Nuclear charge radii of Cr46–62 isotopes and reaction cross sections for p−Cr

Abstract

The nuclear charge radii and density distributions for $^{46--62}\mathrm{Cr}$ have been calculated in the frameworks of both relativistic and nonrelativistic self-consistent mean-field models. The relativistic Hartree-Bogoliubov model with density-dependent meson-exchange functional DD-ME2 and the nonrelativistic Hartree-Fock-Bogoliubov model with the Gogny D1S interaction, hereafter referred to as DIRHB and HFB, respectively, are used to compute ground-state properties of even $^{46--62}\mathrm{Cr}$ isotopes. Both calculations for the root-mean-squared charge radii reveal the characteristic kink at the $N$ = 28 shell closure in accordance with the corresponding experimental radii. The point proton and neutron density distributions calculated from both DIRHB and HFB are used to obtain the optical potentials for $p$-Cr at an incident proton energy of 65 MeV. The elastic scattering differential and total reaction cross sections, computed from the semimicroscopic proton optical potentials, have been derived by folding each of the target matter densities with the Jeukenne-Lejeune-Mahaux-Bruye\ifmmode \acute{r}\else \'{r}\fi{}es (JLMB) energy- and density-dependent internucleon interaction. The calculated elastic scattering differential cross sections for stable even isotopes, $^{50,52,54}\mathrm{Cr}$, using the respective DIRHB and HFB densities in the folding model reproduce the corresponding cross-section data well. The correlation between root-mean-squared charge radii and nuclear reaction observables obtained from the DIRHB and HFB calculations have been used in the folding model approach to predict the reaction cross sections for $p\text{\ensuremath{-}}^{46--62}\mathrm{Cr}$ at an incident proton energy of 65 MeV.