Effective-range approximations for resonant scattering of cold atoms

Abstract

. (2014) 'Eective-range approximations for resonant scattering of cold atoms.', Physical review A., 89 (4). p. 42701.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevA.89.042701Publisher's copyright statement:Reprinted with permission from the American Physical Society: Phys. Rev. A 89, 042701 c (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, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 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 6 Li, 39 K, and 133 Cs 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.

Ultracold atoms in quasi-one-dimensional traps: A step beyond the Lieb-Liniger model

“…Numerical multichannel scattering calculations have verified that this expression holds close to open-channel Feshbach resonances, but can fail on the closed-channel dominated ones [51]. However, an effective formula for the effective range as a function of magnetic field B in the vicinity of the resonance can be given as [51] …”

“…For atoms interacting via a single-channel van der Waals potential the 3D effective range can be calculated analytically and has a universal form depending only on the scattering length [50,51] …”

“…However, an effective formula for the effective range as a function of magnetic field B in the vicinity of the resonance can be given as [51] …”

Three-body parameter for Efimov states inLi6

“…The effective range behaves very differently in the vicinity of Feshbach resonances of different types [52]. For a resonance that is strongly entrance-channeldominated [6], the effective range takes a small and fairly constant value close to 2.8r vdW at fields near the resonance pole [53].…”

Supersymmetric inversion of effective-range expansions

“…The local nature of these potentials makes them quite different from other realistic nucleon-nucleon interactions but a comparison between different models could be made directly through their effective-range-function or scattering-matrix-poles properties. Further developments of the method might include the link between different partial waves, the comparison between the neutral and charged cases, generalization to the coupledchannel case [7,11], and application to elastic collisions in atomic physics [26].…”