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 models, one based on the algebra SO(5) and the other on the algebra SO(8). The analysis suggests that approximations based solely on pair correlations cannot describe the ground states of these models, unless symmetries are fully restored. If not, it is necessary to explicitly include four-body a-like correlations in the theory.