Density dependence of the nuclear symmetry energy: a microscopic perspective

TL;DR

This paper investigates the density dependence of nuclear symmetry energy using a microscopic Brueckner-Hartree-Fock approach with realistic interactions, comparing results with effective models and experimental constraints, and exploring implications for neutron star matter.

Contribution

It provides a microscopic analysis of the symmetry energy's density dependence and compares it with various models and experimental data, highlighting correlations with neutron skin and neutron star transition density.

Findings

BHF results align with effective model predictions and experimental constraints.

The slope parameter L is found to be 66.5 MeV, consistent with recent data.

An inverse correlation exists between neutron skin thickness and transition density.

Abstract

We perform a systematic analysis of the density dependence of the nuclear symmetry energy within the microscopic Brueckner--Hartree--Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three body force of Urbana type. Our results are compared thoroughly to those arising from several Skyrme and relativistic effective models. The values of the parameters characterizing the BHF equation of state of isospin asymmetric nuclear matter fall within the trends predicted by those models and are compatible with recent constraints coming from heavy ion collisions, giant monopole resonances or isobaric analog states. In particular we find a value of the slope parameter $L=66.5$ MeV, compatible with recent experimental constraints from isospin diffusion, $L=88 \pm 25$ MeV. The correlation between the neutron skin thickness of neutron-rich isotopes and the slope, $L$, and curvature, $K_{sym}$, parameters of the symmetry energy is studied. Our BHF results are in very good agreement with the correlations already predicted by other authors using non-relativistic and relativistic effective models. The correlations of these two parameters and the neutron skin thickness with the transition density from non-uniform to $\beta$-stable matter in neutron stars are also analyzed. Our results confirm that there is an inverse correlation between the neutron skin thickness and the transition density.