  We model collisionless collective conversion of a degenerate Fermi gas into
bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a
classical field and seeding the pairing amplitudes with random phases. A
dynamical instability of the Fermi sea against association into molecules
initiates the conversion. The model qualitatively reproduces several
experimental observations {[Regal et al., Nature {\bf 424}, 47 (2003)]}. We
predict that the initial temperature of the Fermi gas sets the limit for the
efficiency of atom-molecule conversion.
