This book is intended for any student of physics who wants a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for a reader who is already familiar with the general principles of quantum mechanics (as taught, for example, in the first year graduate course at most American universities) and who has some small acquaintance with scattering theory, as would be acquired in the same first-year course. It is my hope to bring the student of atomic or nuclear physics to the point where he can begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For the student of high-energy physics I have tried to provide the necessary background for his later study of relativistic problems.

Concerning my choice of subject matter, the one feature that seems to need explanation here is the decision to exclude relativistic scattering theory. I made this decision for a variety of reasons: The theory of nonrelativistic collisions has wide application in the low-energy processes of atomic, nuclear, and particle physics; and is sufficiently extensive to make up a book by itself. The basic laws of nonrelativistic quantum mechanics are well understood and, in sharp contrast to the relativistic case, nonrelativistic scattering theory is a logically complete and selfcontained structure. Moreover, there are many important features common to the nonrelativistic and relativistic theories. (For example, both are formulated in terms of the unitary scattering operator S.) This makes the former an excellent introduction to the latter, and wherever possible I have presented the material so as to emphasize its relevance in the relativistic, as well as the nonrelativistic, domains.

Concerning my treatment of the subject, two comments are in order. First, the reader will find that I have tried always to present a topic in terms of the simplest relevant example (the most complicated atomic process discussed in any detail is electron-hydrogen scattering; the polarization experiment chosen for discussion is the scattering of spin-half particles off a spinless target; and the first two thirds of the book deal exclusively with the

in their simplest context. Once these concepts are really well understood on their extension to more general situations is usually a straightforward matter and can often be left to the reader. This policy means that the coverage of the book is less comprehensive and general than that of most books on the subject) [Mott and Massey (1933), Goldberger and Watson (1964), and Newton (1966)] and, hence, perhaps less useful as a reference for the active researcher. However, it is my hope that in this way it may prove more useful to the student struggling to learn the subject. Second, the reader will find a greater emphasis than is traditional on the time-dependent approach to the subject. Historically, scattering theory developed in the late twenties and thirties around the time-independent stationary scattering states. Only in the late fifties was this formalism properly justified with the development of a realistic time-dependent theory. Now, however, it is possible to develop scattering theory in a much more satisfactory way, beginning with the timedependent formalism and using this to define all of the basic concepts, and only then introducing the time-independent theory as a tool for computation and for establishing certain general properties.

With the exception of a few chapters, the book is designed to be read systematically from the beginning to the end, and I hope that this is how the reader will choose to use it.? I also hope that the reader will try to do most, if not all, of the small number of problems at the end of each chapter. Most of these have been tested by three successive groups of students at the University of Colorado. They are intended to improve the reader's grasp of the not treated in the text. material just covered and to introduce him to some important developments

A large number of colleagues and friends have helped me in the writing of this book. Special thanks are due to Professor Thomas Jordan, Professor Michael Whippman, Mr. Rayner Rosich, and Mr. David Goodmanson, all of whom read large portions of the manuscript and made numerous helpful suggestions and criticisms. Also to Martin Hidalgo, Alan Hunt, Rayner Rosich and Robert Stolt who did the calculations behind several of the graphs and tables. I am grateful to Professor Paul Matthews for hospitality at Imperial College where I began serious work on the book; and to several colleagues at Imperial College and the University of Colorado-Kenneth Barnes, Wesley Brittin, Chris Zafiratos and many others-for invaluable conversations and encouragement. Above all I want to thank my wife Debby. She not only bore with three years of authorship agonies in a most wifely way; she edited the whole manuscript and typed it twice.

1* All references are given by author's name and date and can be found on p. 463. *

2* The principal exceptions are Chapters 7, 14, 15, 20, and 21. The reader can omit or postpone some or all of the material in these chapters without seriously affecting his understanding of the subsequent material.