  We determine the adiabatic phase diagram of a resonantly-coupled system of
Fermi atoms and Bose molecules confined in the harmonic trap by using the local
density approximation. The adiabatic phase diagram shows the fermionic
condensate fraction composed of condensed molecules and Cooper pair atoms. The
key idea of our work is conservation of entropy through the adiabatic process,
extending the study of Williams et al. [Williams et al., New J. Phys. 6, 123
(2004)] for an ideal gas mixture to include the resonant interaction in a
mean-field theory. We also calculate the molecular conversion efficiency as a
function of initial temperature. Our work helps to understand recent
experiments on the BCS-BEC crossover, in terms of the initial temperature
measured before a sweep of the magnetic field.
