Structure and correlations in two-dimensional classical artificial atoms confined by a Coulomb potential

The ordering of N equally charged particles (-e) moving in two dimensions and confined by a Coulomb potential, resulting from a displaced positive charge 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 approximately 1 in an inner structure of particles which is separated by an outer ring of particles. For N/Z<<1, the Hamiltonian of the parabolic confinement case is recovered. For N/Z approximately 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.