Neutron skin in ${}^{48}$Ca determined from p+${}^{48}$Ca and ${}^{48}$Ca+${}^{12}$C scattering

Abstract

In our previous paper, we determined $r_{\mathrm{skin}}^{208}(\exp )=0.278\pm 0.035$~fm from $\ddot{I}{ƒ}_{\mathrm{R}}$ for p+${}^{208}$Pb scattering, using the Kyushu (chiral) $g$-matrix folding model with the densities calculated with D1S-GHFB with the angular momentum projection (AMP). The value agrees with that of PREX2. Reaction cross sections $\ddot{I}{ƒ}_{\mathrm{R}}$ are available for p+${}^{48}$Ca scattering, whereas interaction cross sections $\ddot{I}{ƒ}_{\mathrm{I}}$ are available for ${}^{48}$Ca + ${}^{12}$C scattering. As for ${}^{48}$Ca, the high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{\mathrm{skin}}^{48}(E1\mathrm{pE})=0.14\sim 0.20\mathrm{fm}$. We determine $r_{\mathrm{skin}}^{48}(\exp )$ from the data on $\ddot{I}{ƒ}_{\mathrm{R}}$ for p+${}^{48}$Ca scattering and from the data on $\ddot{I}{ƒ}_{\mathrm{I}}$ for ${}^{48}$Ca+${}^{12}$C scattering. We use the Kyushu $g$-matrix folding model with the densities calculated with the D1M-GHFB+AMP densities. The D1M-GHFB+AMP proton and neutron densities are scaled so as to reproduce the data under the condition that the radius $r_{\mathrm{p}}$ of the scaled proton density equals the data $r_{\mathrm{p}}(\exp )$ determined from the electron scattering. We deduce skin values $r_{\mathrm{skin}}=r_{\mathrm{n}}(\exp )-r_{\mathrm{p}}(\exp )$ from the resulting $r_{\mathrm{n}}(\exp )$ and the $r_{\mathrm{p}}(\exp )$ determined from electron scattering. The same procedure is taken for D1S-GHFB+AMP. We regard $r_{\mathrm{skin}}^{48}(E1\mathrm{pE})$ as a reference skin value. Using the reference skin value and taking D1M-GHFB+AMP, we determine $r_{\mathrm{skin}}^{48}(\exp )=0.158\pm 0.025$~fm for p+${}^{48}$Ca scattering and $0.160\pm 0.058$~fm for ${}^{48}$Ca + ${}^{12}$C scattering. We take the weighted mean and its error for the two skin values. The result is $r_{\mathrm{skin}}^{48}(\exp )=0.158\pm (0.023{)}_{\exp }\pm (0.012{)}_{\mathrm{th}}\mathrm{fm}$.

arXiv admin note: substantial text overlap with arXiv:2107.06441