  We investigate the Feshbach conversion of fermion atomic pairs to condensed
boson molecules with a microscopic model that accounts the repulsive
interactions among all the particles involved. We find that the conversion
efficiency is enhanced by the interaction between boson molecules while
suppressed by the interactions between fermion atoms and between atom and
molecule. In certain cases, the combined effect of these interactions leads to
a ceiling of less than 100% on the conversion efficiency even in the adiabatic
limit. Our model predicts a non-monotonic dependence of the efficiency on mean
atomic density. Our theory agrees well with recent experiments on $^6$Li and
$^{40}$K.
