  We extend the well-known Cooper's problem beyond one pair and study how this
dilute limit is connected to the many-pair BCS condensate. We find that, all
over from the dilute to the dense regime of pairs, Pauli blocking induces the
same "moth-eaten effect" as the one existing for composite boson excitons. This
effect makes the average pair binding energy decrease linearly with pair
number, bringing it, in the standard BCS configuration, to half the single-pair
value. This proves that, at odds with popular understanding, the BCS gap is far
larger than the broken pair energy. The increase comes from Pauli blocking
between broken and unbroken pairs. Possible link between our result and the
BEC-BCS crossover is also discussed.
