  We consider the normal state of a dense ultracold atomic Fermi gas in the
presence of a Feshbach resonance. We study the BCS and the molecular
instabilities and their interplay, within the framework of a recent many-body
approach. We find surprisingly that, in the temperature domain where the BCS
phase is present, there is a non zero lower bound for the binding energy of
molecules at rest. This could give an experimental mean to show the existence
of the BCS phase without observing it directly.
