QUASI-PARTICLE EQUATION FROM THE CONFIGURATION-INTERACTION (CI) WAVE-FUNCTION METHOD

The Green-function method is a well-known way to reduce the quantum mechanical problem of n electrons moving in the field of clamped nuclei to the problem of solving a one-electron Schrodinger equation (the quasi-particle equation) involving a pseudopotential (the self-energy). This method is widely used in solid-state, low-energy electron-molecule scattering, ionization, and electron attachment theory, and much work has focused on finding accurate self-energy approximations. Unfortunately, the operator nature of the fundamental quantity (Green function) in the usual quasi-particle equation formalism significantly complicates the derivation of self-energy approximations, in turn significantly complicating applications to inelastic scattering and multiconfigurational bound-state problems. For these problems or wherever the operator approach becomes inconvenient, we propose an alternative quasi-particle equation derived wholely within a configuration interaction wave-function formalism and intended to describe the same phenomenology as does the Green function quasi-particle equation. Our derivation refers specifically to electron removal but is readily generalized to electron attachment and scattering. Although the Green function and wave-function quasi-particle equations are different, we emphasize the parallels by rederiving both equations within the equations-of-motion formalism and then producing a wave-function analog of the Green function two-particle-hole Tamm-Dancoff approximation.