Nuclear matter fourth-order symmetry energy in the relativistic mean field models

Abstract

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{sym,4}(\rho )$. Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of $E_{sym,4}(\rho )$ at normal nuclear matter density ${\rho }_0$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at ${\rho }_0$. On the other hand, we find that the $E_{sym,4}(\rho )$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{sym,4}(\rho )$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{sat}(\delta )=K_0+K_{sat,2}{\delta }^2+K_{sat,4}{\delta }^4+\mathcal{O}({\delta }^6)$ where $\delta =({\rho }_n-{\rho }_p)/\rho$ is the isospin asymmetry, and we find that the value of $K_{sat,4}$ is generally small compared with that of the $K_{sat,2}$. In addition, we study the effects of the $E_{sym,4}(\rho )$ on the proton fraction $x_p$ and the core-crust transition density ${\rho }_t$ and pressure $P_t$ in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the $E_{sym,4}(\rho )$ contribution can significantly enhance the $x_p$ at high densities and strongly reduce the ${\rho }_t$ and $P_t$ in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the $x_p$ at high densities as well as the ${\rho }_t$ and $P_t$ in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.

10 pages, 3 figures, 2 tables. Title changed a little, typos fixed. Published version in PRC

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