The relationship of the neutron-skin thickness to the symmetry energy and its slope

TL;DR

This paper derives a formula linking neutron-skin thickness to nuclear matter properties like symmetry energy and its slope, and examines this relationship in lead-208, highlighting model-dependent correlations.

Contribution

The paper introduces a relational formula for neutron-skin thickness based on the Hugenholtz-Van Hove theorem, incorporating multiple nuclear matter parameters, and analyzes its implications for $^{208}$Pb.

Findings

Neutron-skin thickness depends on Coulomb energy, symmetry energy, its slope, and incompressibility.

A linear correlation between slope $L$ and neutron-skin thickness is observed.

Model-dependent correlations influence the interpretation of the $L$-delta R relationship.

Abstract

The neutron-skin thickness of asymmetric semi-infinite nuclear matter is shown to be a function of Coulomb energy, the asymmetry-energy coefficient($J$), the slope($L$) of the asymmetry energy, and the incompressibility coefficient, in addition to he Fermi momentum and the asymmetry parameter. The relational formula is derived on the basis of the Hugenholtz-Van Hove theorem in the mean-field approximation for nuclear matter. Using the formula as a guide, the neutron-skin thickness($\delta R$) in $^{208}$Pb is examined. The linear correlation between $L$ and $\delta R$ appears as a kind of spurious ones through the model-dependent correlation of $L$ with $J$ which is included in the main components of the formula.