Neutron skin $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}^{48}$ determined from reaction cross section of proton+${}^{48}$Ca scattering

{\bf Background:} Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with GHFB+AMP, we determined $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}^{208}=0.25$fm from the central values of ${\sigma }_{\mathrm{R}}$ of p+${}^{208}$Pb scattering in $E_{\mathrm{i}\mathrm{n}}=40-81$MeV. The high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}^{48}(E1\mathrm{p}\mathrm{E})=0.14-0.20$fm. The data on ${\sigma }_{\mathrm{R}}$ are available as a function of $E_{\mathrm{i}\mathrm{n}}$ for $p$+${}^{48}$Ca scattering. {\bf Aim:} Our aim is to determine $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}^{48}$ from the central values of ${\sigma }_{\mathrm{R}}$ for $p$+${}^{48}$Ca scattering by using the folding model. {\bf Results:} As for ${}^{48}$Ca, we determine $r_n(E1{\rm pE})=3.56$fmfromthecentralvalue0.17fmof$r_{\rm skin}^{48}(E1{\rm pE})$and$r_p({\rm EXP})=3.385$fmofelectronscattering,andevaluate$r_m(E1{\rm pE})=3.485$fmfromthe$r_n(E1{\rm pE})$andthe$r_p({\rm EXP})$ of electron scattering. The folding model with GHFB+AMP densities reproduces $\sigma_{\rm R}$in$23 \leq E_{\rm in} \leq 25.3$MeVinone-$\sigma$ level, but slightly overestimates the central values of ${\sigma }_{\mathrm{R}}$ there. In $23 \leq E_{\rm in} \leq 25.3$MeV, the small deviation allows us to scale the GHFB+AMP densities to the central values of $r_p(\mathrm{E}\mathrm{X}\mathrm{P})$ and $r_n(E1\mathrm{p}\mathrm{E})$. The ${\sigma }_{\mathrm{R}}(E1\mathrm{p}\mathrm{E})$ obtained with the scaled densities almost reproduce the central values of ${\sigma }_{\mathrm{R}}$ when $E_{\mathrm{i}\mathrm{n}}=23-25.3$MeV, so that the ${\sigma }_{\mathrm{R}}(\mathrm{G}\mathrm{H}\mathrm{F}\mathrm{B}+\mathrm{A}\mathrm{M}\mathrm{P})$ and the $\sigma_{\rm R}(E1{\rm pE})$arein1-$\sigma$of$\sigma_{\rm R}$there\mathrm{.}In$E_{\rm in}=23-25.3$MeV, we determine the $r_m(\mathrm{E}\mathrm{X}\mathrm{P})$ from the central values of ${\sigma }_{\mathrm{R}}$ and take the average for the $r_m(\mathrm{E}\mathrm{X}\mathrm{P})$. The averaged value is $r_m(\mathrm{E}\mathrm{X}\mathrm{P})=3.471$fm. Eventually, we obtain $r_{\rm skin}^{48}({\rm EXP})=0.146$fmfrom$r_{m}({\rm EXP})=3.471$fmand$r_p({\rm EXP})=3.385$fm.