Analytic theory of resonances, virtual states and bound states ion electron-molecule scattering and related processes

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Abstract
Using the formalism of discrete state-continuum interaction as introduced, for example, by Feshbach and Fano, formally exact operator expressions are derived for the cross sections of resonant electron scattering, dissociative attachment and related processes. Concentrating on the fixed-nuclei limit, a rigorous description of resonances, virtual states and bound states and their connection at threshold is developed. In principle the approach is to impose the threshold law on the decay width of the resonance and to take proper account of the energy-dependent level shift. The analytic structure of the fixed-nuclei S matrix for electron scattering is obtained by analytic continuation into the complex momentum and energy planes. At energies sufficiently close to threshold the results are of universal validity, depending only on angular momentum and the leading multipole moments of the molecular charge distribution. The approach is exemplified for s-wave and p-wave scattering by short-range potentials, where it reproduces the well-known results of general analytic S-matrix theory. New results are then obtained for the behaviour of resonances and bound states of polar molecules close to threshold.

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