Neutron skin thickness of ${}^{208}$Pb determined from reaction cross section for proton scattering

Abstract

The reaction cross section $\ddot{I}{ƒ}_R$ is useful to determine the neutron radius $R_n$ as well as the matter radius $R_m$. The chiral (Kyushu) $g$-matrix folding model for ${}^{12}$C scattering on ${}^9$Be, ${}^{12}$C, ${}^{27}$Al targets was tested in the incident energy range of $30 \lsim E_{\rm in} \lsim 400 $ MeV, and it is found that the model reliably reproduces the $\ddot{I}{ƒ}_R$ in $30 \lsim E_{\rm in} \lsim 100 $ MeV and $250 \lsim E_{\rm in} \lsim 400$ MeV. \item[Aim] We determine $R_n$ and the neutron skin thickness $R_{\mathrm{skin}}$ of ${}^{208}\mathrm{Pb}$ by using high-quality $\ddot{I}{ƒ}_R$ data for the $p+{}^{208}\mathrm{Pb}$ scattering in $30\le E_{\mathrm{in}}\le 100$ MeV. The theoretical model is the Kyushu $g$-matrix folding model with the densities calculated with Gongny-D1S HFB (GHFB) with the angular momentum projection (AMP). \item[Results] The Kyushu $g$-matrix folding model with the GHFB+AMP densities underestimates $\ddot{I}{ƒ}_{\mathrm{R}}$ in $30\le E_{\mathrm{in}}\le 100$~MeV only by a factor of 0.97. Since the proton radius $R_p$ calculated with GHFB+AMP agrees with the precise experimental data of 5.444 fm, the small deviation of the theoretical result from the data on $\ddot{I}{ƒ}_R$ allows us to scale the GHFB+AMP neutron density so as to reproduce the $\ddot{I}{ƒ}_R$ data. In $E_{\mathrm{in}}$ = 30--100 MeV, the experimental $\ddot{I}{ƒ}_R$ data can be reproduced by assuming the neutron radius of ${}^{208}\mathrm{Pb}$ as $R_n$ = $5.722\pm 0.035$ fm. \item[Conclusion] The present result $R_{\mathrm{skin}}$ = $0.278\pm 0.035$ fm is in good agreement with the recent PREX-II result of $r_{\mathrm{skin}}$ = $0.283\pm 0.071$ fm.