  Many-body effects may influence properties, such as scattering parameters,
nature of pairing, etc., close to a Feshbach resonance in the fermion BEC-BCS
crossover problem. We study effects such as these using a tractable
crossing-symmetric approach. This method allow us to include quantum
fluctuations, such as, density, current, spin, spin-current and the
higher-order fluctuations in a self-consistent fashion. The underlying fermion
interaction is reflected in the "driving" term. We perform calculations here on
both Bose-Einstein condensate (BEC) and BCS sides, and taking the driving term
to be finite range, and of arbitrary strength. These are related to two-body
singlet and triplet scattering parameters, and can be connected with
experimental s- and p-wave Feshbach resonances. We include the $\ell=0$ density
and spin fluctuations, as well as $\ell=1$ current and spin-current
fluctuations. We calculate renormalized scattering amplitudes, pairing
amplitudes, nature of pairing, etc., on both the BEC and BCS sides. We then
compare our results qualitatively with experiments.
