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 $r_{ \rm n}^{ 208}({ \rm PREX2})$ and the proton radius of the electron scattering, we found that the model reproduces $\sigma_R$ for p+ $^{ 208}$Pb scattering at $E_{ \rm lab} = 534.1, 549, 806$MeV. Zenihiro { \it el al. } deduce neutron radii $r_{ \rm n}^{ 48,40}({ \rm exp})$ from proton elastic scattering, whereas we determine $r_{ \rm m}^{ \rm 40}({ \rm exp})=3.361 \pm 0.075$fm from measured $\sigma_R$ for $^{ 4}$He+ $^{ 40}$Ca scattering. Our first aim is to determine $r_{ \rm skin}^{ \rm 208}$ from measured $\sigma_R$ of p+$^{ 208}$Pb scattering at $E_{ \rm lab} = 534.1, 549, 806$MeV by using the LF $t$-matrix folding model. Our second aim is to determine $r_{ \rm skin}^{ \rm 48}$ from the $r_{ \rm m}^{ \rm 40}({ \rm exp})$ and $\Delta \equiv r_{ \rm m}^{ \rm 48}({ \rm exp})-r_{ \rm m}^{ \rm 40}({ \rm exp})$ that is evaluated from the $r_{ \rm n}^{ 48,40}({ \rm exp})$ and the $r_{ \rm p}^{ 48,40}({ \rm exp})$ 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 $r_{ \rm skin}^{ \rm 208}= 0.324 \pm 0.047$fm for D1S and $r_{ \rm skin}^{ \rm 208}({ \rm exp})=0.333 \pm 0.047 $fm for D1M. The $\Delta=0.109$fm and $r_{ \rm m}^{ \rm 40}({ \rm exp})=3.361 \pm 0.075$fm yield $r_{ \rm m}^{ \rm 48}=3.470 \pm 0.075$fm, leading to $r_{ \rm skin}^{ \rm 48}=0.144 \pm 0.075$fm. We conclude that $r_{ \rm skin}^{ 208}({ \rm exp})=0.324 \pm (0.047)_{ \rm exp} \pm (0.009)_{ \rm th}~{ \rm fm}$ for p scattering at $E_{ \rm lab} = 534.1, 549, 806$MeV. Our skin values are consistent with the PREX2 and CREX values.
Categories: nucl-th nucl-ex