Determination of matter radius and neutron skin of ${}^{58}$Ni from reaction cross section of proton+${}^{58}$Ni scattering based on chiral $g$-matrix model

Abstract

Background: Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with Gogny-HFB (GHFB) with the angular momentum projection (AMP), we determined the central values of matter radius and neutron skin from the central values of reaction cross sections $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})$ of p+${}^{40,48}$Ca and p+${}^{208}$Pb scattering. As for p+${}^{58}$Ni scattering, $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})$ are available as a function of incident energy $E_{\mathrm{in}}$. Aim: Our aim is to determine matter radius $r_m$ and skin $r_{\mathrm{skin}}$ for ${}^{58}$Ni from the $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})$ of p+${}^{58}$Ni scattering by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. Results: For p+${}^{58}$Ni scattering, the Kyushu $g$-matrix folding model with the GHFB+AMP densities reproduces $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})$ in $8.8\le E_{\mathrm{in}}\le 81$MeV. For $E_{\mathrm{in}}=81$MeV, we define the factor $F$ as $F=\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})/\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{AMP})=0.9775$. The $F\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{AMP})$ be much the same as the center values of $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})$ in $8.8\le E_{\mathrm{in}}\le 81$MeV. We then determine $r_{\mathrm{m}}(\mathrm{EXP})$ from the center values of $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})$, using $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{EXP})=C{r}_m^2(\mathrm{EXP})$ with $C=r_m^2(\mathrm{AMP})/(F\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{AMP}))$. The $r_m(\mathrm{EXP})$ thus obtained are averaged over $E_{\mathrm{in}}$. The averaged value is $r_m(\mathrm{EXP})=3.697$fm. Eventually, we obtain $r_{\mathrm{skin}}(\mathrm{EXP})=0.023$fm from $r_{\mathrm{m}}=3.697$fm and $r_p(\mathrm{EXP})=3.685$fm of electron scattering.

arXiv admin note: substantial text overlap with arXiv:2011.12235, arXiv:2012.01063