Neutron skin thickness of Pb208, Sn116,120,124 , and Ca40 determined from reaction cross sections of He4 scattering

Abstract

Background: We constructed the Kyushu chiral $g$ matrix and confirmed its reliability at $30\ensuremath{\lesssim}{E}_{\mathrm{in}}\ensuremath{\lesssim}100$ MeV and $250\ensuremath{\lesssim}{E}_{\mathrm{in}}\ensuremath{\lesssim}400$ MeV for $^{12}\mathrm{C}$ scattering. Reaction cross-section data of $^{4}\mathrm{He}$ scattering are available for some nuclides including $^{208}\mathrm{Pb}$. The PREX II collaboration reported a thick neutron skin for $^{208}\mathrm{Pb}$.Purpose: Our purpose is to deduce neutron skin thicknesses of $^{208}\mathrm{Pb}$ and some other nuclides from reaction cross sections calculated in terms of the double folding model with the $g$ matrix.Methods: We fold the $g$ matrix and densities given by mean-field calculations. To remedy the weaker constraint of the neutron sector, we renormalize densities so as to reproduce the observed cross sections.Results: We found that a $3.4%$ renormalization is necessary for $^{208}\mathrm{Pb}$. The neutron density obtained from renormalization results in ${R}_{\mathrm{skin}}=0.416\ifmmode\pm\else\textpm\fi{}0.146$ fm by confronting the precision proton radius.Conclusions: Our result is consistent with PREX II and therefore supports larger slope parameter $L$. Results for $^{40}\mathrm{Ca}$ and $^{124}\mathrm{Sn}$ are also consistent with ${R}_{\mathrm{skin}}$ deduced from other experiments. For $^{116,120}\mathrm{Sn}$ the present method gives thicker skins.