Analytic description of atomic interaction at ultracold temperatures: The case of a single channel

Bo Gao
Phys. Rev. A 80, 012702 – Published 2 July 2009

Abstract

We present analytic descriptions of atomic interaction at ultracold temperatures using both single-channel and multichannel quantum-defect theories. In the case of a single channel, addressed in this paper, the expansion of Gao [Phys. Rev. A 58, 4222 (1998)] is generalized to higher orders for angular momentum l2 to give a more complete description of ultracold scattering, including an analytic description of ultracold shape resonances of arbitrary l. We also introduce a generalized scattering length that is well defined and useful for all partial waves to replace the traditional definition that fails for l2 due to the long-range van der Waals interaction. The results are used in a companion paper to derive analytic descriptions of atomic interaction around a magnetic Feshbach resonance of arbitrary angular momentum l.

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  • Received 27 April 2009

DOI:https://doi.org/10.1103/PhysRevA.80.012702

©2009 American Physical Society

Authors & Affiliations

Bo Gao*

  • Department of Physics and Astronomy, University of Toledo, MS 111, Toledo, Ohio 43606, USA

  • *bo.gao@utoledo.edu; http://bgaowww.physics.utoledo.edu

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Vol. 80, Iss. 1 — July 2009

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