CLASSICAL MANY-PARTICLE CLUSTERS IN 2 DIMENSIONS

We report on a study of a classical, finite system of confined particl es in two dimensions with a two-body repulsive interaction. We first d evelop a simple analytical method for obtaining equilibrium configurat ions and energies for a few particles. When the confinement is harmoni c, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be indepen dent of the strength of the interaction and dependent only on its func tional form. It is also found to be independent of the magnetic field strength when this is included. We further study the effect of the fun ctional form of the confinement potential on the shell structure. Fina lly, we report some interesting results obtained when a three-body int eraction is included, albeit in a particular model.