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soq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods–Saxon and wine-bottle potentials, and to the classification scheme using the 3n+l pseudo-quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that uq(3), which is a non-linear extension of the u(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.
doi:10.1016/0375-9601(96)00630-5 
Copyright © 1996 Published by Elsevier Science B.V.
Density of states for Bose-Einstein condensation in harmonic oscillator potentials
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Received 3 June 1996;
revised 7 August 1996;
accepted 7 August 1996;
Communicated by B. Fricke
Available online 15 February 1999.
Abstract
We discuss how it is possible to obtain a reliable approximation for the density of states for a system of particles in an anisotropic harmonic oscillator potential. A direct application of the result to study Bose-Einstein condensation of atomic gases in a potential trap can be given. In contrast to a previous study, our method involves only analytic calculations.
