). | |
double | t2_fun (double barn) |
Compute t2 for gradient_qij(). | |
Protected Attributes | |
fermion_nonrel | nrf |
Non-relativistic fermion thermodyanmics. | |
bool | mu_deriv_set |
True of the derivative object has been set. | |
deriv_base * | mu_deriv_ptr |
The derivative object. | |
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mroot * | eos_mroot |
The EOS solver. | |
root * | sat_root |
The solver to compute saturation properties. | |
deriv_base * | sat_deriv |
The derivative object for saturation properties. | |
deriv_base * | sat_deriv2 |
The second derivative object for saturation properties. | |
fermion * | neutron |
The neutron object. | |
fermion * | proton |
The proton object. | |
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thermo * | eos_thermo |
A pointer to the thermo object. | |
The mode for the energy() function [protected] | |
int | mode |
static const int | nmode =1 |
static const int | pmode =2 |
static const int | normal =0 |
Additional Inherited Members | |
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typedef boost::numeric::ublas::vector< double > | ubvector |
The single particle energy is defined by the functional derivative of the energy density with respect to the distribution function
The effective mass is defined by
In all of the models, the kinetic energy density is where
and the number density is
When form is equal to mdi_form or gbd_form, the potential energy density is given by Das03 :
where . If form is equal to mdi_form, then
where and
. Later parameterizations in this form are given in Chen05.
Otherwise if form is equal to gbd_form, then
where
Otherwise, if form is equal to bgbd_form, bpal_form or sl_form, then the potential energy density is given by Bombaci01 :
where
The term is:
where
For form is equal to bgbd_form or form is equal to bpal_form, the form factor is given by
while for form is equal to sl_form, the form factor is given by
where is specified in the parameter
Lambda
when necessary.
Definition at line 158 of file eos_had_potential.h.
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