Isoscalar-isovector proton-neutron pairing and quartet condensation in N =Z nuclei

We show that the correlations generated in the ground state of $N=Z$ nuclei by the isovector and isoscalar pairing forces can be treated with high precision as a condensate of alpha-like quartets. To treat these correlations, the quartet condensation model (QCM) is extended to the treatment of spherically symmetric isovector $(T=1,J=0)$ and isoscalar $(T=0,J=1)$ pairing forces. Within the QCM, we discuss the competition between $T=1$ and $T=0$ pairing correlations in the case of a two-level model and for $N=Z$ nuclei with nucleons moving in the open shells above $^{16}\mathrm{O},\phantom{\rule{0.16em}{0ex}}^{40}\mathrm{Ca}$, and $^{100}\mathrm{Sn}$. We show that, in $N=Z$ systems, isovector and isoscalar proton-neutron pairing correlations always coexist.