  We investigate spherical macroions in the strong Coulomb coupling regime
within the primitive model in salt-free environment. We first show that the
ground state of an isolated colloid is naturally overcharged by simple
electrostatic arguments illustrated by the Gillespie rule. We furthermore
demonstrate that in the strong Coulomb coupling this mechanism leads to ionized
states and thus to long range attractions between like-charged spheres. We use
molecular dynamics simulations to study in detail the counterion distribution
for one and two highly charged colloids for the ground state as well as for
finite temperatures. We compare our results in terms of a simple version of a
Wigner crystal theory and find excellent qualitative and quantitative
agreement.
