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Effective-range approximations for resonant scattering of cold atoms

Blackley, C.L.; Julienne, P.S.; Hutson, J.M.

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C.L. Blackley

P.S. Julienne


Studies of cold atom collisions and few-body interactions often require the energy dependence of the scattering phase shift, which is usually expressed in terms of an effective-range expansion. We use accurate coupled-channel calculations on 6Li, 39K, and 133Cs to explore the behavior of the effective range in the vicinity of both broad and narrow Feshbach resonances. We show that commonly used expressions for the effective range break down dramatically for narrow resonances and near the zero crossings of broad resonances. We present an alternative parametrization of the effective range that is accurate through both the pole and the zero crossing for both broad and narrow resonances. However, the effective-range expansion can still fail at quite low collision energies, particularly around narrow resonances. We demonstrate that an analytical form of an energy and magnetic-field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length.


Blackley, C., Julienne, P., & Hutson, J. (2014). Effective-range approximations for resonant scattering of cold atoms. Physical Review A, 89(4), Article 042701.

Journal Article Type Article
Publication Date Apr 1, 2014
Deposit Date Apr 30, 2014
Publicly Available Date Jul 11, 2014
Journal Physical Review A
Print ISSN 1050-2947
Electronic ISSN 1094-1622
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 89
Issue 4
Article Number 042701


Published Journal Article (975 Kb)

Copyright Statement
Reprinted with permission from the American Physical Society: Phys. Rev. A 89, 042701 © (2014) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

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