New Theoretical Approaches for Studying Electron Collisions with Small Molecules^*

Abstract

There has been a recent resurgence of interest in the use of algebraic variational methods for studying a variety of collision problems. Much of this interest stems from the discovery that spurious singularities, which plagued the traditional methods, can be eliminated when the variational principle is formulated with outgoing-wave boundary conditions.¹,² Another reason for the recent activity is the obvious suitability of these methods to present-day supercomputers. My purpose here is to describe an implementation of the complex Kohn method³, an algebraic variational technique, for studying electron collisions with small molecules, both linear and non-linear. Unlike variational principles based on the integral form of the Schroedinger equation (Lippmann-Schwinger equation), the method only requires Hamiltonian matrix elements. I will also show how the formalism allows one to develop a variational principle for computing first-order properties, such as bound-free dipole transition amplitudes. I will show results for the electron-impact dissociation of hydrogen as a function of initial vibrational quantum number. I will also illustrate the method for polyatomic molecules with results for elastic scattering of electrons by formaldehyde.

This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore Laboratory under contract No. W-7405-ENG-48.