Properties of Nuclear and Neutron Matter in the Nonlinear $\sigma$-$\omega$-$\rho$ Dirac-Hartree-Fock Approximation

\newcommand{\bkappa}{\mbox{\boldmath $\kappa$}} \newcommand\kfermi{k_{\scriptscriptstyle F}} \newcommand\Mstar{M^{\ast}} \newcommand\kstar{k^{\ast}} \newcommand\rhoB{\rho_{\scriptscriptstyle B}} \newcommand\szero{\scriptscriptstyle (0)} \newcommand{\bftau}{\mbox{\boldmath $\tau$}} A self-consistent relativistic Dirac-Hartree-Fock (DHF) approximation in a nonlinear $\sigma$-$\omega$-$\rho$ mean-field model is discussed by employing conditions of the theory of conserving approximations. The approximation is applied to Fermi-liquid properties of nuclear matter and properties of neutron stars in order to produce the effective mass of nucleon, $M^{\ast}/M \sim 0.7$, incompressibility $ \sim 250$ MeV, symmetry energy $a_4 \sim 30$ MeV, the maximum mass of neutron star $M_{star}/M_{\odot} = 2.5$, by adjusting coupling constants of nonlinear interactions. The results of nonlinear $\sigma$-$\omega$-$\rho$ Hartree approximation (NHA) and the linear Hartree ($\sigma$-$\omega$) approximation (LHA) are listed in the table. % \vspace{-0.5cm} \begin{center} \arrayrulewidth=1.0pt \doublerulesep=0pt \begin{tabular}{lcccccc} \\ \hline\hline & $M^{\ast}/M$ & $m_{\sigma}^{\ast}/m_{\sigma}$ & $m_{\omega}^{\ast}/m_{\omega}$ & $K$ (MeV) & $a_4$ (MeV) &$M_{max}$ \\ \hline\hline LHA & 0.54 & 1.00 & 1.00 & 530 & 19.3 & 3.03 \\ NHA & 0.68 & 1.09 & 1.05 & 303 & 25.7 & 2.50 \\ \hline\hline \end{tabular} \end{center} Since nonlinear self-interactions of mesons are renormalized as effective masses of mesons by self-consistency and strictly restricted by coupled equations of motion for mesons and baryons, the validity of nonlinear self-interactions of mesons would be examined by analyzing nuclear experimental data and properties of neutron stars.