Class eos_had_schematic (o2scl)

O2scl : Class List

class eos_had_schematic : public o2scl::eos_had_eden_base

Schematic hadronic equation of state.

A schematic equation of state defined by the energy density:

\[\begin{split}\begin{eqnarray*} \varepsilon &=& n_n m_n + n_p m_p + n \left\{ eoa+\frac{comp}{18}(n/n0-1)^2+ \frac{kprime}{162}(n/n0-1)^3+ \frac{kpp}{1944}(n/n0-1)^4 \right. \nonumber \\ && \left. + (1- 2 x)^2 \left[a \left(\frac{n}{n0}\right)^{2/3}+ b \left(\frac{n}{n0}\right)^{\gamma} \right] \right\} \end{eqnarray*}\end{split}\]

The symmetry energy at nuclear matter density is \( a+b \).

Public Functions

eos_had_schematic()

inline virtual ~eos_had_schematic()

virtual int calc_e(fermion &ln, fermion &lp, thermo &lth)

Equation of state as a function of density.

inline virtual int set_kprime_zeroden()

Set kprime so that the energy per baryon of zero-density matter is zero.

inline virtual int set_kpp_zeroden()

Set kpp so that the energy per baryon of zero-density matter is zero.

inline 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.

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

• In eos_had_schematic::set_a_from_mstar(): This was computed in schematic_sym.nb, which might be added to the documentation?

inline virtual double eoa_zeroden()

Return the energy per baryon of matter at zero density.

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 \( \mathrm{fm}^{-1} \).

inline virtual double baryon_suscep(double n, double x)

Return the baryon number susceptibility, \( \partial \mu_B / \partial n_B \) in \( \mathrm{fm}^{2} \).

Todo

• This function, eos_had_schematic::baryon_suscep() is untested.

inline virtual const char *type()

Return string denoting type (“eos_had_schematic”)

Public Members

double a

The kinetic energy symmetry coefficient in inverse fm (default \( 17~\mathrm{MeV}~/(\hbar c) \))

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

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)