#include <apr_eos.h>
Taken from Akmal98.
The chemical potentials include the rest mass energy and the energy density includes the rest mass energy density.
Note that APR seems to have been designed to be used with non-relativistic neutrons and protons with equal masses of 939 MeV. This gives a saturation density very close to 0.16.
The Hamiltonian is:
The following are definitions for in the low-density phase (LDP) or the high-density phase (HDP):
The variables and
contain the expressions
and
respectively, where
is the potential part of the single particle energy for particle i (i.e. the derivative of the Hamiltonian w.r.t. density while energy density held constant). Equivalently,
is just
.
The finite temperature approximations from Prakash97 (see also the "Windsurfing the Fermi Sea" proceedings) are used in testing.
Definition at line 112 of file apr_eos.h.
Choose phase | |
0 = use phase which minimizes energy (default) 1 = LDP (no pion condensation) 2 = HDP (pion condensation) | |
static const int | best = 0 |
static const int | ldp = 1 |
static const int | hdp = 2 |
int | pion |
Public Member Functions | |
virtual int | calc_e (fermion &n, fermion &p, thermo &th) |
Equation of state as a function of density. | |
virtual int | calc_temp_e (fermion &n, fermion &pr, const double temper, thermo &th) |
Equation of state as a function of densities. | |
int | last_phase () |
Return the phase of the most recent call to calc_e(). | |
double | fcomp (double nb) |
Compute the compressibility. | |
double | fesym_diff (double nb) |
Calculate symmetry energy of matter as energy of neutron matter minus the energy of nuclear matter. | |
void | select (int model_index) |
Select model. | |
int | gradient_qij2 (double nn, double np, double &qnn, double &qnp, double &qpp, double &dqnndnn, double &dqnndnp, double &dqnpdnn, double &dqnpdnp, double &dqppdnn, double &dqppdnp) |
Calculate Q's for semi-infinite nuclear matter. | |
double | get_par (int n) |
Get the value of one of the parameters. | |
int | set_par (int n, double x) |
Set the value of one of the parameters. | |
virtual const char * | type () |
Return string denoting type ("apr_eos"). | |
Data Fields | |
nonrel_fermion | def_nr_neutron |
Default nonrelativistic neutron. | |
nonrel_fermion | def_nr_proton |
Default nonrelativistic proton. | |
bool | parent_method |
If true, use the methods from hadronic_eos for fcomp(). | |
Protected Attributes | |
double * | par |
Storage for the parameters. | |
int | lp |
An integer to indicate which phase was used in calc_e(). | |
int | choice |
The variable indicating which parameter set is to be used. |
double fcomp | ( | double | nb | ) | [virtual] |
Compute the compressibility.
See general notes at hadronic_eos::fcomp(). This computes the compressibility (at fixed proton fraction = 0.5) exactly, unless parent_method is true in which case the derivative is taken numerically in hadronic_eos::fcomp().
Reimplemented from hadronic_eos.
double fesym_diff | ( | double | nb | ) | [virtual] |
Calculate symmetry energy of matter as energy of neutron matter minus the energy of nuclear matter.
This function returns the energy per baryon of neutron matter minus the energy per baryon of nuclear matter. This will deviate significantly from the results from fesym() only if the dependence of the symmetry energy on is not quadratic.
Reimplemented from hadronic_eos.
void select | ( | int | model_index | ) |
Select model.
Valid values for model_index
are:
1 - A18+UIX*+deltav (preferred by Akmal, et. al. - this is the default)
2 - A18+UIX*
3 - A18+deltav
4 - A18
If any other integer is given, A18+UIX*+deltav is assumed.
int gradient_qij2 | ( | double | nn, | |
double | np, | |||
double & | qnn, | |||
double & | qnp, | |||
double & | qpp, | |||
double & | dqnndnn, | |||
double & | dqnndnp, | |||
double & | dqnpdnn, | |||
double & | dqnpdnp, | |||
double & | dqppdnn, | |||
double & | dqppdnp | |||
) |
Calculate Q's for semi-infinite nuclear matter.
For general discussion, see the documentation to hadronic_eos::qs().
For APR, we set so that
and then
This gives
See the Mathematica notebook apr_eos.nb, and apr_eos.ps.
bool parent_method |
If true, use the methods from hadronic_eos for fcomp().
This can be set to true to check the difference in the compressibility wbetween the exact expressions and the numerical values from class hadronic_eos.