AbstractIf a quantummechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well known mathematical formalism of classical mechanics in the casenλ3≪ 1. The two‐particle quantummechanical potential is determined by the two particle Slater sum. In this paper we calculated the two particle Slater sum using a development according toe2and the resolvent formalism. From the binary distribution function the correlation energy as well as the free energy were determined up to the ordere4. Symmetry effects were taken into acc