Origin of the neutron skin thickness of 208Pb in nuclear mean-field models

TL;DR

This paper investigates the origin of the neutron skin thickness in 208Pb within nuclear mean-field models, revealing its dependence on the symmetry energy's stiffness and distinguishing bulk versus surface contributions.

Contribution

It provides a detailed analysis of how the neutron skin thickness arises from bulk and surface effects, linked to the symmetry energy properties, and offers a formula for parity-violating asymmetry predictions.

Findings

Bulk contribution dominates in stiff symmetry energy models.

Surface contribution becomes significant with soft or supersoft symmetry energy.

Most models predict a mixed-type neutron distribution in 208Pb.

Abstract

We study whether the neutron skin thickness (NST) of 208Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to NST arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical relativistic models, predict a bulk contribution in NST of 208Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that NST of 208Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of NST of 208Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of NST. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208Pb nucleon densities.