  We discuss the occupation number correlations in an ultracold system of
interacting fermionic atoms. For a system with a special energy-level
distribution, viz. two multiply-degenerate levels, explicit expressions for the
correlation functions are derived in a canonical approach using the exact
ground state wavefunction of the reduced BCS Hamiltonian. We evaluate the
correlators numerically for different interaction strength and find analytical
expressions in some limiting cases. Due to the underlying fermionic nature of
the pairs the occupations are predominantly anti-correlated and their
statistics is a multinomial distribution.
