Neutron-skin values and matter and neutron radii determined from reaction cross sections of proton scattering on $^{12}$C, $^{40,48}$Ca, $^{58}$Ni, $^{208}$Pb

Abstract

Very lately, the PREX and the CREX collaboration present skin values, $r_{\rm skin}^{208}({\rm newPREX2}) =0.278 \pm 0.078\ {\rm (exp)} \pm 0.012\ {\rm (theor.)}\,{\rm fm}$ and $r_{\rm skin}^{48}=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$, respectively. We recently determined a neutron-skin value $r_{\rm skin}^{208}=0.278 \pm 0.035$fm from measured reaction cross sections $\sigma_{\rm R}({\rm exp})$ of p+$^{208}$Pb scattering in a range of incident energies 10 \lsim E_{\rm in} \lsim 100 MeV where the chiral (Kyushu) $g$-matrix folding model is reliable for $^{12}$C+$^{12}$C scattering. The data $\sigma_{\rm R}({\rm exp})$ are available for proton scattering on $^{58}$Ni, $^{40,48}$Ca, $^{12}$C targets. Our first aim is to test the Kyushu $g$-matrix folding model for p+$^{208}$Pb scattering in 20 \lsim E_{\rm in} \lsim 180 MeV. Our second aim is to determine skin values $r_{\rm skin}$ and matter and neutron radii, $r_{\rm m}$ and $r_{\rm n}$, for $^{208}$Pb, $^{58}$Ni, $^{40,48}$Ca, $^{12}$C from the $\sigma_{\rm R}({\rm exp})$. Our method is the Kyushu $g$-matrix folding model with the densities scaled from the D1S-GHFB+AMP densities, where D1S-GHFB+AMP stands for Gogny-D1S HFB (GHFB) with the angular momentum projection (AMP). As for proton scattering, we find that our model is reliable in 20 \lsim E_{\rm in} \lsim 180 MeV. For $^{208}$Pb, the skin value deduced from $\sigma_{\rm R}({\rm exp})$ in 20 \lsim E_{\rm in} \lsim 180 MeV is $r_{\rm skin}^{208}(\sigma_{\rm R})=0.299 \pm 0.020$ fm. Our results on $r_{\rm skin}$ are compared with the previous works. Our result $r_{\rm skin}^{208}(\sigma_{\rm R}) = 0.299 \pm 0.020$ fm agrees with $r_{\rm skin}^{208}({\rm PREX2}) = 0.283\pm 0.071$ fm. In addition, our result $r_{\rm skin}^{48}=0.103 \pm 0.022$ fm is consistent with the CREX value