The solution of the mean-spherical approximation for the primitive model of electrolytes by a direct method

A method introduced by Krienke to derive the Percus-Yevick solution for a fluid of neutral hard spheres is enlarged and used to solve the mean-spherical approximation (MSA) for the primitive model of electrolytes in a direct way. The method exploits the fact that the long range part of the potential is a Green's function. This is used to show that the effect of this part of the potential is merely to introduce a constant into the equations for the short range part of the direct correlation function. These equations can then be solved formally and the new constant can be obtained from an equation previously derived by the author. It is shown, too, that the same method can be used to derive the solution to the MSA for the problem of hard spheres interacting through Yukawa potential tails.