Unified BCS-like model for pairing and alpha correlations

Recent studies of nuclei far from stability set a problem of understanding the features of nuclear structure for systems with an unusual neutron-proton composition. Medium and heavy nuclei with $N$ close to $Z$, such as in the vicinity of $^{100}$Sn, give a unique example of a two-component fermionic system with coexisting pairwise and quartic correlations. To describe these collective effects we generalize the variational BCS ground state wave function including $p-p$, $n-n$, $p-n$ and $2p-2n$ components under the assumption of attractive interaction in time-conjugate orbitals. The analytical solution reveals the possibility of different condensates being a nuclear analog of the BCS-BEC crossover in mesoscopic physics.