  We use the quantum threshold laws combined with a classical capture model to
provide an analytical estimate of the chemical quenching cross sections and
rate coefficients of two colliding particles at ultralow temperatures. We apply
this quantum threshold model (QT model) to indistinguishable fermionic polar
molecules in an electric field. At ultracold temperatures and in weak electric
fields, the cross sections and rate coefficients depend only weakly on the
electric dipole moment d induced by the electric field. In stronger electric
fields, the quenching processes scale as d^{4(L+1/2)} where L>0 is the orbital
angular momentum quantum number between the two colliding particles. For p-wave
collisions (L=1) of indistinguishable fermionic polar molecules at ultracold
temperatures, the quenching rate thus scales as d^6. We also apply this model
to pure two dimensional collisions and find that chemical rates vanish as
d^{-4} for ultracold indistinguishable fermions. This model provides a quick
and intuitive way to estimate chemical rate coefficients of reactions occuring
with high probability.
