Skin values of ${}^{208}$Pb and ${}^{48}$Ca determined from reaction cross sections (published in Results in Physics)

Abstract

The PREX and the CREX group reported their skin values. Using the Love-Franey (LF) $t$-matrix folding model with the neutron and proton densities scaled to the neutron radius $r_{\mathrm{n}}^{208}(PREX2)$ and the proton radius of the electron scattering, we found that the model reproduces $\ddot{I}{ƒ}_R$ for p+ ${}^{208}$Pb scattering at $E_{\mathrm{lab}}=534.1,549,806$MeV. Zenihiro {\it el al. } deduce neutron radii $r_{\mathrm{n}}^{48,40}(\exp )$ from proton elastic scattering, whereas we determine $r_{\mathrm{m}}^{40}(\exp )=3.361\pm 0.075$fm from measured $\ddot{I}{ƒ}_R$ for ${}^4$He+ ${}^{40}$Ca scattering. Our first aim is to determine $r_{\mathrm{skin}}^{208}$ from measured $\ddot{I}{ƒ}_R$ of p+${}^{208}$Pb scattering at $E_{\mathrm{lab}}=534.1,549,806$MeV by using the LF $t$-matrix folding model. Our second aim is to determine $r_{\mathrm{skin}}^{48}$ from the $r_{\mathrm{m}}^{40}(\exp )$ and $\hat{I}”\equiv r_{\mathrm{m}}^{48}(\exp )-r_{\mathrm{m}}^{40}(\exp )$ that is evaluated from the $r_{\mathrm{n}}^{48,40}(\exp )$ and the $r_{\mathrm{p}}^{48,40}(\exp )$ calculated with the isotope shift method based on the electron scattering. For the first aim, we use the LF $t$-matrix model with the densities scaled from the D1S-GHFB+AMP neutron density. The D1M-GHFB+AMP is used to estimate a theoretical error. The resulting skin values are $r_{\mathrm{skin}}^{208}=0.324\pm 0.047$fm for D1S and $r_{\mathrm{skin}}^{208}(\exp )=0.333\pm 0.047$fm for D1M. The $\hat{I}”=0.109$fm and $r_{\mathrm{m}}^{40}(\exp )=3.361\pm 0.075$fm yield $r_{\mathrm{m}}^{48}=3.470\pm 0.075$fm, leading to $r_{\mathrm{skin}}^{48}=0.144\pm 0.075$fm. We conclude that $r_{\mathrm{skin}}^{208}(\exp )=0.324\pm (0.047{)}_{\exp }\pm (0.009{)}_{\mathrm{th}}\mathrm{fm}$ for p scattering at $E_{\mathrm{lab}}=534.1,549,806$MeV. Our skin values are consistent with the PREX2 and CREX values.

4 pages, 1 figure