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Zhur. Eksptl'. i Teoret. Fiz.

GREEN'S FUNCTION OF ODD NUCLEI

Yu.T. Grind, S.I. Drozdov, Д.Ф. Зарецкий

Published Jan 1, 1960• 0 citations
OpenAlex

Abstract

The techniques of the many body theory are applied to a study of pair correlation in finite systems with an odd number of particles. The Green's function was found and the perturbation theory developed. (auth)

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The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the Correlated Iteration Theory, which has been developed by the author. This approach differs from all other known variants of perturbation theory for Green's functions by the combination of two factors: the systematic formulation of an algorithm for obtaining subsequent approximations and the consistent consideration of interparticle correlations at each step of the procedure.