  We study the conversion efficiency of heteronuclear Feshbach molecules in
population imbalanced atomic gases formed by ramping the magnetic field
adiabatically. We extend the recent work [J. E. Williams et al., New J. Phys.,
8, 150 (2006)] on the theory of Feshbach molecule formations to various
combinations of quantum statistics of each atomic component. A simple
calculation for a harmonically trapped ideal gas is in good agreement with the
recent experiment [S. B. Papp and C. E. Wieman, Phys. Rev. Lett., 97, 180404
(2006)] without any fitting parameters. We also give the conversion efficiency
as an explicit function of initial peak phase space density of the majority
species for population imbalanced gases. In the low-density region where
Bose-Einstein condensation does not appear, the conversion efficiency is a
monotonic function of the initial peak phase space density, but independent of
statistics of a minority component. The quantum statistics of majority atoms
has a significant effect on the conversion efficiency. In addition,
Bose-Einstein condensation of an atomic component is the key element
determining the maximum conversion efficiency.
