  We use Richardson-Gaudin exact equations to derive the ground-state energy of
$N$ composite bosons (cobosons) interacting via a potential which acts between
fermion pairs having zero center-of-mass momentum, that is, a potential similar
to the reduced BCS potential used in conventional superconductivity. Through a
density expansion, we show that while, for 2D systems, the $N$-coboson
correlation energy undergoes a surprising cancellation which leaves the
interaction part with a $N(N-1)$ dependence only, such a cancellation does not
exist in 1D, 3D, and 4D systems --- which corresponds to 2D parabolic traps ---
nor when the cobosons interact via a similar short-range potential but between
pairs having an arbitrary center-of-mass momentum. This shows that the
previously-found cancellation which exists for the Cooper-pair correlation
energy results not only from the very peculiar form of the reduced BCS
potential, but also from a quite mysterious dimensionality effect, the density
of states for Cooper pairs feeling the BCS potential being essentially
constant, as for 2D systems.
