Neutron skin thickness of ${}^{208}$Pb, ${}^{116,120,124}$Sn, and ${}^{40}$Ca determined from reaction cross sections of ${}^4$He scattering

Abstract

[Background] We constructed the Kyushu chiral $g$-matrix and confirmed its reliability at $30\lesssim E_{\mathrm{in}}\lesssim 100$~MeV and $250\lesssim E_{\mathrm{in}}\lesssim 400$~MeV for ${}^{12}$C scattering. Reaction cross section data of ${}^4$He scattering are available for some nuclides including ${}^{208}$Pb. PREX II collaboration reported a thick neutron skin for ${}^{208}$Pb. [Purpose] Our purpose is to deduce neutron skin thicknesses of ${}^{208}$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. In order to remedy less-constrainedness 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 ${}^{208}$Pb. The neutron density obtained from renormalization results in $R_{\mathrm{skin}}=$ 0.416$\pm$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 ${}^{40}$Ca and ${}^{124}$Sn are also consistent with $R_{\mathrm{skin}}$ deduced from other experiments. For ${}^{116,120}$Sn the present method gives thicker skins.

arXiv admin note: substantial text overlap with arXiv:2003.06168