ON THE ACCELERATION OF CONVERGENCE OF MANY-BODY PERTURBATION-THEORY .1. GENERAL-THEORY

The theoretical background of schemes for accelerating convergence of Moller-Plesset-Goldstone perturbation theory is discussed. Aiming at practical applications we consider approximate formulations of the many-body theory of atoms and molecules in finite-dimensional Hilbert spaces. A key role is played by nearby singularities of energy levels and eigenfunctions considered as functions of a suitably chosen coupling parameter. Infinite subsummations in the perturbation series are performed such that the influence of these singularities is eliminated or, at least, sufficiently attenuated. The danger of double counting of diagrammatic contributions already included in these infinite subsummations is avoided by the very construction of our scheme.