The 3-Dimensional g-Deformed Harmonic Oscillator and a Unified Description of Magic Numbers of Metal Clusters

Abstract

Magic numbers predicted by a 3-dimensional (/-deformed harmonic oscillator with u9(3) D soq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n + / pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional çr-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), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that ug(3), which is a nonlinear 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 several metal clusters.