  In this paper we formulate the time-dependent many-body theory of
photoassociation in an atomic Bose-Einstein condensate with realistic
interatomic interactions, using and comparing two approximations: the
first-order cumulant approximation, originally developed by Kohler and Burnett
[Phys. Rev. A 65, 033601 (2002)], and the reduced pair wave approximation,
based on a previous paper [Phys. Rev. A 68 033612 (2003)] generalizing to two
channels the Cherny-Shanenko approach [Phys. Rev. E 62, 1046 (2000)]. The two
approximations differ only by the way a pair of condensate atoms is influenced
by the mean field at short interatomic separations. For these approximations we
identify two different regimes of photoassociation: the adiabatic regime and
the coherent regime. The threshold for the so-called "rogue dissociation"
[Phys. Rev. Lett. 88, 090403 (2002)] (where mean-field theory breaks down) is
found to be different in each regime, which sheds new light on the experiment
of McKenzie et al [Phys. Rev. Lett. 88, 120403 (2002)] and previous theoretical
calculations. We then use the two approximations to investigate numerically the
effects of rogue dissociation in a sodium condensate under conditions similar
to the McKenzie et al experiment. We find two different effects: reduction of
the photoassociation rate at short times, and creation of correlated pairs of
atoms, confirming previous works. We also observe that the photoassociation
line shapes become asymmetric in the first-order cumulant approximation, while
they remain symmetric in the reduced pair wave approximation, giving the
possibility to experimentally distinguish between the two approximations.
