Study of the neutron skin thickness of ${}^{208}$Pb in mean field models

TL;DR

This study investigates the origin of neutron skin thickness in lead-208 within mean field models, linking it to the symmetry energy slope and nucleon density shapes, with implications for parity-violating electron scattering experiments.

Contribution

It clarifies the relationship between neutron skin origin, symmetry energy slope, and density shape predictions in mean field models, and provides an approximate formula for parity-violating asymmetry.

Findings

Bulk contribution to neutron skin depends on symmetry energy slope.

Surface contribution to neutron skin is model-independent.

An approximate formula relates parity asymmetry to density shape parameters.

Abstract

We study whether the neutron skin thickness $\Delta r_{np}$ of ${}^{208}$Pb originates from the bulk or from the surface of the neutron and proton density distributions in mean field models. We find that the size of the bulk contribution to $\Delta r_{np}$ of ${}^{208}$Pb strongly depends on the slope of the nuclear symmetry energy, while the surface contribution does not. We note that most mean field models predict a neutron density for ${}^{208}$Pb between the halo and skin type limits. We investigate the dependence of parity- violating electron scattering at the kinematics of the PREX experiment on the shape of the nucleon densities predicted by the mean field models for ${}^{208}$Pb. We find an approximate formula for the parity-violating asymmetry in terms of the central radius and the surface diffuseness of the nucleon densities of ${}^{208}$Pb in these models.