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The Debye-Huckel (DH) formalism of bulk electrolytes equivalent to thegaussian-level closure of the electrostatic Schwinger-Dyson identities withoutthe interionic hard-core (HC) coupling is extended via the cumulant treatmentof these equations augmented by HC interactions. By confronting the monovalention activity and pressure predictions of our cumulant-corrected DH (CCDH)theory with hypernetted-chain results and Monte-Carlo simulations from theliterature, we show that this rectification extends the accuracy of the DHformalism from submolar into molar salt concentrations. In the case of internalenergies or the general case of divalent electrolytes mainly governed by chargecorrelations, the improved accuracy of the CCDH theory is limited to submolarion concentrations. Comparison with experimental data from the literature showsthat via the adjustment of the hydrated ion radii, the CCDH formalism canequally reproduce the non-uniform effect of salt increment on the ionicactivity coefficients up to molar concentrations. The inequality satisfied bythese HC sizes coincides with the cationic branch of the Hofmeister series.

Systematic incorporation of the ionic hard-core size into the Debye-Huckel theory via the cumulant expansion of the Schwinger-Dyson equations