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

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 ${\sigma }_{\mathrm{R}}(\mathrm{E}\mathrm{X}\mathrm{P})$ of p+${}^{40,48}$Ca and p+${}^{208}$Pb scattering. As for p+${}^{58}$Ni scattering, ${\sigma }_{\mathrm{R}}(\mathrm{E}\mathrm{X}\mathrm{P})$ are available as a function of incident energy $E_{\mathrm{i}\mathrm{n}}$. Aim: Our aim is to determine matter radius $r_m$ and skin $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}$ for ${}^{58}$Ni from the ${\sigma }_{\mathrm{R}}(\mathrm{E}\mathrm{X}\mathrm{P})$ 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\mathrm{.}For$E_{\rm in}=81$MeV, we define the factor $F$ as $F=\sigma_{\rm R}({\rm EXP})/\sigma_{\rm R}({\rm AMP})=0.9775$\mathrm{.}The$F\sigma_{\rm R}({\rm AMP})$ be much the same as the center values of ${\sigma }_{\mathrm{R}}(\mathrm{E}\mathrm{X}\mathrm{P})$ in $8.8\le E_{\mathrm{i}\mathrm{n}}\le 81$MeV. We then determine $r_{\mathrm{m}}(\mathrm{E}\mathrm{X}\mathrm{P})$ from the center values of $\sigma_{\rm R}({\rm EXP})$,using$\sigma_{\rm R}({\rm EXP})=C r_{m}^{2}({\rm EXP})$with$C=r_{m}^{2}({\rm AMP})/ (F\sigma_{\rm R}({\rm AMP}))$\mathrm{.}The$r_{m}({\rm EXP})$thusobtainedareaveragedover$E_{\rm in}$\mathrm{.}Theaveragedvalueis$r_{m}({\rm EXP})=3.697$fm\mathrm{.}Eventually,weobtain$r_{\rm skin}({\rm EXP})=0.023$fmfrom$r_{\rm m}=3.697$fmand$r_p({\rm EXP})=3.685$fm of electron scattering.