Neutron Skin Thickness of Ca48 from a Nonlocal Dispersive Optical-Model Analysis

Abstract

A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in 48 Ca. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator resulting from these self-energies, we have determined the charge and neutron matter distributions in 48 Ca. A best fit neutron skin of 0.249±0.023 fm is deduced, but values up to 0.33 fm are still consistent. The energy dependence of the total neutron cross sections is shown to have strong sensitivity to the skin thickness.A fundamental question in nuclear physics is how the constituent neutrons and protons are distributed in the nucleus. In particular, for a nucleus which has a large excess of neutrons over protons, are the extra neutrons distributed evenly over the nuclear volume or is this excess localized in the periphery of the nucleus forming a neutron skin? A quantitative measure is provided by the neutron-skin thickness ∆r np defined as the difference between neutron and proton rms radii, i.e., ∆r np = r n − r p .The nuclear symmetry energy which characterizes the variation of the binding energy as a function of neutronproton asymmetry, opposes the creation of nuclear matter with excesses of either type of nucleon. The extent of the neutron skin is determined by the relative strengths of the symmetry energy between the central near-saturation and peripheral less-dense regions. Therefore ∆r np is a measure of the density dependence of the symmetry energy around saturation [1][2][3][4]. This dependence is very important for determining many nuclear properties, including masses, radii, and the location of the drip lines in the chart of nuclides. Its importance extends to astrophysics for understanding supernovae and neutron stars [5,6], and to heavy-ion reactions [7].Given the importance of the neutron-skin thickness in these various areas of research, a large number of studies (both experimental and theoretical) have been devoted to it [8]. While the value of r p can be determined quite accurately from electron scattering [9], the experimental determinations of r n are typically model dependent [8]. However, the use of parity-violating electron scattering does allow for a nearly model-independent extraction of this quantity [10]. The present value for 208 Pb extracted with this method from the PREX collaboration yields a skin thickness of ∆r np =0.33 +0.16−0.18 fm [11]. Future electron-scattering measurements are expected to reduce the experimental uncertainty.In this work we present an alternative method of determining r n using a dispersive-optical-model (DOM) analysis of bound and scattering data to constrain the nucleon self-energy Σ ℓj . This self-energy is a complex and nonlocal potential that unites the nuclear structure and reaction domains [12,13]. The DOM was originally developed by Mahaux and Sarto...

Dispersive optical model analysis of Pb208 generating a neutron-skin prediction beyond the mean field

“…Our analysis of 208 Pb is similar to that of our previous work on 48 Ca in Ref. [23], reporting a neutron skin of ∆r np = 0.249 ± 0.023 fm in 48 Ca. A detailed comparison of the neutrons skins of 208 Pb and 48 Ca will be presented in this article.…”

“…we present both the DOM results for48 Ca[23] and the current one for 208 Pb represented by a shaded rectangle. The figure is adapted from Ref [62].…”

Electroweak probes of ground state densities

“…Specifically, we want to explore the limits that PREX-II and CREX may impose on the 0 0.5 1 1. 48 Ca, but now including the predictions from the dispersive optical model [75] and the NNLO sat interaction [76]. The location of the CREX point is arbitrary but includes realistic experimental errors.…”

Investigating the link between proton reaction cross sections and the quenching of proton spectroscopic factors in 48Ca

“…The remainder of the fit did not change significantly from Ref. [24]. The parameterization of the 48 Ca self-energy as well as the updated parameters are presented in the supplementary material.…”