Topics in Atomic Collision Theory

Topics in Atomic Collision Theory originated in a course of graduate lectures given at the University of Colorado and at University College in London. It is recommended for students in physics and related fields who are interested in the application of quantum scattering theory to low-energy atomic collision phenomena. No attention is given to the electromagnetic, nuclear, or elementary particle domains. The book is organized into three parts: static field scattering, electron-atom collisions, and atom-atom collisions. These are in the order of increasing physical complexity and hence necessarily in the order of decreasing mathematical tractability. The topics and methods selected were those which contributed most significantly to the understanding of the physics and the calculation of reliable cross sections. The attempt has been made to treat each of the sections in a complete and self-contained manner. The limited scope of this book has unfortunately made it necessary to omit discussion of many promising methods.

Preface

Part I. Static Field Scattering

1. Classical Scattering and Quantum Formulation

2. Partial Wave Analysis

3. Scattering Matrix and Bound States

4. Resonance Effects

5a. Normalization of Continuum States

5b. Coulomb Scattering

6. Integral Equation Formulation

7. Variational Methods for Phase Shifts

8. Variational Methods for Scattering Amplitudes

9. Bounding Principle for Scattering Length

10. Nonspherical Potential Fields

Part II. Electron-Atom Collisions

11. Formulation of Many-Channel Problem

12. Role of Pauli Principle

13. Integral Expression for Scattering Amplitude

14. Born, Bethe, and Oppenheimer Approximations

15. Variational Methods

16. Close Coupling Method

17. Ionization

18. Resonances and Compound Atom States

19. Threshold Behavior of Cross Sections

20. Anomalous Threshold Behaviors

Part III. Atom-Atom Collisions

21. General Kinematic Considerations

22. Expansion in Molecular States

23. Identical Nuclei and the Pauli Principle

24. Impact Parameter Method and Perturbation Solutions

25a. Unitarized Approximation

25b. Variational Principle for Time-Dependent Case

26. Coupled Equations for Proton-Hydrogen Collisions

27. Crossing of Potential Energy Curves

28. Adiabatic Symmetric Charge Transfer

29. General Formulation for Rearrangement Collisions

30. Charge Transfer in Fast Collisions

Index