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Semiclassical approximation for the Scattering Volume in Cold-Atom Collisions

Lookup NU author(s): Professor Alan Dickinson

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Abstract

A semiclassical result is derived for the scattering volume for near-threshold p-wave scattering by a potential falling off as 1/R^n, n >= 6, R being the interatomic separation. This result depends only on the s-wave zero-energy classical action and properties of the long-range potential and hence can be related to the semiclassical result for the scattering length. The exact result for the scattering volume for the Lennard-Jones (2n-2,n), n >=6 is derived and it is shown that the corresponding semiclassical result is within 1% for potentials supporting at least two rotationless bound levels. Comparisons are made for the scattering volume with a variety of results in the literature for a range of systems supporting between 0 and 83 rotationless bound levels. The semiclassical result is generally within 5% and was never in error by more than 15%, which occurred for a case supporting no bound states.

Publication metadata

Author(s): Dickinson AS

Publication type: Article

Publication status: Published

Journal: Journal of Physics B: Atomic, Molecular and Optical Physics

Year: 2008

Volume: 41

Issue: 175302

Pages: 5

Date deposited: 27/08/2008

ISSN (print): 0953-4075

ISSN (electronic): 1361-6455

Publisher: Institute of Physics

URL: http://dx.doi.org/10.1088/0953-4075/41/17/175302

DOI: 10.1088/0953-4075/41/17/175302

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