Strong screening in the plum pudding model

We study a generalized Thomson problem that appears in several condensed matter settings: identical point-charge particles can penetrate inside a homogeneously charged sphere, with global electro-neutrality. The emphasis is on scaling laws at large Coulombic couplings, and deviations from mean-field behaviour, by a combination of Monte Carlo simulations and an analytical treatment within a quasi-localized charge approximation, which provides reliable predictions. We also uncover a local overcharging phenomenon driven by ionic correlations alone.