Neutron skin thickness for ${}^{208}$Pb from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness for ${}^{48}$Ca, O, N, C isotopes from reaction and interaction cross sections

Abstract

Foster {\it et al.} measured total neutron cross sections $\ddot{I}{ƒ}_{\mathrm{T}}$ of n+${}^{208}$Pb scattering at $14.137$MeV. Carlson {\it et al.} measured $\ddot{I}{ƒ}_{\mathrm{R}}$ for $p$+${}^{48}$Ca scattering in $23\text{–}48$MeV. Tanaka {\it et al.} measured $\ddot{I}{ƒ}_{\mathrm{I}}$ for ${}^{42\text{–}51}$Ca + ${}^{12}$C scattering at 280MeV/u. Bagchi {\it et al.} measured the charge-changing (CC) cross sections and determined proton radii $r_{\mathrm{p}}(\mathrm{CC})$ for ${}^{14,15,17\text{–}22}$N from the CC cross sections. Kanungo {\it et al.} measured the CC cross sections and extracted $r_{\mathrm{p}}(\mathrm{CC})$ for ${}^{12\text{–}19}$C. Kaur {\it et al.} measured the CC cross sections and determined $r_{\mathrm{p}}(\mathrm{CC})$ for ${}^{16,18\text{–}24}$O. Our 1st aim is to extract $r_{\mathrm{skin}}^{208}$ from the the $\ddot{I}{ƒ}_{\mathrm{T}}$ of n+${}^{208}$Pb scattering at $14.137$MeV. Our 2nd aim is to determine $r_{\mathrm{skin}}^{48}(\mathrm{skin})$ from $\ddot{I}{ƒ}_{\mathrm{R}}$ on p+${}^{48}$Ca scattering in $E_{\mathrm{lab}}=23\text{–}48$MeV. Our 3rd aim is to find light stable nuclei having nuclei having large $r_{\mathrm{skin}}$. We use the Kyushu $g$-matrix folding model for lower $E_{\mathrm{lab}}$ and the folding model based on the Love-Franey $t$-matrix for higher $E_{\mathrm{lab}}$. We determine $r_{\mathrm{skin}}^{48}(\mathrm{skin})=0.163\pm 0.037\mathrm{fm}$ from the $\ddot{I}{ƒ}_{\mathrm{R}}$ on p+${}^{48}$Ca scattering, using the Kyushu $g$-matrix folding model with the D1M-GHFB+AMP proton and neutron densities. We show that D1M-GHFB+AMP is better than D1S-GHFB+AMP for the matter radius and the binding energy. Our skin value is consistent with $r_{\mathrm{skin}}^{48}(\mathrm{CREX})$. For C, N, O isotopes, we find that $r_{\mathrm{skin}}=0.267\pm 0.056$~fm for ${}^{14}$N and $r_{\mathrm{skin}}=0.197\pm 0.067$~fm for ${}^{17}$O. Our value $r_{\mathrm{skin}}^{208}=0.309\pm 0.057$fm agrees with $r_{\mathrm{skin}}^{208}(PREX2)$.