  We investigate the dynamics of converting cold bosonic atoms to molecules
when an external magnetic field is swept across a Feshbach resonance. Our
analysis relies on a zero temperature quantum microscopic model that accounts
for many-body effects, triggering the association process. We show that the
picture of two-body molecular production depicted by Landau-Zener model is
significantly altered due to many-body effects. In nonadiabatic regime, we
derive an analytic expression for molecular conversion efficiency that explains
the discrepancy between the prediction of Landau-Zener formula and experimental
data[Hodby et al., Phys. Rev. Lett. {\bf 94}, 120402 (2005)]. Our theory is
further extended to the formation of heteronuclear diatomic molecules and gives
some interesting predictions.
