Background: The neutron skin thickness $R_{ \rm skin}^{ \rm PV}$ of PREX-II is presented in Phys. Rev. Lett. { \bf 126}, 172502 (2021). The reaction cross section $\sigma_R$ is useful to determine the matter radius $R_m$ and $R_{ \rm skin}$. For proton scattering, the reaction cross section $\sigma_R$ are available for $E_{ \rm in} > 400$ MeV. Method and results: We determine $R_n^{ \rm exp}=5.727 \pm 0.071$ fm and $R_m^{ \rm exp}=5.617 \pm 0.044$ fm from $R_p^{ \rm exp}$ = 5.444 fm and $R_{ \rm skin}^{ \rm PV}$. The $R_p^{ \rm GHFB}$ calculated with D1S-GHFB with the angular momentum projection (AMP). agrees with $R_p^{ \rm exp}$. The neutron density calculated with GHFB+AMP is scaled so as to $R_n^{ \rm scaling}=5.727$ fm. The Love-Franey $t$-matrix model with the scaled densities reproduces the data on $\sigma_R$. Aim: Our aim is to find the $\sigma_R$ of proton scattering consistent with $R_{ \rm skin}^{ \rm PV}$. Conclusion: The $\sigma_R$ of proton scattering consistent with $R_{ \rm skin}^{ \rm PV}$ are $\sigma_R^{ \rm exp}$ at $E_{ \rm in} = 534.1, 549, 806$ MeV.
Categories: nucl-th