  We revisit the mean-field treatment of photoassociation and Feshbach
resonances in a Bose-Einstein condensate previously used by various authors.
Generalizing the Cherny and Shanenko approach (Phys. Rev. E 62, 1646-59 (2000)
) where the finite size of the potentials is explicitly introduced, we develop
a two-channel model for a mixed atomic-molecular condensate. Besides the
individual dynamics of the condensed and non-condensed atoms, the model also
takes into account their pair dynamics by means of pair wave functions. We show
that the resulting set of coupled equations can be reduced to the usual coupled
Gross-Pitaevskii equations when the time scale of the pair dynamics is short
compared to that of the individual dynamics. Such time scales are discussed in
the case of typical photoassociation experiments with cw lasers. We show that
the individual dynamics plays a minor role, demonstrating the validity of the
rates predicted by the usual models describing photoassociation in a
nondegenerate gas.
