Evaluation of operator Padé approximants for perturbative expansions in scattering theory
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Abstract
Considering scattering amplitudes as integral operators, the formal summation of their perturbation expansions can be done using operator Pad\'e approximants. The lowest-order approximant can be considered a natural improvement of the Bethe-Salpeter equation in ladder approximation if one includes one-loop diagrams other than the direct box graph. The problem of how to evaluate the approximants arises. Variational principles for their calculation have been proposed earlier but yielded ambiguous results. A new variational technique, the method of the variational gradient, is presented which provides a unique though elaborate procedure. The applicability of the method is demonstrated in two cases: a simple potential model and the Bethe-Salpeter equation in ladder approximation for nucleon-nucleon scattering.
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