Neutron skin thickness for ${}^{nat}$Pb, ${}^{159}$Tb and effects of deformation on matter radii for Mg, Na, Ar isotopes

Data on reaction cross section ${\sigma }_{\mathrm{R}}$ of proton scattering are available for ${}^{nat}$Pb (natural lead) and ${}^{159}$Tb. In addition, data on ${\sigma }_{\mathrm{R}}$ and/or interaction ones ${\sigma }_{\mathrm{I}}$ are available for Mg, Na, Ar isotopes. Our aim is to determine neutron skin thickness $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}$ for ${}^{nat}$Pb, ${}^{159}$Tb and to investigate effects of deformation for Mg, Na, Ar isotopes. We use the chiral (Kyushu) $g$-matrix folding model for lower energies and the folding model based on the Love-Franey (LF) $t$-matrix for higher energies. For ${}^{159}$Tb, our skin value is $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}=0.273\pm 0.073$~fm. As for ${}^{24}$Mg, our matter radius $r_{\mathrm{m}}({\sigma }_{\mathrm{R}})=3.03\pm 0.08$~fm determined from ${\sigma }_{\mathrm{R}}$ includes effects of deformation, whereas the corresponding $r_{\mathrm{m}}({\sigma }_{\mathrm{I}})=2.79\pm 0.15$~fm does not. Effects of deformation are seen for Mg isotopes, ${}^{21,23}$Na, ${}^{40}$Ar. Our result $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}=0.271\pm 0.008$~fm for ${}^{nat}$Pb agrees with $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}^{208}(\mathrm{P}\mathrm{R}\mathrm{E}\mathrm{X}\text{-}\mathrm{I}\mathrm{I})=0.283\pm 0.071$~fm for ${}^{208}$Pb, where we assume $A=208$ for ${}^{nat}$Pb.