Abstract

The Bethe-Goldstone-equation is replaced by a rigorous nonlinear integro-differential equation determining the two particle correlations and the interaction energy. This nonlinear equation has been solved for vanishing total momentum and separable potential. The hole-hole and particle-hole interactions as well as the three and four particle clusters have been neglected. There are no singularities in this more rigorous equation. For those values of the two particle energy for which singularities occur, if one neglects the quadratic terms, the solutions are of “compound type”, i.e. the localized part has a large (but finite) amplitude compared with the unperturbed plane wave.

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