Supershells in deformed harmonic oscillators and atomic clusters

From the mathematical point of view, the appearance of supershells is a general feature of potentials having relatively sharp edges. In physics, supershells have been observed in systems of metal clusters, which are also known to exhibit an underlying shell structure with magic numbers intermediate between the magic numbers of the 3‐D isotropic harmonic oscillator and those of the 3‐D square well. In the present study, Nilsson's modified harmonic oscillator (without any spin–orbit interaction), as well as the 3‐D q‐deformed harmonic oscillator with uq(3) ⊃ soq(3) symmetry, are considered. The former model has been used for an early schematic description of shell structure in metal clusters, while the latter has been found to successfully reproduce the magic numbers of metal clusters up to 1500 atoms, the expected limit of validity for theories based on the filling of electronic shells. The systematics of the appearance of supershells in the two models will be considered, putting emphasis on the differences between the spectra of the two oscillators. While the validity of Nilsson's modified harmonic oscillator framework is limited to relatively low particle numbers, the 3‐D q‐deformed harmonic oscillator gives reliable descriptions of the first supershell in metal clusters, which lies within its region of validity. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002