  The influence of a tight isotropic harmonic trap on photoassociation of two
ultracold alkali atoms forming a homonuclear diatomic is investigated using
realistic atomic interaction potentials. Confinement of the initial atom pair
due to the trap leads to a uniform strong enhancement of the photoassociation
rate to most, but also to a strongly suppressed rate for some final states.
Thus tighter traps do not necessarily enhance the photoassociation rate. A
further massive enhancement of the rate is found for strong interatomic
interaction potentials. The details of this interaction play a minor role,
except for large repulsive interactions for which a sharp window occurs in the
photoassociation spectrum as is known from the trap-free case. A comparison
with simplified models describing the atomic interaction like the
pseudopotential approximation shows that they often provide reasonable
estimates for the trap-induced enhancement of the photoassociation rate even if
the predicted rates can be completely erroneous.
