Neutron skin thickness of ${}^{116,118,120,122,124}$Sn determined from reaction cross sections of proton scattering

Abstract

The cross sections of SDR in the Sb isotopes have been measured. Within the model used, the neutron-skin thicknesses $r_{\mathrm{skin}}(\exp )$ deduced $0.12\pm 0.06$fm for ${}^{116}$Sn, $0.13\pm 0.06$fm for ${}^{118}$Sn, $0.18\pm 0.07$fm for ${}^{120}$Sn, $0.22\pm 0.07$fm for ${}^{122}$Sn, $0.19\pm 0.07$fm for ${}^{124}$Sn. We tested the chiral (Kyushu) $g$-matrix folding model for ${}^{12}$C+${}^{12}$C scattering, and found that the Kyushu $g$-matrix folding model is reliable for reaction cross sections $\ddot{I}{ƒ}_{\mathrm{R}}$ in $30<E_{\mathrm{in}}<100$MeV and $250<E_{\mathrm{in}}<400$MeV. We determine neutron skin thickness $r_{\mathrm{skin}}(\exp )$, using measured $\ddot{I}{ƒ}_{\mathrm{R}}$ of ${}^4$He+${}^{116,120,224}$Sn scattering. The results are $r_{\mathrm{skin}}(\exp )=0.242\pm 0.140$fm for ${}^{116}$Sn, $r_{\mathrm{skin}}(\exp )=0.377\pm 0.140$fm for ${}^{120}$Sn, $r_{\mathrm{skin}}(\exp )=0.180\pm 0.142$fm for ${}^{124}$Sn. The $\ddot{I}{ƒ}_{\mathrm{R}}$ are available for proton scattering on ${}^{116,118,120,122,124}$Sn with high accuracy. Our aim is to determine $r_{\mathrm{skin}}(\exp )$ for ${}^{116,118,120,122,124}$Sn with small errors by using the Kyushu $g$-matrix folding model. Our model is the folding model with the densities scaled from the D1S-GHFB+AMP neutron density. The proton radii of D1S-GHFB+AMP agree with those calculated with the isotope shift method based on the electron scattering. We then scale the neutron densities so as to reproduce the $\ddot{I}{ƒ}_{\mathrm{R}}(\exp )$. In $30<E_{\mathrm{in}}<65$MeV, we determine $r_{\mathrm{skin}}(\exp )$ from measured $\ddot{I}{ƒ}_{\mathrm{R}}$. The values are $r_{\mathrm{skin}}(\exp )=0.118\pm 0.021$~fm for ${}^{116}$Sn, $0.112\pm 0.021$fm for ${}^{118}$Sn, $0.124\pm 0.021$fm for ${}^{120}$Sn, $0.156\pm 0.022$fm for ${}^{124}$Sn. As for ${}^{122}$Sn, the skin value in $30<E_{\mathrm{in}}<50$MeV is $0.122\pm 0.024$fm. Our results are consistent with the previous values.

arXiv admin note: text overlap with arXiv:2211.16688