Second and fourth moments of the charge density and neutron-skin thickness of atomic nuclei

TL;DR

This paper introduces a method to estimate neutron-skin thickness of nuclei using moments of charge distribution, highlighting the importance of proton moments and their correlations, but faces limitations due to uncertainties in proton moments.

Contribution

The paper proposes a novel approach utilizing second and fourth moments of charge distribution and correlations among proton moments to determine neutron-skin thickness.

Findings

Proposed a method linking charge moments to neutron-skin thickness.

Identified the dominant uncertainty from proton fourth moments.

Provided analytic expressions for spin-orbit contributions to charge moments.

Abstract

A method is presented to extract the neutron-skin thickness of atomic nuclei from the second and fourth moments of the electric charge distribution. We show that the value of the proton fourth moment must be independently known in order to estimate the neutron skin thickness experimentally. To overcome this problem, we propose the use of a strong linear correlation among the second and fourth moments of the proton distribution as calculated with several energy density functionals of common use. We take special care in estimating the errors associated with the different contributions to the neutron radius and show, for the first time, the analytic expressions for the spin-orbit contribution to the charge fourth moments of neutrons and protons. To reduce the uncertainty on the extraction of the neutron radius, two neighboring even-even isotopes are used. Nevertheless, the error on the fourth moment of the proton distribution, even if determined or assumed with large accuracy, dominates and prevents the present method from being applied for a sound determination of the neutron skin thickness.