A Lippmann-Schwinger approach for the determination of photoionization and photodetachment cross sections based on a partial wave Green's function expansion and configuration interaction wave functions

摘要

A computational approach is presented for determining partial differential cross sections for molecular photodetachment and photoionization. The approach, which extends a recent treatment of negative ion photodetachment, uses multireference configuration interaction wave functions to describe both the target or residual molecule and its interaction with the scattered electron and can treat states of the residual molecule which can be described adiabatically or are non-adiabatically coupled by conical intersections. Antisymmetry is taken into account in an approximate manner and a Lippmann-Schwinger equation is used to treat the interaction of the ionized/detached electron with the residual molecule. A partial wave expansion of the requisite Green's functions enables a unified treatment of photoionization and photodetachment and achieves computational efficiencies. A matrix representation of the quantities appearing in the iterated solution to the Lippmann-Schwinger equation using the radial Green's function permits the iterated solution to be summed eliminating potential convergence issues. Two methods for determining the radial Green's functions are presented. In the standard approach the Green's function is determined using the regular and irregular solutions to the corresponding homogeneous equation. The numerical issues associated with this well-studied form of the Green's function are non-trivial. An alternative approach is introduced which uses the complex scaling technique to construct the relevant matrix elements of the Green's function. The degree of simplification achieved in this way is significant.