Model dependence of the neutron-skin thickness on the symmetry energy

TL;DR

This paper investigates how different microscopic mean field models influence the correlation between neutron-skin thickness and symmetry energy parameters, highlighting the importance of the effective symmetry energy slope in understanding model variability.

Contribution

It introduces the concept of an effective symmetry energy slope $L_{ m eff}$ that explains the spread in neutron-skin thickness across different models with similar $L$ values.

Findings

$L_{ m eff}$ accounts for model spread in neutron-skin thickness.

Differences in surface nucleon densities influence symmetry energy effects.

Model dependence varies with the behavior of symmetry energy at subsaturation densities.

Abstract

The model dependence in the correlations of the neutron-skin thickness in heavy nuclei with various symmetry energy parameters is analyzed by using several families of systematically varied microscopic mean field models. Such correlations show a varying degree of model dependence once the results for all the different families are combined. Some mean field models associated with similar values of the symmetry energy slope parameter at saturation density $L$, and pertaining to different families, yield a greater-than-expected spread in the neutron-skin thickness of the $^{208}$Pb nucleus. The effective value of the symmetry energy slope parameter $L_{\rm eff}$, determined by using the nucleon density profiles of the finite nucleus and the density derivative $S^\prime(\rho)$ of the symmetry energy starting from about saturation density up to low densities typical of the surface of nuclei, seems to account for the spread in the neutron-skin thickness for the models with similar $L$. The differences in the values of $L_{\rm eff}$ are mainly due to the small differences in the nucleon density distributions of heavy nuclei in the surface region and the behavior of the symmetry energy at subsaturation densities.