  The pioneering works by Eagles, Leggett, and Nozieres/Schmitt-Rink (reviewed
and augmented by Randeria) emphasize that in the limits of the models studied
both at T = 0 and, the cross-over from a BCS-type to a BEC-type superconductor
is continuous. The BCS and BEC end points seem to be well-established. However,
in the intermediate region, home to fulleride and high temperature
superconductors, considerable extrapolation of the models must be done as there
still is no exact theory. Yet, considerable current literature is devoted to
what appears to be more singular-type phenomena such as quantum critical
points, stripe formation, insulator to superconductor phase transitions, loss
of validity of the Fermi liquid theory, etc.
  Using a connection we have made with cold atom Fermion-Boson crossover
theory, we can establish that the resonance previously discussed is a result of
the crossing of the Fermion band by the Boson band. While the ground and singly
excited states appear to remain continuous, the collective modes due to the
resonance transform the nature of the superconductivity. We discuss features of
the resonance and the experimentally observed pre-formed BEC Cooper pair
formation in fullerides, essential to the Boson-Fermion resonance theory. In
addition some of the various singular phenomena discussed above can be put into
perspective.
  PACS numbers: 61.48.+c, 74.20.-z, 81.05Tp

Superconductivity;Strongly Correlated Electrons