  We propose a coherent framework allowing to deal with many-body effects in
dense ultracold Fermi gases in the presence of a Feshbach resonance. We show
that the simple effect of Pauli exclusion induces a strong modification of the
basic scattering properties, leading in particular to an energy dependence of
the effective scattering length on the scale of the chemical potential. This
results in a smearing of the Feshbach resonance and provides a natural
explanation for recent experimental findings.
