Strong screening in the plum pudding model

TL;DR

This paper investigates a generalized Coulomb problem involving penetrating charges within a charged sphere, analyzing scaling laws, deviations from mean-field theory, and discovering a local overcharging phenomenon through simulations and analytical methods.

Contribution

It introduces a generalized Thomson problem with penetrating charges, providing new insights into scaling laws, correlation effects, and overcharging phenomena in condensed matter systems.

Findings

Scaling laws at large Coulombic couplings

Deviations from mean-field behavior

Discovery of local overcharging driven by ionic correlations

Abstract

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.