Identification of Siegert states in molecular scattering calculations and application to analysis of dissociative electron attachment

Formation of scattering resonant and virtual states (Siegert states) are one of the most striking phenomena of quantum physics. Those states appear as poles of the S-matrix and are solutions of the Schrödinger equation for complex energies. Siegert states localized in the vicinity of the real energy axis cause a dramatic modification of the cross section for various processes including impact dissociation. Identification of such narrow resonances can be done straightforwardly, e.g. by inspecting the eigenhpase sums. However, identification of virtual states and broad resonances is typically more difficult, especially in multi-electron ab initio scattering calculations which do not lend themselves easily to calculations for complex energies. Our inability to identify unambiguously all Siegert states in ab initio data has led to disputes in the community concerning the mechanism of dissociative electron attachment in complex molecules such as HCOOH.

In this talk I will describe a general method for localization and analysis of Siegert states in multi-electron molecules. The method is based on the R-matrix division of space [1] which enables a numerically stable and computationally efficient search for the exponentially diverging resonant and virtual states and the very diffuse weakly bound dipole-bound states. We show that all Siegert states in a selected part of the complex plane can be readily localized, including broad resonances. Finally, we study Siegert states as a function of geometry in electron collisions with a series of molecules (N₂, HNCO, HCOOH, pyrrole). We identify near-threshold dipole-bound or virtual states as the source of the so-called ``σ* mechanism" in dissociative electron attachment to polar molecules.

[1] L.A. Morgan and P.G. Burke, J. Phys. B: At. Mol. Opt. Phys. 21, 2091 (1988).