Symmetry energy at subsaturation densities and the neutron skin thickness of 208Pb

TL;DR

This study analyzes the symmetry energy at subsaturation densities and predicts the neutron skin thickness of 208Pb using symmetry energy coefficients and density profiles, finding a linear relation with the slope parameter.

Contribution

It introduces a method to extract symmetry energy coefficients from nuclear mass differences and relates the slope parameter to neutron skin thickness in 208Pb.

Findings

The slope parameter L_{0.11} ranges from 40.5 to 60.3 MeV.

A linear relation between L_{0.11} and neutron skin thickness is established.

Predicted neutron skin thickness of 208Pb is 0.15 - 0.21 fm.

Abstract

The mass-dependent symmetry energy coefficients $a_{sym}(A)$ has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work. Taking advantage of the obtained symmetry energy coefficient $a_{sym}(A)$ and the density profiles obtained by switching off the Coulomb interaction in $^{208}\text{Pb}$, we calculated the slope parameter $L_{0.11}$ of the symmetry energy at the density of $0.11\text{fm}^{-3}$. The calculated $L_{0.11}$ ranges from 40.5 MeV to 60.3 MeV. The slope parameter $L_{0.11}$ of the symmetry energy at the density of $0.11\text{fm}^{-3}$ is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of $^{208}\text{Pb}$, which is the difference of the neutron and proton rms radii of the nucleus. With the linear relation the neutron skin thickness $ \Delta R_{np} $ of $^{208}\text{Pb}$ is predicted to be 0.15 - 0.21 fm.