Reanalyses for ${}^{42-51}$Ca scattering on a ${}^{12}$C target at $280$ MeV/nucleon based on chiral $g$ folding mode with Gogny-D1S Hartree-Fock-Bogoliubov densities (published in Results in Physics)

Abstract

In the previous paper, we predicted reaction cross sections ${\sigma }_{\mathrm{R}}$ for ${}^{40-60,62,64}$Ca+${}^{12}$C scattering at $280$~MeV/nucleon, since Tanaka {\it el al.} measured interaction cross sections ${\sigma }_{\mathrm{I}}$ for ${}^{42-51}$Ca in RIKEN and determined neutron skin $r_{\mathrm{skin}}(\mathrm{RIKEN})$ using the optical limit of the Glauber model with the Woos-Saxon densities. Our purpose is to reanalyze the $r_{\mathrm{skin}}$ from the ${\sigma }_{\mathrm{I}}$. Our analysis is superior to theirs, since the chiral $g$-matrix folding model (the GHFB and GHFB+AMP densities) is much better than the optical limit of the Glauber model (the Woos-Saxon densities). Our model is the chiral $g$-matrix folding model with the densities scaled from the GHFB and GHFB+AMP densities. We scale the GHFB and GHFB+AMP densities so that the ${\sigma }_{\mathrm{R}}$ of the scaled densities can agree with the central values of ${\sigma }_{\mathrm{I}}$ under the condition that the proton radius of the scaled proton density equals the data determined from the isotope shift based on the electron scattering. The $r_{\mathrm{skin}}$ thus determined are close to their results $r_{\mathrm{skin}}^{42-51}(\mathrm{RIKEN})$. For ${}^{48}$Ca, our value $r_{\mathrm{skin}}^{48}$ is 0.105 $\pm$ 0.06~fm, while their value is $r_{\mathrm{m}}^{48}(\mathrm{RIKEN})=0.146\pm 0.06$~fm. We take the weighted mean and its error of $r_{\mathrm{skin}}^{48}({\sigma }_{\mathrm{I}})=0.105\pm 0.06$~fm and $r_{\mathrm{skin}}^{48}(E1\mathrm{pE})=0.17\pm 0.03$~fm of the high-resolution $E1$ polarizability experiment (E1{\rm pE}). Our final result is $r_{\mathrm{skin}}^{48}=0.157\pm 0.027$~fm. Our conclusion is $r_{\mathrm{skin}}^{48}=0.157\pm 0.027$~fm for ${}^{48}$Ca. For ${}^{42-47,49-51}$Ca, our results on $r_{\mathrm{skin}}$ are similar to theirs. Our result for ${}^{48}$Ca is related to CREX.

Comments: 6 pages, 3 figure