  In the context of a simple model featuring an explicit, central interaction
potential, and using a standard functional-integral technique, we study
superconductivity with angular momentum quantum number l=2 as an emergent
property of the many-body system. Our interaction potential is attractive at a
finite distance r_0, and the breaking of the rotational symmetry is the result
of an interplay between r_0 and the inter-particle distance r_s which we deem
generic to interactions of this type. However such interplay, responsible for
the preference of a d-wave state for a range of intermediate densities, takes
place only in the BCS limit. In contrast, as the Bose-Einstein (BE) limit is
approached the internal energy of the "preformed pairs" becomes the dominant
contribution and there is a quantum phase transition in which the s-wave
symmetry is restored. We also find that the limiting value of the critical
temperature is k_B T_c --> 3.315(\hbar^2/2m*)[n/2(2l+1)]^{2/3}, which coincides
with the usual result only for l=0; for l>0, it differs in the degeneracy
factor 1/(2l+1), which lowers T_c. Our results thus place constraints on exotic
pairing in the BE limit, while at the same time indicating a particularly
interesting route to pairing with l>0 in a BCS superconductor.
