Density dependence of the "symmetry energy" in the lattice gas model

TL;DR

This study investigates how the symmetry energy in nuclear matter depends on density using an isospin-dependent lattice gas model, revealing a power-law relationship with density and insensitivity to temperature.

Contribution

It introduces a detailed analysis of the density dependence of symmetry energy using the lattice gas model, highlighting a specific power-law form and the influence of nucleon-nucleon potential asymmetry.

Findings

Symmetry energy is insensitive to temperature changes.

Symmetry energy follows a power-law dependence on density.

The form C_{sym} = 30(ρ/ρ_0)^{0.62} fits the data.

Abstract

Isoscaling behavior of the statistical emission fragments from the equilibrated sources with $Z$ = 30 and $N$ = 30, 33, 36 and 39, resepectively, is investigated in the framework of isospin dependent lattice gas model. The dependences of isoscaling parameters $\alpha$ on source isospin asymmetry, temperature and freeze-out density are studied and the "symmetry energy" is deduced from isoscaling parameters. Results show that "symmetry energy" $C_{sym}$ is insensitive to the change of temperature but follows the power-law dependence on the freeze-out density $\rho$. The later gives $C_{sym}$ = 30$(\rho/\rho_0)^{0.62}$ if the suitable asymmetric nucleon-nucleon potential is taken. The effect of strength of asymmetry of nucleon-nucleon interaction potential on the density dependence of the "symmetry energy" is dicussed.