Complex coordinate rotation of the electron propagator

Abstract

It is now widely appreciated that the real poles of the electron propagator G(E) yield information on the ionization potentials and electron affinities of the stationary states of an atom or molecule. It is herein shown that application of the Aguilar–Balslev–Combes–Simon coordinate transformation, r→r exp(iΘ), to G(E) yields an analytically continued complex propagator G(Z, Θ) whose complex poles correspond to the complex electron affinities associated with nonstationary, resonance states of an atomic or molecular anion. As an initial application of the coordinate rotation technique we derive and discuss the working equations for a coordinate rotated propagator which is correct to second order in the electron–electron interaction. This is followed by use of the formalism in a model study of a 2P shape resonance in the Be atom. Our second-order results for this system are then compared to those obtained by previous authors employing static exchange, and static-exchange plus cutoff polarization methods.