Higher order bulk characteristic parameters of asymmetric nuclear matter

TL;DR

This paper estimates higher order bulk characteristic parameters of asymmetric nuclear matter using Skyrme Hartree-Fock functional, providing insights into the equation of state at densities up to twice the normal nuclear density.

Contribution

It introduces a method to estimate higher order bulk parameters of nuclear matter and analyzes their correlations with lower order parameters.

Findings

Estimated values for third- and fourth-order parameters of symmetric nuclear matter.

Identified key parameters characterizing the EOS up to twice the normal density.

Provided constraints on symmetry energy parameters at normal nuclear density.

Abstract

The bulk parameters characterizing the energy of symmetric nuclear matter and the symmetry energy defined at normal nuclear density $\rho_0 $ provide important information on the equation of state (EOS) of isospin asymmetric nuclear matter. While significant progress has been made in determining some lower order bulk characteristic parameters, such as the energy $E_0(\rho_0)$ and incompressibility $K_0$ of symmetric nuclear matter as well as the symmetry energy $E_{sym}(\rho_0)$ and its slope parameter $L$, yet the higher order bulk characteristic parameters are still poorly known. Here, we analyze the correlations between the lower and higher order bulk characteristic parameters within the framework of Skyrme Hartree-Fock energy density functional and then estimate the values of some higher order bulk characteristic parameters. In particular, we obtain $J_0=-355 \pm 95$ MeV and $I_0=1473 \pm 680$ MeV for the third-order and fourth-order derivative parameters of symmetric nuclear matter at $\rho_0 $ and $K_{sym} = -100 \pm 165$ MeV, $J_{sym} = 224 \pm 385$ MeV, $I_{sym} = -1309 \pm 2025$ MeV for the curvature parameter, third-order and fourth-order derivative parameters of the symmetry energy at $\rho_0 $, using the empirical constraints on $E_0(\rho_0)$, $K_0$, $E_{sym}(\rho_0)$, $L$, and the isoscalar and isovector nucleon effective masses. Furthermore, our results indicate that the three parameters $E_0(\rho_0)$, $K_0$, and $J_0$ can reasonably characterize the EOS of symmetric nuclear matter up to $2\rho_0 $ while the symmetry energy up to $2\rho_0 $ can be well described by $E_{sym}(\rho_0)$, $L$, and $K_{sym}$.