A phenomenological equation of state for isospin asymmetric nuclear matter

TL;DR

This paper develops a phenomenological model to describe the equation of state for isospin asymmetric nuclear matter, revealing correlations among key nuclear matter parameters and estimating the second-order isospin asymmetry coefficient.

Contribution

A momentum-independent model is introduced that accurately describes the EOS and symmetry energy, establishing correlations among nuclear matter parameters and estimating the second-order asymmetry coefficient.

Findings

Identifies linear correlations between $K_{sym}$ and $L$, and between $J_0/K_0$ and $K_0$.

Estimates the second-order isospin asymmetry coefficient $K_{sat,2}$ to be between -477 MeV and -241 MeV.

Demonstrates the model's consistency with existing sophisticated models and approaches.

Abstract

A phenomenological momentum-independent (MID) model is constructed to describe the equation of state (EOS) for isospin asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{\text{\textrm{sym}}}(\rho)$. This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach. We find that there exists a nicely linear correlation between $K_{\mathrm{sym}}$ and $L$ as well as between $J_{0}/K_{0} $ and $K_{0}$, where $L$ and $K_{\mathrm{sym}}$ represent, respectively, the slope and curvature parameters of the symmetry energy at the normal nuclear density $\rho_{0}$ while $K_{0}$ and $J_{0}$ are, respectively, the incompressibility and the third-order derivative parameter of symmetric nuclear matter at $\rho_{0}$. These correlations together with the empirical constraints on $K_{0}$, $L$ and $E_{\text{\textrm{sym}}}(\rho_{0}) $ lead to an estimation of -477 MeV $\leq K_{\mathrm{sat,2}}\leq -241 $ MeV for the second-order isospin asymmetry expansion coefficient for the incompressibility of asymmetric nuclear matter at the saturation point.