Neutron skin $r_{\rm skin}^{48}$ determined from reaction cross section of proton+$^{48}$Ca scattering

Abstract

{\bf Background:} Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with GHFB+AMP, we determined $r_{\rm skin}^{208}=0.25$fm from the central values of $\sigma_{\rm R}$ of p+$^{208}$Pb scattering in $E_{\rm in}=40-81$MeV. The high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{\rm skin}^{48}(E1{\rm pE}) =0.14-0.20$fm. The data on $\sigma_{\rm R}$ are available as a function of $E_{\rm in}$ for $p$+$^{48}$Ca scattering. {\bf Aim:} Our aim is to determine $r_{\rm skin}^{48}$ from the central values of $\sigma_{\rm R}$ for $p$+$^{48}$Ca scattering by using the folding model. {\bf Results:} As for $^{48}$Ca, we determine $r_n(E1{\rm pE})=3.56$fm from the central value 0.17fm of $r_{\rm skin}^{48}(E1{\rm pE})$ and $r_p({\rm EXP})=3.385$fm of electron scattering, and evaluate $r_m(E1{\rm pE})=3.485$fm from the $r_n(E1{\rm pE})$ and the $r_p({\rm EXP})$ of electron scattering. The folding model with GHFB+AMP densities reproduces $\sigma_{\rm R}$ in $23 \leq E_{\rm in} \leq 25.3$ MeV in one-$\sigma$ level, but slightly overestimates the central values of $\sigma_{\rm R}$ 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 $r_p({\rm EXP})$ and $r_n(E1{\rm pE})$. The $\sigma_{\rm R}(E1{\rm pE})$ obtained with the scaled densities almost reproduce the central values of $\sigma_{\rm R}$ when $E_{\rm in}=23-25.3$MeV, so that the $\sigma_{\rm R}({\rm GHFB+AMP})$ and the $\sigma_{\rm R}(E1{\rm pE})$ are in 1-$\sigma$ of $\sigma_{\rm R}$ there. In $E_{\rm in}=23-25.3$MeV, we determine the $r_{m}({\rm EXP})$ from the central values of $\sigma_{\rm R}$ and take the average for the $r_{m}({\rm EXP})$. The averaged value is $r_{m}({\rm EXP})=3.471$fm. Eventually, we obtain $r_{\rm skin}^{48}({\rm EXP})=0.146$fm from $r_{m}({\rm EXP})=3.471$fm and $r_p({\rm EXP})=3.385$fm.