Proton-neutron pairing correlations in N=Z nuclei with Deformed Skyrme+pnBCS model

We investigate the effects of neutron-neutron (nn), proton-proton (pp) and proton-neutron (pn) pairing correlations on the ground-states of $N = Z$ even-even $pf$-shell nuclei by using an axially symmetric deformed Hartree-Fock (HF)+pnBardeen-Cooper-Schrieffer (BCS) model. We adopt a Skyrme energy density functional (EDF) SGII, together with contact volume- and surface-type pairing interactions, whose strengths are adjusted to reproduce empirical pairing gaps of each nucleus. It is shown that the strength of the IS pairing is correlated to the nuclear deformation: for oblate deformation with $-0.3<\beta_2<0.0$, a stronger IS pairing is required to reproduce the empirical pairing gap, while for prolate deformation a weaker one is enough. Among the eight $N=Z$ nuclei, we found that $^{64}$Ge, $^{68}$Se and $^{72}$Kr show the dominance of isovector (IV) spin-singlet superfluidity, while lighter 5 nuclei $^{44}$Ti, $^{48}$Cr, $^{52}$Fe, $^{56}$Ni and $^{60}$Zn exhibit the coexistence of IV spin-singlet and isoscalar (IS) spin-triplet superfluidities. We found also that the IS abnormal density always exhibits the oblate deformation, regardless of whether the normal density is prolate, spherical or oblate.