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

TL;DR

This paper derives the fourth-order symmetry energy in nuclear matter using relativistic mean field models, analyzing its impact on neutron star properties and highlighting limitations of the empirical parabolic approximation at high densities.

Contribution

The paper provides an analytical expression for the fourth-order symmetry energy in relativistic mean field models and explores its effects on nuclear matter and neutron star characteristics.

Findings

$E_{sym,4}( ho)$ is less than 1 MeV at normal density

Including $E_{sym,4}( ho)$ significantly affects proton fraction and transition density in neutron stars

The empirical parabolic approximation may cause large errors at high densities

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.