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Canadian Journal of Physics

Simple derivation of the exp(S) equations

J. Dąbrowski

Published Oct 1, 1983• 2 citations
Publisher

Abstract

It is shown that equations for the n-particle, n-hole amplitudes of the exp (S) theory of the interacting many-body system may be easily obtained by analyzing the structure of the Goldstone diagrams for the wave function of the system.
DOI
10.1139/p83-186

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A new approach to the diagrammatic formulation of many-body perturbation theory for open-shell systems is presented. The formalism is based on a generalized form of the Bloch equation that also generates the Rayleigh-Schrödinger perturbation expansion for a system with several open shells. Second quantization in the particle-hole formulation is used together with Wick's theorem in order to derive graphical rules in the usual way. The linked-diagram property of the wave operator and of the effective interaction is shown by expanding the wave operator in terms of normal products of connected diagram clusters, in analogy with the exp(S) formalism of Coester and Kümmel for closed-shell systems. Self-consistent “coupled-cluster” equations are derived for the open-shell case from the generalized Bloch equation by a straightforward extension of the procedure of Čížek and Paldus. The application of such equations for investigating different properties of open-shell atoms is discussed.
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