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)

TL;DR

This paper reanalyzes neutron skin thickness in calcium isotopes using advanced folding models and updated densities, providing more accurate results that support recent experimental findings and have implications for nuclear structure and neutron-rich matter.

Contribution

It introduces a reanalysis method using chiral g-matrix folding models with scaled densities, improving the accuracy of neutron skin thickness estimates for calcium isotopes.

Findings

Neutron skin for $^{48}$Ca is 0.157 ± 0.027 fm.

Results are consistent with recent experiments like CREX.

Improved modeling yields more reliable neutron skin measurements.

Abstract

In the previous paper, we predicted reaction cross sections $\sigma_{\rm R}$ for $^{40-60,62,64}$Ca+$^{12}$C scattering at $280$~MeV/nucleon, since Tanaka {\it el al.} measured interaction cross sections $\sigma_{\rm I}$ for $^{42-51}$Ca in RIKEN and determined neutron skin $r_{\rm skin}({\rm RIKEN})$ using the optical limit of the Glauber model with the Woos-Saxon densities. Our purpose is to reanalyze the $r_{\rm skin}$ from the $\sigma_{\rm I}$. 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 $\sigma_{\rm R}$ of the scaled densities can agree with the central values of $\sigma_{\rm I}$ 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 $r_{\rm skin}$ thus determined are close to their results $r_{\rm skin}^{42-51}({\rm RIKEN})$. For $^{48}$Ca, our value $r_{\rm skin}^{48}$ is 0.105 $\pm$ 0.06~fm, while their value is $r_{\rm m}^{48}({\rm RIKEN})=0.146 \pm 0.06$~fm. We take the weighted mean and its error of $r_{\rm skin}^{48}(\sigma_{\rm I})= 0.105 \pm 0.06$~fm and $r_{\rm skin}^{48}(E1{\rm pE}) =0.17 \pm 0.03$~fm of the high-resolution $E1$ polarizability experiment (E1{\rm pE}). Our final result is $r_{\rm skin}^{48}=0.157 \pm 0.027$~fm. Our conclusion is $r_{\rm skin}^{48}=0.157 \pm 0.027$~fm for $^{48}$Ca. For $^{42-47,49-51}$Ca, our results on $r_{\rm skin}$ are similar to theirs. Our result for $^{48}$Ca is related to CREX.