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

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy E-sym,E-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). However, we find that the E-sym,(4)(rho) may become non-negligible at high densities. Furthermore, the analytical form of the E-sym,E-4(rho) provides the possibility to study the higher- order effects on the isobaric incompressibility of asymmetric nuclear matter, that is, K-sat(delta) = K-0 + K-sat,(2)delta(2) + K-sat,(4)delta(4) + 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 theE(sym),(4)(rho) contribution can significantly enhance the xp 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.