Electron–Molecule Collisions in Low-Temperature Plasmas: The Role of Theory

This chapter discusses the contribution that theoretical methods can make to a knowledge of electron-molecule collision behavior, and thereby to an understanding of low-temperature plasmas. Its aim is to survey both the relevant problems and the methods that have been developed to treat those problems. Without delving deeply into the workings of any specific method, we will try to convey both the capabilities and the limitations of present theoretical approaches, and to point out directions for future progress. If one hopes to develop detailed, predictive models of plasmas, microscopic information such as electron-molecule collision probabilities clearly is needed. But why obtain that information from theory? The short answer is that experimental data are often absent and-given the difficulty of the measurements and the paucity of research groups conducting them-in many cases are likely to remain so indefinitely. A longer answer would add that, as both theoretical methods and computer hardware improve, theory is, at least in some areas, becoming competitive with experiment in terms of accuracy and time to solution. To set the stage for the subsequent discussion, let us briefly recall some features of the electron-molecule collision problem as it arises in low-temperature, nonequilibrium plasmas. Most salient is that the electron kinetic energies are low, with the energy distribution often peaking at a few e V Thus electrons in the higher-energy tail of the distribution may be responsible for important inelastic processes, such as electronic excitation and ionization of molecules, whose thresholds often lie above 10 e V, but very little of the plasma chemistry will be driven by truly high-energy electrons-that is, electrons whose energies greatly exceed the average kinetic energies of molecular valence electrons. This simple fact has profound consequences for both theory and experiment, because in both instances it is far more difficult to work with low-energy electrons. In the case of theory, many simplifying approximations that can be applied at high energy are excluded, and it becomes necessary to employ a many-body approach that treats the projectile electron and the electrons belonging to the molecule on an equal footing, with a proper accounting being made for the indistinguishability of electrons. As we will see later, the low-energy electron-molecule collision problem is far from hopeless; certain simplifications can usually be made without seriously impairing accuracy. What remains to be solved, however, is still formidable-a version of Schrodinger's equation for the motion of several (perhaps several dozen) electrons. As this is a second-order partial differential equation with three spatial degrees of freedom per electron, direct integration is completely out of the question. The goal of theory, then, is to develop practical methods of approximation that allow one to extract reliable collision information