Summation of regularized perturbative expansions for singular interactions

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Abstract
In this paper we give a first application of a general method whose mathematical aspects will be fully developed in a forthcoming article. We are concerned with strongly singular perturbative series. Here we shall restrict ourselves to the most general two‐body repulsive singular potential for which a regularization exists. Various extensions of this case are discussed in the conclusion. We show that, knowing only a finite number of regularized Born terms, it is possible to construct an upper bound to the exact phase shifts and that this upper bound is the best possible for the given regularization. The method uses the construction of the [N/N] Padé approximation indifferently on the regularized partial waves of the K or T matrix and exploits the fact that the approximate corresponding phase shifts have an absolute minimum as a function of the regularization parameter (cutoff). Three numerical examples are provided which show, even for very large phase shifts, an excellent convergence.

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