Neutron-proton pairing correlations and deformation for N=Z nuclei in the pf shell within the deformed BCS and Hartree-Fock-Bogoliubov approach

Abstract

We investigated neutron-proton pairing correlations effects on the shell evolution of ground-state energies by the deformation for $N=Z$ nuclei in $pf$ shell, such as $^{44}\mathrm{Ti}$, $^{48}\mathrm{Cr}$, $^{52}\mathrm{Fe}$, $^{64}\mathrm{Ge}$, $^{68}\mathrm{Se}$, $^{72}\mathrm{Kr}$, and $^{76}\mathrm{Sr}$. We started from a simple shell-filling model constructed by a deformed Woods-Saxon potential with ${\ensuremath{\beta}}_{2}$ deformation, and included pairing correlations in the residual interaction, which give rise to smearing of the Fermi surface revealing interesting evolution of the Fermi energy along the shell evolution. In this work, like-pairing and unlike-pairing correlations decomposed as isovector $T=1$ and isoscalar $T=0$ components are explicitly taken into account. Finally, we estimate ground-state energies comprising the mean-field energy, the pairing energy, and the self-energy due to the pairing correlations, in terms of the deformation. The enhanced $T=0$ pairing interaction supports oblate deformations for $^{72}\mathrm{Kr}$ and $^{68}\mathrm{Se}$, whose features are different from other $pf$-shell $N=Z$ nuclei considered in this work.