$g$-matrix folding-model approach to reaction cross sections for scattering of Ca isotopes on a C target

TL;DR

This paper combines advanced nuclear structure calculations with a folding model to predict reaction cross sections for calcium isotopes, validating the approach against experimental data and proposing improvements.

Contribution

It introduces a $g$-matrix folding-model approach to accurately predict reaction cross sections for Ca isotopes, integrating ground-state properties from GHFB calculations.

Findings

Predicted dripline nuclei $^{64}$Ca and $^{59}$Ca.

Reaction cross sections agree with experimental data within certain energy ranges.

Validated the folding model's reliability across multiple target nuclei.

Abstract

We first predict the ground-state properties of Ca isotopes, using the Gogny-D1S Hartree-Fock-Bogoliubov (GHFB) with and without the angular momentum projection (AMP). We find that $^{64}$Ca is an even-dripline nucleus and $^{59}$Ca is an odd-dripline nucleus, using $A$ dependence of the one-neutron separation energy $S_{1}$ and the two-neutron separation energy, $S_{2}$. As for $S_{1}$, $S_{2}$ and the binding energies $E_{\rm B}$, our results agree with the experimental data in $^{40-58}$Ca. As other ground-state properties of $^{40-60,62,64}$Ca, we predict charge, proton, neutron, matter radii, neutron skin and deformation. As for charge radii, our results are consistent with the experimental data in $^{40-52}$Ca. For $^{48}$Ca, our results on proton, neutron, matter radii agree with the experimental data. Very lately, Tanaka et. al. measured interaction cross sections for $^{42-51}$Ca scattering on a $^{12}$C target at an incident energy per nucleon of $E_{\rm lab}=280$MeV. Secondly, we predict reaction cross sections $\sigma_{\rm R}$ for $^{40-60,62,64}$Ca, using a chiral $g$-matrix double-folding model (DFM). To show the reliability of the present DFM for $\sigma_{\rm R}$, we apply the DFM for the data on $^{12}$C scattering on $^{9}$Be, $^{12}$C, $^{27}$Al targets in $30 < E_{\rm lab} < 400 $MeV, and show that the present DFM is good in $30 < E_{\rm lab} < 100 $MeV and $250 < E_{\rm lab} < 400 $MeV. For $110 < E_{\rm lab} < 240 $MeV, our results have small errors. To improve the present DFM for $\sigma_{\rm R}$, we propose two prescriptions.