The ordering of N equally charged particles $\left(-e\right)$ moving in two dimensions and confined by a Coulomb potential, resulting from a displaced positive charge $\mathrm{Ze}$ is discussed. This is a classical model system for atoms. We obtain the configurations of charged particles which, depending on the value of N and Z, may result in ring structures, hexagonal-type configurations, and for $N/Z\approx 1$ in an inner structure of particles which is separated by an outer ring of particles. For $N/Z\ll 1,$ the Hamiltonian of the parabolic confinement case is recovered. For $N/Z\approx 1,$ the configurations are very different from those found in the case of a parabolic confinement potential. A hydrodynamic analysis is presented in order to highlight the correlations effects.

• Received 29 October 2002

DOI:https://doi.org/10.1103/PhysRevE.67.046601