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 $E_{4}(\rho)$.
Our results show that the value of $E_{4}(\rho)$ 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 $E_{4}(\rho)$ may become
nonnegligible at high densities. Furthermore, the analytical form of the
$E_{4}(\rho)$ provides the possibility to study the higher-order effects on the
isobaric incompressibility of asymmetric nuclear matter, i.e.,
$K_{\mathrm{sat}}(\delta)=K_{0}+K_{\mathrm{{sat},2}}\delta
^{2}+K_{\mathrm{{sat},4}}\delta ^{4}+\mathcal{O}(\delta ^{6})$ where $\delta
=(\rho_{n}-\rho_{p})/\rho $ is the isospin asymmetry, and we find that the
value of $K_{\mathrm{{sat},4}}$ is generally comparable with that of the
$K_{\mathrm{{sat},2}}$. In addition, we study the effects of the
$E_{\mathrm{{sym},4}}(\rho)$ 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 $E_{4}(\rho)$ 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 relativistic mean field model.
View original:
http://arxiv.org/abs/1111.4124
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