The 3-dimensional q-deformed harmonic oscillator and magic numbers of alkali metal clusters

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with uq(3)⊃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.