Variational Methods in Electron-Atom Scattering Theory

The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena.

Springer Book Archives

1. Quantum Mechanics of Electron-Atom Scattering.- 1.1. Structure of the Wave Function.- 1.2. Cross Sections.- 1.3. Close-Coupling Expansion.- 1.4. Polarization Potentials and Pseudostates.- 1.5. Continuum Bethe-Goldstone Equations.- 1.6. Generalizations of the Bethe-Goldstone Approximation.- 2. Variational Theory.- 2.1. Formalism for Multichannel Scattering.- 2.2. The Hulthén-Kohn Variational Principle and Variational Bounds.- 2.3. Anomalies in the Kohn Formalism.- 2.4. Anomaly-Free Methods.- 2.5. Variational R-Matrix Method.- 2.6. Hybrid Methods.- 2.7. The Schwinger Variational Principle.- 3. Resonances and Threshold Effects.- 3.1. Electron Scattering Resonances.- 3.2. Theory of Resonances.- 3.3. Scattering Near Thresholds.- 3.4. The Stabilization Method.- 3.5. Adiabatic Theory of Perturbed Target States.- 4. Computational Technique.- 4.1. Reduction to One- and Two-Electron Integrals.- 4.2. Vector Coupling and Angular Integrals.- 4.3. Radial Integrals.- 4.4. Structure of a Computer Program.- 5. Applications to One-Electron Atoms.- 5.1. Hydrogen: Elastic Scattering.- 5.2. Hydrogen: Inelastic Scattering.- 5.3. Alkali Metal Atoms.- 6. Applications to Other Atoms.- 6.1. Helium: Elastic Scattering.- 6.2. Helium: Inelastic Scattering.- 6.3. Carbon, Nitrogen, and Oxygen.- References.