Neutron skin thickness of Pb 208 determined from the reaction cross section for proton scattering

Background: The reaction cross section ${\ensuremath{\sigma}}_{R}$ 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 $^{12}\mathrm{C}$ scattering on $^{9}\mathrm{Be}, ^{12}\mathrm{C}, ^{27}\mathrm{Al}$ targets was tested in the incident energy range of $30\ensuremath{\lesssim}{E}_{\mathrm{in}}\ensuremath{\lesssim}400$ MeV, and it is found that the model reliably reproduces the ${\ensuremath{\sigma}}_{R}$ in $30\ensuremath{\lesssim}{E}_{\mathrm{in}}\ensuremath{\lesssim}100$ MeV and $250\ensuremath{\lesssim}{E}_{\mathrm{in}}\ensuremath{\lesssim}400$ MeV.Purpose: Our aim is to determine ${r}_{\mathrm{skin}}^{208}(\mathrm{EXP})$ from ${\ensuremath{\sigma}}_{\mathrm{R}}(\mathrm{EXP})$ for $p+^{208}\mathrm{Pb}$ scattering in $30\ensuremath{\le}{E}_{\mathrm{lab}}\ensuremath{\le}100$ MeV.Methods: Our model is the Kyushu $g$-matrix folding model with the densities calculated with Gongny-D1S HFB (GHFB) with the angular momentum projection (AMP).Results: The Kyushu $g$-matrix folding model with the $\text{GHFB}+\text{AMP}$ densities underestimates ${\ensuremath{\sigma}}_{\mathrm{R}}$ in $30\ensuremath{\le}{E}_{\mathrm{in}}\ensuremath{\le}100$ MeV only by a factor of 0.97. Since the proton radius ${R}_{p}$ calculated with $\text{GHFB}+\text{AMP}$ agrees with the precise experimental data of 5.444 fm, the small deviation of the theoretical result from the data on ${\ensuremath{\sigma}}_{R}$ allows us to scale the $\text{GHFB}+\text{AMP}$ neutron density so as to reproduce the ${\ensuremath{\sigma}}_{R}$ data. In ${E}_{\mathrm{in}}=30$--100 MeV, the experimental ${\ensuremath{\sigma}}_{R}$ data can be reproduced by assuming the neutron radius of $^{208}\mathrm{Pb}$ as ${R}_{n}=5.722\ifmmode\pm\else\textpm\fi{}0.035$ fm.Conclusion: The present result ${R}_{\mathrm{skin}}=0.278\ifmmode\pm\else\textpm\fi{}0.035$ fm is in good agreement with the recent PREX-II result of ${r}_{\mathrm{skin}}=0.283\ifmmode\pm\else\textpm\fi{}0.071$ fm.