1111.4124 (Bao-Jun Cai et al.)

Nuclear matter fourth-order symmetry energy in nonlinear relativistic
mean field models    [PDF]

Bao-Jun Cai, Lie-Wen Chen

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.

View original: http://arxiv.org/abs/1111.4124