Baym-Pethick-Sutherland equation of state. More...

#include <eos_crust.h>

Inheritance diagram for o2scl::eos_crust:

Detailed Description

This calculates the equation of state of electrons and nuclei using the approach of Baym71tg (based on the discussion in Shapiro83) between about $8 \times 10^{6} ~\mathrm{g}/\mathrm{cm}^3$ and $4.3 \times 10^{11} ~\mathrm{g}/\mathrm{cm}^3$ . Below these densities, more complex Coulomb corrections need to be considered, and above these densities, neutron drip is important.

The default mass formula is semi-empirical

$\begin{eqnarray*} M(A,Z)&=&(A-Z) m_n+Z (m_p+m_e)- 15.76 A-17.81 A^{2/3} \\ && -0.71 Z^2 /A^{1/3}- 94.8/A \left(A/2-Z\right)^2+E_{\mathrm{pair}} \end{eqnarray*}$

where

$E_{\mathrm{pair}} = \pm 39/A^{3/4}$

if the nucleus is odd-odd (plus sign) or even-even (minus sign) and $E_{\mathrm{pair}}$ is zero for odd-even and even-odd nuclei. The nuclei are assumed not to contribute to the pressure. The electronic contribution to the pressure is assumed to be equal to the Fermi gas contribution plus a "lattice" contribution

$\varepsilon_L = -1.444 Z^{2/3} e^2 n_e^{4/3}$

This is Eq. 2.7.2 in Shapiro83. The rest mass energy of the nucleons is included in the energy density.

The original results from Baym71tg are stored as a table in file data/o2scl/bps.eos. The testing code for this class compares the calculations to the table and matches to within .2 percent for the energy density and 9 percent for the pressure (for a fixed baryon number density).

Idea for Future:

Can the pressure be made to match more closely?

Convert to a o2scl::eos_had_base object and offer an associated interface?

Definition at line 84 of file eos_crust.h.

Public Types
typedef boost::numeric::ublas::vector< double >	ubvector

Public Member Functions
virtual int	calc_density (double barn, thermo &th, int &Z, int &A)
	Calculate the equation of state as a function of the baryon number density `barn`. More...

virtual int	calc_pressure (thermo &th, double &barn, int &Z, int &A)
	Calculate the equation of state as a function of the pressure. More...

virtual double	lattice_energy (int Z)
	The electron lattice energy.

virtual const fermion &	get_electron ()
	Get a pointer to the electron.

virtual double	mass_formula (int Z, int A)
	The mass formula. More...

virtual const char *	type ()
	Return string denoting type ("eos_crust")

int	set_mass_formula (nucmass &nm)
	Set the nuclear mass formula to be used.

int	calc_density_fixedA (double barn, thermo &th, int &Z, int A)
	Compute the ground state assuming a fixed atomic number.

Public Member Functions inherited from o2scl::eos_base
virtual void	set_thermo (thermo &th)
	Set class thermo object.

virtual const thermo &	get_thermo ()
	Get class thermo object.

Public Attributes
nucmass_semi_empirical	def_mass
	Default mass formula.

fermion	e
	The electron thermodynamics. More...

Public Attributes inherited from o2scl::eos_base
thermo	def_thermo
	The default thermo object.

Protected Member Functions
virtual int	eq274 (size_t nv, const ubvector &nx, ubvector &ny, int Zt)
	Solve Equation 2.7.4 for a given pressure.

double	gibbs (int Z, int A)
	The Gibbs free energy.

double	energy (double barn, int Z, int A)
	The energy density.

Protected Attributes
fermion_zerot	fzt
	Zero-temperature thermodynamics for the electrons.

mroot_hybrids< mm_funct >	gs
	A solver to solve Eq. 2.7.4.

nucmass *	nmp
	The nuclear mass formula.

Protected Attributes inherited from o2scl::eos_base
thermo *	eos_thermo
	A pointer to the thermo object.

Member Function Documentation

◆ calc_density()

virtual int o2scl::eos_crust::calc_density	(	double	barn,
		thermo &	th,
		int &	Z,
		int &	A
	)

virtual

This calculates the equation of state as a function of the baryon number density in $\mathrm{fm}^{-3}$ , returning the representative nucleus with proton number Z and atomic number A. The pressure and energy density are returned in th in $\mathrm{fm}^{-4}$ .

◆ calc_pressure()

virtual int o2scl::eos_crust::calc_pressure	(	thermo &	th,
		double &	barn,
		int &	Z,
		int &	A
	)

virtual

This calculates the equation of state as a function of the pressure, returning the representative nucleus with proton number Z and atomic number A and the baryon number density barn in $\mathrm{fm}^{-3}$ . The energy density is also returned in $\mathrm{fm}^{-4}$ in th.

◆ mass_formula()

virtual double o2scl::eos_crust::mass_formula	(	int	Z,
		int	A
	)

virtual

The nuclear mass without the contribution of the rest mass of the electrons. The electron rest mass energy is included in the electron thermodynamics elsewhere.

Member Data Documentation

◆ e

fermion o2scl::eos_crust::e

Note: The electron rest mass is included by default in the energy density and the chemical potential

Definition at line 151 of file eos_crust.h.

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

/home/awsteiner/wcs/o2scl/src/eos/eos_crust.h

Detailed Description

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Member Function Documentation

◆ calc_density()

◆ calc_pressure()

◆ mass_formula()

Member Data Documentation

◆ e