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

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 $E_{\mathrm{B}}$, 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 $E_{\mathrm{lab}}=280$MeV. Secondly, we predict reaction cross sections $\ddot{I}{ƒ}_{\mathrm{R}}$ for ${}^{40-60,62,64}$Ca, using a chiral $g$-matrix double-folding model (DFM). To show the reliability of the present DFM for $\ddot{I}{ƒ}_{\mathrm{R}}$, we apply the DFM for the data on ${}^{12}$C scattering on ${}^9$Be, ${}^{12}$C, ${}^{27}$Al targets in $30<E_{\mathrm{lab}}<400$MeV, and show that the present DFM is good in $30<E_{\mathrm{lab}}<100$MeV and $250<E_{\mathrm{lab}}<400$MeV. For $110<E_{\mathrm{lab}}<240$MeV, our results have small errors. To improve the present DFM for $\ddot{I}{ƒ}_{\mathrm{R}}$, we propose two prescriptions.