  By including the effect of a trap with characteristic energy given by the
Fermi temperature $T_F$ in a two-body two-channel model for Feshbach
resonances, we reproduce the experimental closed-channel fraction $Z$ across
the BEC-BCS crossover and into the BCS regime of a $^6$Li atomic Fermi gas. We
obtain the expected behavior $Z \propto \sqrt{T_F}$ at unitarity, together with
the recently measured proportionality constant. Our results are also in
agreement with recent measurements of the $Z$ dependency on $T_F$ on the BCS
side, where a significant discrepancy between experiments and theory has been
repeatedly reported.
