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We revisit the mean-field treatment of photoassociation and Feshbachresonances 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 developa two-channel model for a mixed atomic-molecular condensate. Besides theindividual dynamics of the condensed and non-condensed atoms, the model alsotakes into account their pair dynamics by means of pair wave functions. We showthat the resulting set of coupled equations can be reduced to the usual coupledGross-Pitaevskii equations when the time scale of the pair dynamics is shortcompared to that of the individual dynamics. Such time scales are discussed inthe case of typical photoassociation experiments with cw lasers. We show thatthe individual dynamics plays a minor role, demonstrating the validity of therates predicted by the usual models describing photoassociation in anondegenerate gas.Comment: 15 pages, 4 figures: updated with respect to the published versio

Pair dynamics in the formation of molecules in a Bose-Einstein condensate