Many-body approximations in the presence of proton-neutron pairing

The usefulness of the generalized BCS approximation in systems with strong proton-neutron pairing is studied in the context of two exactly-solvable mo dels, one based on the algebra SO(5) and the other on the algebra SO(8). Th e analysis suggests that approximations based solely on pair correlations c annot describe the ground states of these models, unless symmetries are ful ly restored. If not, it is necessary to explicitly include four-body a-like correlations in the theory.