Constraints on neutron skin thickness in 208Pb and density-dependent symmetry energy

TL;DR

This paper proposes a practical method to constrain the neutron skin thickness of lead-208 using the correlation with symmetry energy parameters, leveraging existing nuclear data for improved accuracy over previous experiments.

Contribution

It introduces a new approach linking neutron skin thickness to symmetry energy parameters, enabling more accessible constraints through nuclear mass and decay data.

Findings

Strong correlation between $ abla R_{np}$ and $J - a_{sym}$

Density dependence of symmetry energy is well constrained

Measurement starting at $R_m=7.61 ext{ fm}$ suffices for $ abla R_{np}$

Abstract

Accurate knowledge about the neutron skin thickness $\Delta R_{np}$ in $^{208}$Pb has far-reaching implications for different communities of nuclear physics and astrophysics. Yet, the novel Lead Radius Experiment (PREX) did not yield stringent constraint on the $\Delta R_{np}$ recently. We employ a more practicable strategy currently to probe the neutron skin thickness of $^{208}$Pb based on a high linear correlation between the $\Delta R_{np}$ and $J-a_{\text{sym}}$, where $J$ and $a_{\text{sym}}$ are the symmetry energy (coefficient) of nuclear matter at saturation density and of $^{208}$Pb. An accurate $J-a_{\text{sym}}$ thus places a strong constraint on the $\Delta R_{np}$. Compared with the parity-violating asymmetry $A_{\text{PV}}$ in the PREX, the reliably experimental information on the $J-a_{\text{sym}}$ is much more easily available attributed to a wealth of measured data on nuclear masses and on decay energies. The density dependence of the symmetry energy is also well constrained with the $J-a_{\text{sym}}$. Finally, with a `tomoscan' method, we find that one just needs to measure the nucleon densities in $^{208}$Pb starting from $R_{m} = 7.61\pm0.04$ fm to obtain the $\Delta R_{np}$ in hadron scattering experiments, regardless of its interior profile that is hampered by the strong absorption.