Classical many-particle clusters in two dimensions

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method for obtaining equilibrium configurations and energies for a few particles. When the confinement is harmonic, 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 independent of the strength of the interaction and dependent only on its functional form. It is also found to be independent of the magnetic field strength when this is included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally, we report some interesting results obtained when a three-body interaction is included, albeit in a particular model