On the calculation of electron-atom collision properties using exterior complex dilatated S- matrix expansions

Abstract

An additive Mittag-Leffler type of partial-wave S-matrix expansion based on resonance poles, their corresponding residues plus a background integral is presented. A particular decomposition of this expression is studied in detail, and the authors emphasise the employment of exterior complex dilatation methods in connection with its investigation. They further give a convenient and simple formula for the residues of the partial-wave S matrix at mirror poles expressed in terms of the residues at the corresponding resonance poles. The restrictions on its applicability are explicitly shown in terms of conditions on the interaction potential. Furthermore, the analytic properties of the various parts of the partition of the expansion are discussed. The considerable advantages and the strength of the formal development are demonstrated by accurate numerical calculations on previously studied electron-atom scattering models using Be, Mg and Ca as targets. The outcome of these investigations is, among other things, a rather appealing (so called) reduced partial-wave S-matrix expansion which may be employed in order to obtain precise scattering information in a very time-saving manner.