  The Debye-Huckel (DH) formalism of bulk electrolytes equivalent to the
gaussian-level closure of the electrostatic Schwinger-Dyson identities without
the interionic hard-core (HC) coupling is extended via the cumulant treatment
of these equations augmented by HC interactions. By confronting the monovalent
ion activity and pressure predictions of our cumulant-corrected DH (CCDH)
theory with hypernetted-chain results and Monte-Carlo simulations from the
literature, we show that this rectification extends the accuracy of the DH
formalism from submolar into molar salt concentrations. In the case of internal
energies or the general case of divalent electrolytes mainly governed by charge
correlations, the improved accuracy of the CCDH theory is limited to submolar
ion concentrations. Comparison with experimental data from the literature shows
that via the adjustment of the hydrated ion radii, the CCDH formalism can
equally reproduce the non-uniform effect of salt increment on the ionic
activity coefficients up to molar concentrations. The inequality satisfied by
these HC sizes coincides with the cationic branch of the Hofmeister series.

Soft Condensed Matter