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, $r_{\mathrm{skin}}^{208}(newPREX2)=0.278\pm 0.078(\exp )\pm 0.012(theor.)\mathrm{fm}$ and $r_{\mathrm{skin}}^{48}=0.121\pm 0.026(\exp )\pm 0.024(\mathrm{model})$, respectively. We recently determined a neutron-skin value $r_{\mathrm{skin}}^{208}=0.278\pm 0.035$fm from measured reaction cross sections $\ddot{I}{ƒ}_{\mathrm{R}}(\exp )$ 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 $\ddot{I}{ƒ}_{\mathrm{R}}(\exp )$ 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 $r_{\mathrm{skin}}$ and matter and neutron radii, $r_{\mathrm{m}}$ and $r_{\mathrm{n}}$, for ${}^{208}$Pb, ${}^{58}$Ni, ${}^{40,48}$Ca, ${}^{12}$C from the $\ddot{I}{ƒ}_{\mathrm{R}}(\exp )$. 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 $\ddot{I}{ƒ}_{\mathrm{R}}(\exp )$ in $20 \lsim E_{\rm in} \lsim 180$ MeV is $r_{\mathrm{skin}}^{208}(\ddot{I}{ƒ}_{\mathrm{R}})=0.299\pm 0.020$ fm. Our results on $r_{\mathrm{skin}}$ are compared with the previous works. Our result $r_{\mathrm{skin}}^{208}(\ddot{I}{ƒ}_{\mathrm{R}})=0.299\pm 0.020$ fm agrees with $r_{\mathrm{skin}}^{208}(PREX2)=0.283\pm 0.071$ fm. In addition, our result $r_{\mathrm{skin}}^{48}=0.103\pm 0.022$ fm is consistent with the CREX value.