  We study translation-invariant quasi-free states for a system of fermions
with two-particle interactions. The associated energy functional is similar to
the BCS functional but includes also direct and exchange energies. We show that
for suitable short-range interactions, these latter terms only lead to a
renormalization of the chemical potential, with the usual properties of the BCS
functional left unchanged. Our analysis thus represents a rigorous
justification of part of the BCS approximation. We give bounds on the critical
temperature below which the system displays superfluidity.
