Abstract
The analytic properties of the effective interaction W as a function of the residual interaction strength are investigated in the frame-work of a simple 2 × 2 model. Brandow's folded diagram expansion taken order by order in the interaction converges to W only as long as the residual interaction does not force an outside level to cross into the model space spectrum. By reordering the series one can construct an approximation to an analytic continuation of W beyond the crossing region. To improve upon the latter approximation one has to resort to iteration methods. The results are generalized to the N × N case and numerical illustration on a 3 × 3 model is provided.
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