Chiral $g$-matrix model for reaction cross section of proton+$^{40}$Ca scattering: Matter radius $r_{rm m}$ and skin $r_{rm skin}$ for $^{40}$Ca

For $^{48}$Ca, we determined $r_{m}$fm and $r_{rm skin}$fm from the central values of $sigma_{rm R}({rm EXP})$ of p+$^{48}$Ca scattering, using the chiral (Kyushu) $g$-matrix folding model with the GHFB+AMP densities. For $^{40}$Ca, Zenihiro {it et al.} determined $r_n({rm RCNP})=3.375$~fm and $r_{rm skin}({rm RCNP})=-0.01 pm 0.023$fm from the differential cross section and the analyzing powers for p+$^{40}$Ca scattering. For $^{40}$Ca, $sigma_{rm R}({rm EXP})$ are available with high accuracy. Our aim is to determine matter radius $r_{m}^{40}$ and skin $r_{rm skin}^{40}$ from $sigma_{rm R}({rm EXP})$ by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. We first determine $r_m({rm RCNP})=3.380$fm from the central value -0.01~fm of $r_{rm skin}({rm RCNP})$ and $r_p({rm RCNP})=3.385$fm. The folding model with the GHFB+AMP densities reproduces $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV, in 2-$sigma$ level. We scale the GHFB+AMP densities so as to $r_p({rm AMP})=r_p({rm RCNP})$ and $r_n({rm AMP})=r_n({rm RCNP})$. The $sigma_{rm R}({rm RCNP})$ thus obtained agrees with the original one $sigma_{rm R}({rm AMP})$ for each $E_{rm in}$. For $E_{rm in}=180$MeV, we define $F$ as $F=sigma_{rm R}({rm EXP})/sigma_{rm R}({rm AMP})=0.929$. The $Fsigma_{rm R}({rm AMP})$ be much the same as the center values of $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV. We then determine $r_{rm m}^{40}({rm EXP})$ 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 $r_{m}({rm EXP})$ are averaged over $E_{rm in}$. The averaged value is $r_{m}({rm EXP})=3.380$fm. Eventually, we obtain $r_{rm skin}({rm EXP})=-0.01$fm from the averaged $r_{rm m}({rm EXP})$~fm and $r_p({rm PCNP})=3.385$fm.