  Fermion systems with more than two components can exhibit pairing condensates
of much more complex structure than the well-known single BCS condensate of
spin-up and spin-down fermions. In the framework of the exactly solvable SO(8)
Richardson-Gaudin model with SU(4)-symmetric Hamiltonians, we show that the BCS
approximation remains valid in the thermodynamic limit of large systems for
describing the ground state energy and the canonical and quasiparticle
excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of
collective excitations, but these do not affect the bulk energy and
quasiparticle gaps.
