Schwinger–Lanczos algorithm for calculation of off-shell [formula omitted]-matrix elements and Wynn's epsilon algorithm

Abstract

A generalization of the Schwinger–Lanczos algorithm for the calculation of the off-shell T-matrix elements is presented and shown to be equivalent to the Wynn's epsilon algorithm for acceleration of the Born series. Both methods are applied to the calculation of cross section for the dissociative attachment of electrons to hydrogen molecule, e −+ H 2→ H+ H − . Although formally fully equivalent both methods behave very differently numerically. It is shown that the Schwinger–Lanczos algorithm is more stable and generally superior to all other methods discussed in this paper.