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.

The aim of the book is to give a coherent and comprehensive account of quantum scattering theory with applications to atomic, molecular and nuclear systems. The motivation for this is to supply the necessary theoretical tools to calculate scattering observables of these many-body systems. Concepts which are seemingly different for atomic/molecular scattering from those of nuclear systems, are shown to be the same once physical units such as energy and length are diligently clarified. Many-body resonances excited in nuclear systems are the same as those in atomic systems and come under the name of Feshbach resonances. We also lean heavily on semi-classical methods to explain the physics of quantum scattering OCo especially the interference seen in the angle dependence of the cross section. Having in mind a wide readership, the book includes sections on scattering in two dimensions which is of use in surface physics. Several problems are also included at the end of each of the chapters.

The authors aim to hone the theory of electron-atom and electron-ion collisions by developing mathematical equations and comparing their results to the wealth of recent experimental data. This first of three parts focuses on potential scattering, and will serve as an introduction to many of the concepts covered in Parts II and III. As these processes occur in so many of the physical sciences, researchers in astrophysics, atmospheric physics, plasma physics, and laser physics will all benefit from the monograph.

This expanded and updated well-established textbook contains an advanced presentationof quantum mechanics adapted to the requirements of modern atomic physics. Itincludes topics of current interest such as semiclassical theory, chaos, atom optics andBose-Einstein condensation in atomic gases. In order to facilitate the consolidationof the material covered, various problems are included, together with completesolutions. The emphasis on theory enables the reader to appreciate the fundamentalassumptions underlying standard theoretical constructs and to embark on independentresearch projects. The fourth edition of Theoretical Atomic Physics contains anupdated treatment of the sections involving scattering theory and near-thresholdphenomena manifest in the behaviour of cold atoms (and molecules). Special attentionis given to the quantization of weakly bound states just below the continuum thresholdand to low-energy scattering and quantum reflection just above. Particular emphasisis laid on the fundamental differences between long-ranged Coulombic potentialsand shorter-ranged potentials falling off faster than 1/r2 at large distances r. The newsections on tunable near-threshold Feshbach resonances and on scattering in two spatialdimensions also address problems relevant for current and future research in the fieldof cold (and ultra-cold) atoms. Graduate students and researchers will find this book avaluable resource and comprehensive reference alike.

The main goal of this book is to elucidate what kind of experiment must be performed in order to determine the full set of independent parameters which can be extracted and calculated from theory, where electrons, photons, atoms, ions, molecules, or molecular ions may serve as the interacting constituents of matter. The feasibility of such perfect' and-or `complete' experiments, providing the complete quantum mechanical knowledge of the process, is associated with the enormous potential of modern research techniques, both, in experiment and theory. It is even difficult to overestimate the role of theory in setting of the complete experiment, starting with the fact that an experiment can be complete only within a certain theoretical framework, and ending with the direct prescription of what, and in what conditions should be measured to make the experiment `complete'. The language of the related theory is the language of quantum mechanical amplitudes and their relative phases. This book captures the spirit of research in the direction of the complete experiment in atomic and molecular physics, considering some of the basic quantum processes: scattering, Auger decay and photo-ionization. It includes a description of the experimental methods used to realize, step by step, the complete experiment up to the level of the amplitudes and phases. The corresponding arsenal includes, beyond determining the total cross section, the observation of angle and spin resolved quantities, photon polarization and correlation parameters, measurements applying coincidence techniques, preparing initially polarized targets, and even more sophisticated methods. The `complete' experiment is, until today, hardly to perform. Therefore, much attention is paid to the results of state-of-the-art experiments providing detailed information on the process, and their comparison to the related theoretical approaches, just to mention relativistic multi-configurational Dirac-Fock, convergent close-coupling, Breit-Pauli R-matrix, or relativistic distorted wave approaches, as well as Green's operator methods. This book has been written in honor of Herbert Walther and his major contribution to the field but even to stimulate advanced Bachelor and Master students by demonstrating that obviously nowadays atomic and molecular scattering physics yields and gives a much exciting appreciation for further advancing the field.

Computational Atomic Physics deals with computational methods for calculating electron (and positron) scattering from atoms and ions, including elastic scattering, excitation, and ionization processes. Each chapter is divided into abstract, theory, computer program with sample input and output, summary, suggested problems, and references. An MS-DOS diskette is included, which holds 11 programs covering the features of each chapter and therefore contributing to a deeper understanding of the field. Thus the book provides a unique practical application of advanced quantum mechanics.