Neutron skin $r_{\mathrm{skin}}^{48}$ determined from reaction cross section of proton+${}^{48}$Ca scattering

Abstract

{\bf Background:} Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with GHFB+AMP, we determined $r_{\mathrm{skin}}^{208}=0.25$fm from the central values of $\ddot{I}{ƒ}_{\mathrm{R}}$ of p+${}^{208}$Pb scattering in $E_{\mathrm{in}}=40-81$MeV. The high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{\mathrm{skin}}^{48}(E1\mathrm{pE})=0.14-0.20$fm. The data on $\ddot{I}{ƒ}_{\mathrm{R}}$ are available as a function of $E_{\mathrm{in}}$ for $p$+${}^{48}$Ca scattering. {\bf Aim:} Our aim is to determine $r_{\mathrm{skin}}^{48}$ from the central values of $\ddot{I}{ƒ}_{\mathrm{R}}$ for $p$+${}^{48}$Ca scattering by using the folding model. {\bf Results:} As for ${}^{48}$Ca, we determine $r_n(E1\mathrm{pE})=3.56$fm from the central value 0.17fm of $r_{\mathrm{skin}}^{48}(E1\mathrm{pE})$ and $r_p(\mathrm{EXP})=3.385$fm of electron scattering, and evaluate $r_m(E1\mathrm{pE})=3.485$fm from the $r_n(E1\mathrm{pE})$ and the $r_p(\mathrm{EXP})$ of electron scattering. The folding model with GHFB+AMP densities reproduces $\ddot{I}{ƒ}_{\mathrm{R}}$ in $23\le E_{\mathrm{in}}\le 25.3$ MeV in one-$\ddot{I}ƒ$ level, but slightly overestimates the central values of $\ddot{I}{ƒ}_{\mathrm{R}}$ there. In $23\le E_{\mathrm{in}}\le 25.3$MeV, the small deviation allows us to scale the GHFB+AMP densities to the central values of $r_p(\mathrm{EXP})$ and $r_n(E1\mathrm{pE})$. The $\ddot{I}{ƒ}_{\mathrm{R}}(E1\mathrm{pE})$ obtained with the scaled densities almost reproduce the central values of $\ddot{I}{ƒ}_{\mathrm{R}}$ when $E_{\mathrm{in}}=23-25.3$MeV, so that the $\ddot{I}{ƒ}_{\mathrm{R}}(\mathrm{GHFB}+\mathrm{AMP})$ and the $\ddot{I}{ƒ}_{\mathrm{R}}(E1\mathrm{pE})$ are in 1-$\ddot{I}ƒ$ of $\ddot{I}{ƒ}_{\mathrm{R}}$ there. In $E_{\mathrm{in}}=23-25.3$MeV, we determine the $r_m(\mathrm{EXP})$ from the central values of $\ddot{I}{ƒ}_{\mathrm{R}}$ and take the average for the $r_m(\mathrm{EXP})$. The averaged value is $r_m(\mathrm{EXP})=3.471$fm. Eventually, we obtain $r_{\mathrm{skin}}^{48}(\mathrm{EXP})=0.146$fm from $r_m(\mathrm{EXP})=3.471$fm and $r_p(\mathrm{EXP})=3.385$fm.

arXiv admin note: text overlap with arXiv:2010.02450