Determination of matter radius and neutron skin of $^{58}$Ni from reaction cross section of proton+$^{58}$Ni scattering based on chiral $g$-matrix model

Abstract

Background: Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with Gogny-HFB (GHFB) with the angular momentum projection (AMP), we determined the central values of matter radius and neutron skin from the central values of reaction cross sections $\sigma_{\rm R}({\rm EXP})$ of p+$^{40,48}$Ca and p+$^{208}$Pb scattering. As for p+$^{58}$Ni scattering, $\sigma_{\rm R}({\rm EXP})$ are available as a function of incident energy $E_{\rm in}$. Aim: Our aim is to determine matter radius $r_{m}$ and skin $r_{\rm skin}$ for $^{58}$Ni from the $\sigma_{\rm R}({\rm EXP})$ of p+$^{58}$Ni scattering by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. Results: For p+$^{58}$Ni scattering, the Kyushu $g$-matrix folding model with the GHFB+AMP densities reproduces $\sigma_{\rm R}({\rm EXP})$ in $8.8 \leq E_{\rm in} \leq 81$MeV. For $E_{\rm in}=81$MeV, we define the factor $F$ as $F=\sigma_{\rm R}({\rm EXP})/\sigma_{\rm R}({\rm AMP})=0.9775$. The $F\sigma_{\rm R}({\rm AMP})$ be much the same as the center values of $\sigma_{\rm R}({\rm EXP})$ in $8.8 \leq E_{\rm in} \leq 81$MeV. We then determine $r_{\rm m}({\rm EXP})$ from the center values of $\sigma_{\rm R}({\rm EXP})$, using $\sigma_{\rm R}({\rm EXP})=C r_{m}^{2}({\rm EXP})$ with $C=r_{m}^{2}({\rm AMP})/ (F\sigma_{\rm R}({\rm AMP}))$. The $r_{m}({\rm EXP})$ thus obtained are averaged over $E_{\rm in}$. The averaged value is $r_{m}({\rm EXP})=3.697$fm. Eventually, we obtain $r_{\rm skin}({\rm EXP})=0.023$fm from $r_{\rm m}=3.697$fm and $r_p({\rm EXP})=3.685$fm of electron scattering.