Complex coordinate rotation of the electron propagator
- 15 September 1980
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 73 (6), 2858-2866
- https://doi.org/10.1063/1.440455
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.Keywords
This publication has 34 references indexed in Scilit:
- Stationarity of resonant pole trajectories in complex scalingInternational Journal of Quantum Chemistry, 1978
- Extensions of the complex-coordinate method to the study of resonances in many-electron systemsPhysical Review A, 1978
- Effects of an external electric field onresonances ofPhysical Review A, 1978
- Theoretical Studies of Negative Molecular IonsAnnual Review of Physical Chemistry, 1977
- Resonances in Electron Impact on Diatomic MoleculesReviews of Modern Physics, 1973
- Application of Many-Body Green's Functions to the Scattering and Bound-State Properties of HeliumPhysical Review A, 1973
- Many-Body Green's Functions for Finite, Nonuniform Systems: Applications to Closed Shell AtomsThe Journal of Chemical Physics, 1972
- Spectral properties of many-body Schrödinger operators with dilatation-analytic interactionsCommunications in Mathematical Physics, 1971
- A class of analytic perturbations for one-body Schrödinger HamiltoniansCommunications in Mathematical Physics, 1971
- Negative ions and shape resonancesJournal of Physics B: Atomic and Molecular Physics, 1970