Punctual Pade Approximants as a Regularization Procedure for Divergent and Oscillatory Partial Wave Expansions of the Scattering Amplitude

摘要

Previous theorems on the convergence of the (n, n+m) Punctual Pade Approximants to the scattering amplitude are extended. The new proofs include the cases of non-forward and backward scattering corresponding to potentials having 1/r and 1/r exp 2 long-range behaviors, for which the partial-wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long-range potentials of interest in potential scattering. (Atomindex citation 09:402386)