  We investigate collisions of polar molecules in quasi-2D traps in the
presence of an external electric field perpendicular to the collision plane. We
use the quantum-defect model characterized by two dimensionless parameters: $y$
and $s$. The first of them is related to the probability of the reaction at
short distances, whereas the latter one defines the wave function phase at
short distances. For $y$ close to unity we obtain universal collision rates
determined by the quantum reflection process from the long-range part of the
interaction potential that depends only on the van der Waals coefficient,
dipole-dipole interaction and the trap frequency. For small short-range
reaction probabilities collision rates are highly nonuniversal and trap induced
shape resonances are visible. For high dipole moments we observe the damping of
reactive collisions, which can stabilize the ultracold gas of polar molecules.
The calculations were performed with help of multichannel wave funcion
propagation by imposing short-range boundary condition derived from the
quantum-defect model.
