rmf_delta_eos Class Reference

Field-theoretical EOS with scalar-isovector meson,. More...

#include <rmf_delta_eos.h>

Inheritance diagram for rmf_delta_eos:

rmf_eos hadronic_eos_temp_pres hadronic_eos_temp hadronic_eos eos

Detailed Description

Field-theoretical EOS with scalar-isovector meson,.

$ \delta $.

This essentially follows the notation in Kubis97, except that our definitions of b and c follow their $ \bar{b} $ and $ \bar{c} $, respectively.

Also discussed in Gaitanos04, where they take $ m_{\delta}=980 $ MeV.

The full Lagragian is:

\[ {\cal L} = {\cal L}_{Dirac} + {\cal L}_{\sigma} + {\cal L}_{\omega} + {\cal L}_{\rho} + {\cal L}_{\delta} \]

\begin{eqnarray*} {\cal L}_{Dirac} &=& \bar{\Psi} \left[ i {{\partial}\!\!\!{\slash}} - g_{\omega} {{\omega}\!\!\!{\slash}} - \frac{g_{\rho}}{2} {{\vec{\rho}}\!\!\!{\slash}}~ \vec{\tau} - M + g_{\sigma} \sigma - \frac{e}{2} \left( 1 + \tau_3 \right) A_{\mu} \right] \Psi \nonumber \\ {\cal L}_{\sigma} &=& {\textstyle \frac{1}{2}} \left( \partial_{\mu} \sigma \right)^2 - {\textstyle \frac{1}{2}} m^2_{\sigma} \sigma^2 - \frac{b M}{3} \left( g_{\sigma} \sigma\right)^3 - \frac{c}{4} \left( g_{\sigma} \sigma\right)^4 \nonumber \\ {\cal L}_{\omega} &=& - {\textstyle \frac{1}{4}} f_{\mu \nu} f^{\mu \nu} + {\textstyle \frac{1}{2}} m^2_{\omega}\omega^{\mu}\omega_{\mu} + \frac{\zeta}{24} g_{\omega}^4 \left(\omega^\mu \omega_\mu\right)^2 \nonumber \\ {\cal L}_{\rho} &=& - {\textstyle \frac{1}{4}} \vec{B}_{\mu \nu} \cdot \vec{B}^{\mu \nu} + {\textstyle \frac{1}{2}} m^2_{\rho} \vec{\rho}^{~\mu} \cdot \vec{\rho}_{~\mu} + \frac{\xi}{24} g_{\rho}^4 \left(\vec{\rho}^{~\mu}\right) \cdot \vec{\rho}_{~\mu} + g_{\rho}^2 f (\sigma, \omega) \vec{\rho}^{~\mu} \cdot \vec{\rho}_{~\mu} \nonumber \\ \end{eqnarray*}

where the additional terms are

\[ {\cal L}_{\delta} = \bar{\Psi} \left( g_{\delta} \vec{\delta} \cdot \vec{\tau} \right) \Psi + \frac{1}{2} (\partial_{\mu} \vec{\delta})^2 - \frac{1}{2} m_{\delta}^2 \vec{\delta}^{~2} \]

The new field equation for the delta meson is

\[ m_{\delta}^2 \delta = g_{\delta} (n_{s,p} - n_{s,n}) \]

Idea for future:
Finish the finite temperature EOS

Definition at line 93 of file rmf_delta_eos.h.


Public Member Functions

virtual int calc_e (fermion &ne, fermion &pr, thermo &lth)
 Equation of state as a function of density.
virtual int calc_p (fermion &neu, fermion &p, double sig, double ome, double rho, double delta, double &f1, double &f2, double &f3, double &f4, thermo &th)
 Equation of state as a function of chemical potentials.
int calc_temp_p (fermion_T &ne, fermion_T &pr, double temper, double sig, double ome, double lrho, double delta, double &f1, double &f2, double &f3, double &f4, thermo &lth)
 Finite temperature (unfinished).
virtual int set_fields (double sig, double ome, double lrho, double delta)
 Set a guess for the fields for the next call to calc_e(), calc_p(), or saturation().
virtual int saturation ()
 Calculate saturation properties for nuclear matter at the saturation density.

Data Fields

double md
 The mass of the scalar-isovector field.
double cd
 The coupling of the scalar-isovector field to the nucleons.
double del
 The value of the scalar-isovector field.

Protected Member Functions

virtual int calc_e_solve_fun (size_t nv, const ovector_base &ex, ovector_base &ey, double *&pa)
 The function for calc_e().
virtual int zero_pressure (size_t nv, const ovector_base &ex, ovector_base &ey, int &pa)
 Compute matter at zero pressure (for saturation()).

Private Member Functions

virtual int set_fields (double sig, double ome, double lrho)
 Forbid setting the guesses to the fields unless all four fields are specified.

Member Function Documentation

virtual int saturation (  )  [virtual]

Calculate saturation properties for nuclear matter at the saturation density.

This requires initial guesses to the chemical potentials, etc.

Reimplemented from rmf_eos.


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

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