Variational Methods in Electron-Atom Scattering Theory
Variational Methods in Electron-Atom Scattering Theory

Author: Robert K. Nesbet

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 234

ISBN-13: 1468484311

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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.

Potential Scattering in Atomic Physics
Potential Scattering in Atomic Physics

Author: P. G. Burke

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 137

ISBN-13: 1461341124

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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.

Theory of Electron—Atom Collisions
Theory of Electron—Atom Collisions

Author: Philip G. Burke

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 264

ISBN-13: 1489915672

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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.

Electron-atom Scattering
Electron-atom Scattering

Author: Maurizio Dapor

Publisher: Nova Biomedical Books

Published: 1999

Total Pages: 252

ISBN-13:

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This book is an introductory approach to the electron-atom scattering theoretical formulation. It focuses on the mathematical tools and on the physics underlying the modern description of electrons, atoms and electron-atom scattering. The first part is devoted to the fundamentals of quantum mechanics, i.e. the Schrodinger equation, the Heisenberg uncertainty principle and the general formalism. The second part concerns the many electron atoms and introduces the scattering of electrons. The third part is devoted to the quantum relativistic theory of the electron and of the electron-atom elastic scattering. The fourth part concerns selected aspects of the interaction of electrons with the matter: absorption, backscattering, transmission, depth distribution of the absorbed electrons, energy and angular distribution of the backscattered electrons, and secondary electrons.

Variational Calculation of Electron Elastic Scattering by Atomic Helium
Variational Calculation of Electron Elastic Scattering by Atomic Helium

Author: Paul Joseph Chernek

Publisher:

Published: 1982

Total Pages: 52

ISBN-13:

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The elastic-scattering of electrons from atomic helium in the ground state is investigated. It is shown that for low energy incident electrons the scattering problem reduced to solving an ordinary integro-differential equation for the scattering wave-function. A method is discussed to obtain approximate solutions to the integro-differential equation by variational principles. The extremum condition of the variational method is formulated into a general N x N matrix equation which reduces to a 2 x 2 eigen-value matrix problem for the phase-shift of the scattering electron. An algorithm is presented to obtain the collisional cross-section for elastic scattering as a function of incident electron energy. (Author).