The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems they can be grouped into two types: those based on the Schroedinger equation and those based on the Lippmann-Schwinger equation. The application of the Schwinger variational (SV) method to e-molecule collisions and photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions

Studies of Elastic and Electronically Inelastic Electron-Molecule Collisions

Cross-sections for the scattering of low-energy electrons by molecules play an important role in the modeling of swarm and plasma etching systems, gas lasers, and planetary atmospheres. In contrast to the related atomic problem, the progress to date in both theoretical and experimental studies of electron-molecule scattering cross-sections has been limited [1]. On the theoretical side, this situation is primarily due to the additional complexities arising from the nonspherical potential fields of molecular targets. Most studies of electronic excitation of molecules by low-energy electrons have hence been carried out using low-order theories. These include plane-wave theories such as the Born Ochkur-Rudge approximations [2, 3], the impact-parameter method [4], and distorted-wave theories [5, 6]. Several studies of elastic scattering by molecules have also used local approximations to the nonlocal exchange potentials [7]. Although such theories and approximations can be computationally easy to apply, they do not contain enough of the collision physics to yield consistently reliable differential and integral cross sections, particularly at low and intermediate energies [8]. What is clearly needed are theoretical methods which can provide quantitatively reliable cross-sections for the elastic and inelastic scattering of low-energy electrons by molecules