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 $sigma_{rm R}({rm EXP})$ 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 $Fsigma_{rm R}({rm AMP})$ 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 $C=r_{m}^{2}({rm AMP})/ (Fsigma_{rm R}({rm AMP}))$. 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.