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

Schematic EOS from Hebeler et al. More...

#include <eos_had_hlps.h>

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

Public Member Functions

void fix_coeffs (double M, double local_n0, double B, double K)
 Fix 'alpha', 'eta' and 'gamma' from saturation properties. More...
 
void fix_neutron_matter (double M, double local_n0, double Eneut, double dEneut)
 Fix 'alphaL' and 'etaL' from neutron matter EOS and its derivative. More...
 
void fix_SL (double M, double local_n0, double S, double L)
 
virtual int calc_e (fermion &ln, fermion &lp, thermo &lth)
 Equation of state as a function of density.
 
virtual const char * type ()
 Return string denoting type ("eos_had_hlps")
 
- 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

Constants (all unitless)
double gamma
 
double alpha
 
double eta
 
double alphaL
 
double etaL
 
- 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.
 

Protected Attributes

quadratic_real_coeff_gsl quad
 To solve quadratic equation for 'gamma'.
 
- 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.
 

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().
 

Detailed Description

The energy per baryon is

\[ E/A = \left( 3 \pi^2 n_0/2 \right)^{2/3} \frac{1}{2 M} \left\{ \frac{3}{5} \left[ x^{5/3} + (1-x)^{5/3} \right] (2 u)^{2/3}- [(2 \alpha - 4 \alpha_L) x (1-x)+\alpha_L] u + \left[ (2 \eta - 4 \eta_L) x (1-x) + \eta_L \right] u^{\gamma} \right\} \]

where $ u = n/n_0 $ .

One can fix the values of $ \alpha, \eta, $ and $ \gamma $ by the requirement that the pressure is zero at saturation and by fixing the binding energy and incompressibility.

Note that the original reference has a typo in the pressure in Eq. 3. The $ 2/5 $ factor in front should be $ 1/5 $ .

See Ref. Hebeler13eo .

Definition at line 59 of file eos_had_hlps.h.

Member Function Documentation

◆ fix_coeffs()

void o2scl::eos_had_hlps::fix_coeffs ( double  M,
double  local_n0,
double  B,
double  K 
)

All inputs must be in $ \mathrm{fm}^{-1} $. This employs a simple iterative method that may not always converge.

◆ fix_neutron_matter()

void o2scl::eos_had_hlps::fix_neutron_matter ( double  M,
double  local_n0,
double  Eneut,
double  dEneut 
)

The parameters M and Eneut must be in $ \mathrm{fm}^{-1} $ and dEneut must be in $ \mathrm{fm}^{2} $


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

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