Neutron skin thickness for $^{nat}$Pb, $^{159}$Tb and effects of deformation on matter radii for Mg, Na, Ar isotopes

TL;DR

This study determines neutron skin thicknesses and investigates deformation effects on matter radii for various isotopes using reaction cross section data and folding models, providing insights into nuclear structure and neutron distribution.

Contribution

It introduces a combined use of chiral and Love-Franey folding models to accurately determine neutron skin thickness and deformation effects for multiple isotopes, including lead and terbium.

Findings

Neutron skin thickness for $^{159}$Tb is $0.273 \, ext{fm}$.

Deformation effects influence matter radius measurements for Mg, Na, Ar isotopes.

Neutron skin for $^{nat}$Pb agrees with PREX-II results.

Abstract

Data on reaction cross section $\sigma_{\rm R}$ of proton scattering are available for $^{nat}$Pb (natural lead) and $^{159}$Tb. In addition, data on $\sigma_{\rm R}$ and/or interaction ones $\sigma_{\rm I}$ are available for Mg, Na, Ar isotopes. Our aim is to determine neutron skin thickness $r_{\rm skin}$ for $^{nat}$Pb, $^{159}$Tb and to investigate effects of deformation for Mg, Na, Ar isotopes. We use the chiral (Kyushu) $g$-matrix folding model for lower energies and the folding model based on the Love-Franey (LF) $t$-matrix for higher energies. For $^{159}$Tb, our skin value is $r_{\rm skin}=0.273 \pm 0.073$~fm. As for $^{24}$Mg, our matter radius $r_{\rm m}(\sigma_{\rm R})=3.03 \pm 0.08$~fm determined from $\sigma_{\rm R}$ includes effects of deformation, whereas the corresponding $r_{\rm m}(\sigma_{\rm I})=2.79 \pm 0.15$~fm does not. Effects of deformation are seen for Mg isotopes, $^{21, 23}$Na, $^{40}$Ar. Our result $r_{\rm skin}=0.271 \pm 0.008$~fm for $^{nat}$Pb agrees with $r_{\rm skin}^{208}({\rm PREX\text{-}II}) = 0.283\pm 0.071$~fm for $^{208}$Pb, where we assume $A=208$ for $^{nat}$Pb.