Robust linear correlations related to neutron skin thickness

TL;DR

This paper uncovers robust linear correlations between neutron skin thickness, mirror charge radius differences, and isospin asymmetry, linking these to the symmetry energy slope to constrain the nuclear matter equation of state.

Contribution

It introduces new linear correlations involving neutron skin and mirror charge radii with isospin asymmetry, and uses these to constrain the symmetry energy slope parameter $L$.

Findings

Linear correlations between $ riangle R_{np}$, $ riangle R_{mirr}$, and $I$ are robust.

The slopes of these correlations are linearly related to the symmetry energy slope $L$.

Constraints on $L$ are refined to 28-36 MeV, indicating a soft nuclear matter equation of state.

Abstract

We observe various robust linear correlations related to neutron skin thickness ($\Delta R_{\rm np}$) within different interaction ensembles, including newly proposed random Skyrme ensemble. The robust linear correlation between $\Delta R_{\rm np}$, or charge radius difference of mirror nuclei ($\Delta R_{\rm mirr}$), and the isospin asymmetry ($I=\frac{N-Z}{A}$) becomes apparent as the model space is enlarged. Shape coexistence, or shape effect on charge radius, is considered to explain the experimental deviation of ${}^{18}$O/Ne and some odd-$A$ $\Delta R_{\rm mirr}$s from the $\Delta R_{\rm mirr}-I$ linearity. The slopes of the linear $\Delta R_{\rm mirr}-I$ and $\Delta R_{\rm np}-I$ correlations ($C_{\rm np}$ and $C_{\rm mirr}$, respectively) are also robustly and linearly correlated to the slope of the symmetry energy ($L$). These linear correlations are further understood with the similar formulation between between $L$ and the symmetry energy coefficient ($J$). The linear correlations between $C_{\rm np}-L$ and $C_{\rm mirr}-L$ are also adopted to constrain $L$ to $20\sim36$ MeV with 1$\sigma$ confidence. Considering the deviation of ${}^{18}$O/Ne $\Delta R_{mirr}$ due to shape coexistence, the 1$\sigma$ range for $L$ is further narrowed to $28\sim36$ MeV, suggesting a relatively soft equation of state for nuclear matter.