Analysis of Threshold Effects in Ultracold Atomic Collisions
F H. Mies, M -. Raoult
At the ultracold temperatures which occur in cold atom traps and Bose-Einstein condensates only a few partial waves contribute to the scattering of ground-state alkali atoms and cross sections are extremely sensitive to threshold effects. We present an analysis of these threshold effects, using a generalized multichannel quantum defect theory (GMQDT) to construct a close-coupled scattering wavefunction which is analytic in energy across thresholds. We illustrate the theory using the hyperfine transitions in Na+Na collisions, and show it gives results completely equivalent to the usual close-coupled cross-sections. The virtue of the GMQDT is that it treats both open and closed channels on an equal footing and all interchannel dynamics is summarized in a single real symmetric matrix Y(E) which is essentially constant across thresholds (and often over excursions of energy which exceed the superfine splittings). The multichannel threshold energy behavior can then be related to calculable properties of the individual channels that are being closed. Many of the smaller spin depolarization cross-sections are determined y very long range alpha2/R3 with a pertubative distorted wave approximation which yields the observed threshold dependences and brings the GMQDT into perfect agreement with the exact close-coupled results.
Physical Review A (Atomic, Molecular and Optical Physics)
atomic collisions, close coupling, hyperfine state transitions, Multichannel Quantum Defect Theory, scattering theory, ultracold atoms, Wigner threshold laws
and Raoult, M.
Analysis of Threshold Effects in Ultracold Atomic Collisions, Physical Review A (Atomic, Molecular and Optical Physics)
(Accessed June 9, 2023)