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# Neutron-skin values and matter and neutron radii determined from reaction cross sections of proton scattering on $^{12}$C, $^{40,48}$Ca, $^{58}$Ni, $^{208}$Pb

Nov 2022

Very lately, the PREX and the CREX collaboration present skin values, $r_{\rmskin}^{208}({\rm newPREX2}) =0.278 \pm 0.078\ {\rm (exp)} \pm 0.012\ {\rm(theor.)}\,{\rm fm}$ and $r_{\rm skin}^{48}=0.121 \pm 0.026\ {\rm (exp)} \pm0.024\ {\rm (model)}$, respectively. We recently determined a neutron-skinvalue $r_{\rm skin}^{208}=0.278 \pm 0.035$fm from measured reaction crosssections $\sigma_{\rm R}({\rm exp})$ of p+$^{208}$Pb scattering in a range ofincident energies $10 \lsim E_{\rm in} \lsim 100$ MeV where the chiral (Kyushu)$g$-matrix folding model is reliable for $^{12}$C+$^{12}$C scattering. The data$\sigma_{\rm R}({\rm exp})$ are available for proton scattering on $^{58}$Ni,$^{40,48}$Ca, $^{12}$C targets. Our first aim is to test the Kyushu $g$-matrixfolding model for p+$^{208}$Pb scattering in $20 \lsim E_{\rm in} \lsim 180$MeV. Our second aim is to determine skin values $r_{\rm skin}$ and matter andneutron radii, $r_{\rm m}$ and $r_{\rm n}$, for $^{208}$Pb, $^{58}$Ni,$^{40,48}$Ni, $^{12}$C from the $\sigma_{\rm R}({\rm exp})$. Our method is theKyushu $g$-matrix folding model with the densities scaled from the D1S-GHFB+AMPdensities, where D1S-GHFB+AMP stands for Gogny-D1S HFB (GHFB) with the angularmomentum projection (AMP). As for proton scattering, we find that our model isreliable in $20 \lsim E_{\rm in} \lsim 180$ MeV. For $^{208}$Pb, the skin valuededuced from $\sigma_{\rm R}({\rm exp})$ in $20 \lsim E_{\rm in} \lsim 180$ MeVis $r_{\rm skin}^{208}(\sigma_{\rm R})=0.299 \pm 0.020$ fm. Our results on$r_{\rm skin}$ are compared with the previous works. Our result $r_{\rmskin}^{208}(\sigma_{\rm R}) = 0.299 \pm 0.020$ fm agrees with $r_{\rmskin}^{208}({\rm PREX2}) = 0.283\pm 0.071$ fm. In addition, our result $r_{\rmskin}^{48}=0.103 \pm 0.022$ fm is consistent with the CREX value.

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