  We determine the adiabatic phase diagrams for a resonantly-coupled system of
Fermi atoms and Bose molecules confined in a harmonic trap by using the local
density approximation. The key idea of our work is conservation of entropy
through the adiabatic process. We also calculate the molecular conversion
efficiency as a function of the 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.
