Analysis of Threshold Effects in Ultracold Atomic Collisions

Published

July 1, 2000

Author(s)

F H. Mies, M -. Raoult

Abstract

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.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Volume

62

Issue

No. 1

Pub Type

Journals

Keywords

atomic collisions, close coupling, hyperfine state transitions, Multichannel Quantum Defect Theory, scattering theory, ultracold atoms, Wigner threshold laws

Citation

Mies, F. and Raoult, M. (2000), Analysis of Threshold Effects in Ultracold Atomic Collisions, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed December 30, 2024)