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

Abstract

The reaction cross section ${\sigma }_R$ 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 ${}^{12}$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 ${\sigma }_R$ 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 ${\sigma }_R$ 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 ${\sigma }_{\mathrm{R}}$ 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 ${\sigma }_R$ allows us to scale the GHFB+AMP neutron density so as to reproduce the ${\sigma }_R$ data. In $E_{\mathrm{in}}$ = 30--100 MeV, the experimental ${\sigma }_R$ 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.

References in corpus (7)

• Accurate Determination of the Neutron Skin Thickness of ${}^{208}$Pb through Parity-Violation in Electron Scattering
• Implications of PREX-II on the equation of state of neutron-rich matter
• Charge radii of exotic neon and magnesium isotopes
• Microscopic optical potentials for ${}^4$He scattering
• Neutron rich matter in the laboratory and in the heavens after GW170817
• $g$-matrix folding-model approach to reaction cross sections for scattering of Ca isotopes on a C target
• Roles of chiral three-nucleon forces in nucleon-nucleus scattering

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