Analysis of threshold effects in ultracold atomic collisions - art. no. 012708

At the ultracold temperatures which occur in cold atom traps and Bose-Einst ein condensates, only a few partial waves contribute to the scattering of g round-state alkali-metal atoms, and cross sections are extremely sensitive to threshold effects. We present an analysis of these threshold effects, us ing a generalized multichannel quantum defect theory (GMQDT) to construct a close-coupled scattering wave function which is analytic in energy across thresholds. We illustrate the theory using the hyperfine transitions in Na + Na collisions, and show that it gives results completely equivalent to th e usual close-coupled cross sections. The virtue of the GMQDT is that it tr eats both open and closed channels on an equal footing, and all interchanne l dynamics is summarized in a single real symmetric matrix Y(E) which is es sentially constant across thresholds (and often over excursions of energy w hich exceed the hyperfine splittings). The multichannel threshold energy be havior can then be related to calculable properties of the individual chann els that are being closed. Many of the smaller spin depolarization cross se ctions are determined by very long-range alpha(2)/R-3 spin-spin interaction s which are not well treated by GMQDT, and we correct these specific elemen ts with a perturbative distorted-wave approximation which yields the observ ed threshold dependences and brings the GMQDT into perfect agreement with t he exact close-coupled results.