A single positive ion is imbedded in an electron gas with overall charge neutrality. A classical statistical mechanics is considered using an electron-ion Coulomb potential regularized at distances within the de Broglie length. The electron charge density and electric field distribution at the ion are studied as a function of ion-electron coupling using molecular dynamics simulation and theoretical models. Agreement between theory and simulation is quite good in general, although differences are observed for very strong ion-electron coupling due to the enhanced importance of close electron-ion configurations.