Removal of divergences in diagram expansions for systems with Coulomb interaction

Functional series in the powers of the Coulomb interaction is constructed for the two-particle correlation function by means of the method of splitting the ion interaction potential into the short-range and the long-range parts. Procedure of resummation of this series is developed which includes the construction of the Dyson equation and the transition to irreducible diagrams and makes it possible to remove all the long-range Coulomb divergences as well as the short-range divergences due to the water-melon type diagrams. The correction terms to the Debye, length are found with the aid of the resummated expansion, including the terms caused by the presence of a neutral medium.