Computing Counterion Densities at Intermediate Coupling

By decomposing the Coulomb interaction into a long distance component appropriate for mean-field theory, and a nonmean-field short distance component, we compute the counterion density near a charged surface for all values of the counterion coupling parameter. A modified strong-coupling expansion that is manifestly finite at all coupling strengths is used to treat the short distance component. We find a nonperturbative correction related to the lateral counterion correlations that modifies the density at intermediate coupling.