Neutron skin thickness for $^{208}$Pb from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness for $^{48}$Ca, O, N, C isotopes from reaction and interaction cross sections

TL;DR

This paper extracts neutron skin thicknesses for various nuclei using total and reaction cross section data at different energies, employing folding models, and finds results consistent with recent experimental measurements.

Contribution

It introduces a method to determine neutron skin thicknesses from scattering cross sections using advanced folding models, providing results that align with recent experimental data.

Findings

r_skin^{48}(skin)=0.163 ± 0.037 fm for ^48Ca

r_skin=0.267 ± 0.056 fm for ^14N

r_skin^{208}=0.309 ± 0.057 fm for ^208Pb

Abstract

Foster {\it et al.} measured total neutron cross sections $\sigma_{\rm T}$ of n+$^{208}$Pb scattering at $14.137$MeV. Carlson {\it et al.} measured $\sigma_{\rm R}$ for $p$+$^{48}$Ca scattering in $23 \text{--} 48$MeV. Tanaka {\it et al.} measured $\sigma_{\rm I}$ for $^{42\text{--}51}$Ca + $^{12}$C scattering at 280MeV/u. Bagchi {\it et al.} measured the charge-changing (CC) cross sections and determined proton radii $r_{\rm p}({\rm CC})$ for $^{14,15,17 \text{--} 22}$N from the CC cross sections. Kanungo {\it et al.} measured the CC cross sections and extracted $r_{\rm p}({\rm CC})$ for $^{12\text{--} 19}$C. Kaur {\it et al.} measured the CC cross sections and determined $r_{\rm p}({\rm CC})$ for $^{16,18 \text{--} 24}$O. Our 1st aim is to extract $r_{\rm skin}^{208}$ from the the $\sigma_{\rm T}$ of n+$^{208}$Pb scattering at $14.137$MeV. Our 2nd aim is to determine $r_{\rm skin}^{48}({\rm skin})$ from $\sigma_{\rm R}$ on p+$^{48}$Ca scattering in $E_{\rm lab}=23 \text{--} 48$MeV. Our 3rd aim is to find light stable nuclei having nuclei having large $r_{\rm skin}$. We use the Kyushu $g$-matrix folding model for lower $E_{\rm lab}$ and the folding model based on the Love-Franey $t$-matrix for higher $E_{\rm lab}$. We determine $r_{\rm skin}^{48}({\rm skin})=0.163 \pm 0.037{\rm fm}$ from the $\sigma_{\rm R}$ on p+$^{48}$Ca scattering, using the Kyushu $g$-matrix folding model with the D1M-GHFB+AMP proton and neutron densities. We show that D1M-GHFB+AMP is better than D1S-GHFB+AMP for the matter radius and the binding energy. Our skin value is consistent with $r_{\rm skin}^{48}({\rm CREX})$. For C, N, O isotopes, we find that $r_{\rm skin}= 0.267 \pm 0.056$~fm for $^{14}$N and $r_{\rm skin}= 0.197 \pm 0.067$~fm for $^{17}$O. Our value $r_{\rm skin}^{208}=0.309 \pm 0.057$fm agrees with $r_{\rm skin}^{208}({\rm PREX2})$.