Shells and supershells in metal clusters

Abstract

Concept of energy shells in finite bound quantum systems and their semi-classical interpretation are reviewed. Level densities are associated with classical periodic orbits of a particle in the mean-field. Orbits responsible for the bunching of levels, or the shells, are those with short trajectory length. The inverse of the trajectory length determines the energy spacing of the shells. When two short orbits have almost equal but slightly different lengths, the corresponding quantum level density shows a global beating pattern enveloping individual shell oscillations. This pattern is called “supershell” and may be observed in metal clusters with more than a thousand valence electrons.