Ultracold atoms have achieved many outstanding successes in a wide variety
of experiments, many of which utilize the exquisite control over collisions
that is possible with tunable scattering resonances. The availability of
cold molecules should greatly extend the range of experimental
possibilities. This talk will emphasize some simple and essential concepts
for understanding the similarities and differences between ultracold atomic
and molecular collisions in gases and lattices. Both atomic and molecular
collisions can be described in terms of a similar framework, based on the
separation of energy, time, and distance scales associated with short range
and long range interactions. The properties of the interacting species and
the long range potentials determine the spectrum of bound and scattering
states, and the available resonances, over a relatively wide range of
energy near a collision threshold. This is readily illustrated for neutral
atoms. Atoms and molecules differ in the nature of their long range
potentials and the spectrum of the \"collision complex\" they form. It is
often convenient to summarize ultracold elastic and inelastic collisional
properties by a complex scattering length, which accounts for both the
coherent interactions and the collisional loss processes. Although
molecules typically have more and stronger loss channels than
atoms, molecules should prove to be especially useful in lattice
experiments, where they can be protected from \"bad\" collisions.
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