  Cold inelastic collisions of atoms or molecules are analyzed using very
general arguments. In free space, the deactivation rate can be enhanced or
suppressed together with the scattering length of the corresponding elastic
collision via a Feshbach resonance, and by interference of deactivation of the
closed and open channels. In reduced dimensional geometries, the deactivation
rate decreases with decreasing collision energy and does not increase with
resonant elastic scattering length. This has broad implications; e.g.,
stabilization of molecules in a strongly confining two-dimensional optical
lattice, since collisional decay of the highly vibrationally excited states due
to inelastic collisions is suppressed. The relation of our results with those
based on the Lieb-Liniger model are addressed.
