This monograph was written while the author was a visitor at the Center for Theoretical Studies at the University of Miami, Coral Gables, Florida. The author wishes to thank Professor Behram Kursunoglu for the warm hospitality extended to him at the Center and to acknowledge the many interesting and fruitful discussions which he had with other visitors and with members of staff at the Center. Philip G. Burke v Contents 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Scattering by a Short-Range Potential. . . . . . . . . . . . . . . 5 3. Scattering by a Coulomb Potential. . . . . . . . . . . . . . . . . . 11 4. Scattering by a Spin-Orbit Potential . . . . . . . . . . . . . . " 17 5. Scattering by One-Electron Atoms. . . . . . . . . . . . . . . . . . 23 6. Low-Energy Effective-Range Theory. . . . . . . . . . . . . . . . 39 7. Bound States and Resonances. . . . . . . . . . . . . . . . . . . . . . 55 8. Variational Methods and Bound Principles. . . . . . . . . . 75 9. Integral Equation Methods and the Born Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 10. Semiclassical and Eikonal Methods . . . . . . . . . . . . . . . . . 117 Appendix. The Coupling of Angular Momenta . . . . . . . . . . . 127 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 vii 1 Introduction In this monograph we study the scattering of a particle by a potential field with particular reference to elastic electron scat tering by a neutral atom or by an ion. This subject is clearly of interest in its own right as a branch of quantum mechanical scattering theory. However, it also serves as an introduction to many of the basic theoretical concepts which are used in inelastic electron scattering and ionization. Consequently this mono graph can be viewed as an introduction to texts where these subjects are treated.

This volume contains the invited papers and selected contributed papers presented at the International Symposium on 'Electron-Molecule Scattering and Photoionization' held at SERC's Daresbury Laboratory, Cheshire, England from 18th to 19th July, 1987. This Symposium was a Satellite Meeting to the XVth International Conference on the Physics of Electronic and Atomic Collisions (ICPEAC I and follows a tradition of Satellite Meetings i. n related areas of collisions held in association with previous ICPEAC's. In order to make this volume as representative of the Symposium as possible 'Hot Topics' presented orally at the meeting together with a few papers selected by the Programme Committee from the contributed posters are included. The Editors are grateful to the authors for responding rapidly to the invitation to submit their contri butions for inclusion in the volume, as indeed they are grateful to all the authors for the high quality of their contributions. The Symposium brought together over 100 scientists from many countries and from broad interdisciplinary backgrounds to hear about current rapid advances in electron-molecule scatteri. ng and photoioniza tion. These advances have been stimulated on the experimental side by the increasing availability of electron beams with millivolt energy resolution, by synchrotron radiation sources and by intense tunable lasers. On the theoretical side the introduction of new computational methods enables accurate predictions to be made, resulting in a new and deeper understanding of the basic physical processes involved."