A theoretical description for the radial density profile of a finite number
of identical charged particles confined in a harmonic trap is developed for
application over a wide range of Coulomb coupling (or, equivalently,
temperatures) and particle numbers. A simple mean field approximation
neglecting correlations yields a density profile which is monotonically
decreasing with radius for all temperatures, in contrast to molecular dynamics
simulations and experiments showing shell structure at lower temperatures. A
more complete theoretical description including charge correlations is
developed here by an extension of the hypernetted chain approximation,
developed for bulk fluids, to the confined charges. The results reproduce all
of the qualitative features observed in molecular dynamics simulations and
experiments. These predictions are then tested quantitatively by comparison
with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory
is obtained for the selected conditions by correcting the hypernetted chain
approximation with a representation for the associated bridge functions.Comment: 10 figures, submitted to Physical Review