Public Member Functions | Public Attributes | List of all members
o2scl::eos_had_schematic Class Reference

Schematic hadronic equation of state. More...

#include <eos_had_schematic.h>

Inheritance diagram for o2scl::eos_had_schematic:
o2scl::eos_had_eden_base o2scl::eos_had_base o2scl::eos_base

Public Member Functions

virtual int calc_e (fermion &ln, fermion &lp, thermo &lth)
 Equation of state as a function of density.
 
virtual int set_kprime_zeroden ()
 Set kprime so that the energy per baryon of zero-density matter is zero.
 
virtual int set_kpp_zeroden ()
 Set kpp so that the energy per baryon of zero-density matter is zero.
 
virtual int set_a_from_mstar (double u_msom, double mnuc)
 Fix the kinetic energy symmetry coefficient from the reduced nucleon effective mass and the saturation density. More...
 
virtual double eoa_zeroden ()
 Return the energy per baryon of matter at zero density. More...
 
virtual double baryon_suscep (double n, double x)
 Return the baryon number susceptibility, $ \partial \mu_B / \partial n_B $ in $ \mathrm{fm}^{2} $. More...
 
virtual const char * type ()
 Return string denoting type ("eos_had_schematic")
 
- Public Member Functions inherited from o2scl::eos_had_eden_base
virtual int calc_p (fermion &n, fermion &p, thermo &th)
 Equation of state as a function of the chemical potentials.
 
- Public Member Functions inherited from o2scl::eos_had_base
virtual double fcomp (double nb, double delta=0.0)
 Calculate the incompressibility in $ \mathrm{fm}^{-1} $ using calc_e() More...
 
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 $ \mathrm{fm}^{-1} $ using calc_e() More...
 
virtual double fesym (double nb, double delta=0.0)
 Calculate symmetry energy of matter in $ \mathrm{fm}^{-1} $ using calc_dmu_delta() . More...
 
virtual double fesym_err (double nb, double delta, double &unc)
 Calculate symmetry energy of matter and its uncertainty in $ \mathrm{fm}^{-1} $. More...
 
virtual double fesym_slope (double nb, double delta=0.0)
 The symmetry energy slope parameter in $ \mathrm{fm}^{-1} $. More...
 
virtual double fesym_curve (double nb, double delta=0.0)
 The curvature of the symmetry energy in $ \mathrm{fm}^{-1} $.
 
virtual double fesym_skew (double nb, double delta=0.0)
 The skewness of the symmetry energy in $ \mathrm{fm}^{-1} $.
 
virtual double fesym_diff (double nb)
 Calculate symmetry energy of matter as energy of neutron matter minus the energy of nuclear matter in $ \mathrm{fm}^{-1} $. More...
 
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 $ \mathrm{fm}^{-1} $ using calc_e() More...
 
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, $ \partial^2 P / \partial \mu_i \mu_j $.
 
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, $ \partial^2 \varepsilon / \partial n_i n_j $.
 
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.
 
- Public Member Functions inherited from o2scl::eos_base
virtual void set_thermo (thermo &th)
 Set class thermo object.
 
virtual const thermoget_thermo ()
 Get class thermo object.
 

Public Attributes

double a
 The kinetic energy symmetry coefficient in inverse fm (default $ 17~\mathrm{MeV}~/(\hbar c) $) More...
 
double b
 The potential energy symmetry coefficient in inverse fm (default $ 13~\mathrm{MeV}~/(\hbar c) $)
 
double kpp
 The coefficient of a density to the fourth term in inverse fm (default 0)
 
double gamma
 The exponent of the high-density symmetry energy (unitless, default 1.0)
 
- Public Attributes inherited from o2scl::eos_had_base
double eoa
 Binding energy (without the rest mass) in $ \mathrm{fm}^{-1} $.
 
double comp
 Compression modulus in $ \mathrm{fm}^{-1} $.
 
double esym
 Symmetry energy in $ \mathrm{fm}^{-1} $.
 
double n0
 Saturation density in $ \mathrm{fm}^{-3} $.
 
double msom
 Effective mass (neutron)
 
double kprime
 Skewness in $ \mathrm{fm}^{-1} $.
 
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...
 
- Public Attributes inherited from o2scl::eos_base
thermo def_thermo
 The default thermo object.
 

Additional Inherited Members

- Public Types inherited from o2scl::eos_had_base
typedef boost::numeric::ublas::vector< double > ubvector
 
- Protected Member Functions inherited from o2scl::eos_had_base
double t1_fun (double barn)
 Compute t1 for gradient_qij().
 
double t2_fun (double barn)
 Compute t2 for gradient_qij().
 
- Protected Attributes inherited from o2scl::eos_had_base
mrooteos_mroot
 The EOS solver.
 
rootsat_root
 The solver to compute saturation properties.
 
deriv_basesat_deriv
 The derivative object for saturation properties.
 
deriv_basesat_deriv2
 The second derivative object for saturation properties.
 
fermionneutron
 The neutron object.
 
fermionproton
 The proton object.
 
- Protected Attributes inherited from o2scl::eos_base
thermoeos_thermo
 A pointer to the thermo object.
 

Detailed Description

A schematic equation of state defined by the energy density:

\[ \epsilon = n_n m_n + n_p m_p + n \left\{ eoa+\frac{comp}{18}(n/n0-1)^2+ \frac{kprime}{162}(n/n0-1)^3+ \frac{kpp}{1944}(n/n0-1)^4+(1- 2 x)^2 \left[a \left(\frac{n}{n0}\right)^{2/3}+ b \left(\frac{n}{n0}\right)^{\gamma} \right] \right\} \]

Symmetry energy at nuclear matter density is $ a+b $.

Definition at line 51 of file eos_had_schematic.h.

Member Function Documentation

◆ baryon_suscep()

virtual double o2scl::eos_had_schematic::baryon_suscep ( double  n,
double  x 
)
inlinevirtual
Todo:
This function is untested.

Definition at line 136 of file eos_had_schematic.h.

◆ eoa_zeroden()

virtual double o2scl::eos_had_schematic::eoa_zeroden ( )
inlinevirtual

This is inaccessible from calc_e() so is available separately here. Using set_kprime_zeroden() or set_kpp_zeroden() will fix kprime or kpp (respectively) to ensure that this is zero.

The result provided here does not include the nucleon mass and is given in $ \mathrm{fm}^{-1} $.

Definition at line 127 of file eos_had_schematic.h.

◆ set_a_from_mstar()

virtual int o2scl::eos_had_schematic::set_a_from_mstar ( double  u_msom,
double  mnuc 
)
inlinevirtual

This assumes the nucleons are non-relativistic and that the neutrons and protons have equal mass. The relativistic corrections are around 1 part in $ 10^{6} $.

Todo:
This was computed in schematic_sym.nb, which might be added to the documentation?

Definition at line 112 of file eos_had_schematic.h.

Member Data Documentation

◆ a

double o2scl::eos_had_schematic::a

The default value corresponds to an effective mass of about 0.7.

Definition at line 61 of file eos_had_schematic.h.


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

Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).