A dispersive optical model analysis of $^{208}$Pb generating a neutron-skin prediction beyond the mean field

TL;DR

This study uses a nonlocal dispersive optical model to analyze $^{208}$Pb, predicting a neutron skin thickness of about 0.25 fm and providing insights into nuclear structure beyond mean-field approximations.

Contribution

It introduces a comprehensive dispersive optical model analysis that accurately predicts neutron skin thickness and nucleon correlations in $^{208}$Pb, extending beyond traditional mean-field approaches.

Findings

Neutron skin of $0.25 ext{ fm} \\pm 0.05$

Protons exhibit more correlations than neutrons

Finite-size effects influence neutron skin formation

Abstract

A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{208}$Pb. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, the charge distribution, and the binding energy have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we have determined the charge and matter distributions in $^{208}$Pb. The predicted spectroscopic factors are consistent with results from the $(e,e'p)$ reaction and inelastic-electron-scattering data to very high spin states. Sensible results for the high-momentum content of neutrons and protons are obtained with protons appearing more correlated, in agreement with experiment and \textit{ab initio} calculations of asymmetric matter. A neutron skin of $0.25\pm0.05$ fm is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a non-negligible role in the formation of the neutron skin in finite nuclei.