Effects of the Coulomb and the spin-orbit interaction in a deformed mean field on the pairing correlations in N=Z nuclei

Abstract

We perform systematic calculations regarding the effects by Coulomb and/or spin-orbit (SO) interaction on like- and unlike-pairing correlations in $sd$-, $pf$-, and $sdgh$-shell $N=Z$ nuclei. The former two interactions are comprised in a deformed mean-field potential and the latter pairing correlations are treated by residual interactions in the mean field. We make use of two different pairing matrix elements (PMEs) for the residual interactions : constant and state-dependent Brueckner $G$ matrix. The constant PME may give rise to meaningful information on the pairing correlations under the Wigner spin-isospin SU(4) symmetry in the absence of the Coulomb and the SO interaction. The state-dependent Brueckner PME takes into account the nuclear medium effect based on a realistic nucleon-nucleon interaction. In this work, through the analyses of the Coulomb and the SO interaction effects on the pairing correlations, we discuss in detail the isoscalar pair condensation and the coexistence of the isoscalar and the isovector pairs in the unlike pairing of the $N=Z$ nuclei. Our results show that the Coulomb and the SO interaction as well as nuclear deformation affect the single-particle state evolution in a deformed mean field and, as a result, give significant impacts on the pairing correlations and the smearing of occupation probabilities near Fermi energy. In particular, the pairing gaps in the heavy nuclei are largely disturbed by the Coulomb interaction as well as the SO interaction.