Direct calculation of complex resonance poles using separable expansions of the potential: Application to the 2 Sigma u+ shape resonance in electron-H2 scattering.

Abstract

We present a novel scheme to calculate directly the complex resonance poles in electron-atom or electron-molecule scattering. The method is based on the many-body Green's-function formalism and the use of separable expansions of the self-energy part. It is shown that the poles are given by the complex zeros of certain determinants, which can be straightforwardly calculated using analytically determined matrix elements of the free-particle Green's function. We introduce a projection procedure which (i) leads to a simple and unified description of shape resonances as quasiparticles and (ii) is essential for the numerical feasibility of the calculations. Exploratory calculations are performed for the $^{2}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ shape resonance in electron-${\mathrm{H}}_{2}$ scattering in the static-exchange approximation. This resonance represents a difficult problem owing to its large width at short and intermediate internuclear distances. The fundamental difficulties which arise when using basis-set representations of the potential in the calculation of complex resonance poles are discussed.