Semiclassical approximation for the scattering volume in cold-atom collisions

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2008-09, Vol.41 (17), p.175302-175302 (5)
• Main Author: Dickinson, A S
• Format: Article
• Language: English
• Subjects: Atomic and molecular collision processes and interactions; Atomic and molecular physics; Atomic properties and interactions with photons; Exact sciences and technology; General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.); Optical cooling of atoms; trapping; Photon interactions with atoms; Physics
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/41/17/175302

A semiclassical result is derived for the scattering volume for near-threshold p-wave scattering by a potential falling off as 1/Rn, n > = 6, with 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.