Probing the Atom: Interactions of Coupled States, Fast Beams, and Loose Electrons

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The many-faceted efforts to understand the structure and interactions of atoms over the past hundred years have contributed decisively and dramatically to the explosive development of physics. There is hardly a branch of modern physical science that does not in some seminal way rely on the fundamental principles and mathematical and experimental insights that derive from these studies. In particular, the drive to understand the singular features of the hydrogen atom—simultaneously the archetype of all atoms and the least typical atom—spurred many of the twentieth century's advances in physics and chemistry. This book gives an in-depth account of the author's own penetrating experimental and theoretical investigations of the hydrogen atom, while simultaneously providing broad lessons in the application of quantum mechanics to atomic structure and interactions.

A pioneer in the combined use of atomic accelerators and radiofrequency spectroscopy for probing the internal structure of the hydrogen atom, Mark Silverman examines the general principles behind this far-reaching experimental approach. Fast-moving protons are directed into gas or foil targets from which they capture electrons to become hydrogen atoms moving uniformly at very high speeds. During their rapid passage through the spectroscopy chamber of the atomic accelerator, these atoms reveal by the light they emit fascinating details of their internal configuration and the interactions that created them. Silverman examines the effects of radiofrequency fields on the hydrogen atom clearly and systematically, explaining the details of these interactions at different levels of complexity and refinement, each level illuminating the physical processes involved from different and complementary perspectives.

Readers interested in diverse areas of physics and physical chemistry will appreciate both the theoretical and practical implications of Silverman's studies and the personal style with which he relays them. This is a work of not only an outstanding research physicist, but a fine teacher who understands how curiosity underlies all science.

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Editorial Reviews

As a comprehensive treatment of a well-defined problem, the book is an excellent choice for advanced quantum mechanics studies on atomic structure. . . Silverman does a masterful job of placing the required mathematics in perspective. . . .
From the Publisher
"As a comprehensive treatment of a well-defined problem, the book is an excellent choice for advanced quantum mechanics studies on atomic structure. . . Silverman does a masterful job of placing the required mathematics in perspective. . . ."Choice
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Product Details

  • ISBN-13: 9780691009629
  • Publisher: Princeton University Press
  • Publication date: 1/17/2000
  • Edition description: New Edition
  • Pages: 248
  • Product dimensions: 6.47 (w) x 9.51 (h) x 0.86 (d)

Table of Contents

Preface: In at the Beginnings xi
Notes xviii
Chapter I Energies and Spectral Lines 3
1.1. Anatomy of Hydrogen 3
1.2. Shapes and Widths 12
Notes 17
Chapter 2 The Driven Two-Level Atom 19
2.1. Dynamics of a Two-Level Atom 19
2.2. Rotating-Wave Approximation 23
2.3. Oscillating-Field Theory 28
2.4. Occupation Probabilities 32
Notes 42
Chapter 3 The Driven Multilevel Atom 43
3.1. Statistical Uncertainties and the Density Matrix 43
3.2. Time Evolution of the Density Matrix 46
3.3. Generalized Resonant Field Theory 48
3.4. Two-State Transitions 54
3.5. Three-State Transitions 56
3.6. Four-State Transitions 60
3.7. Numerical Solution of the N-State System 65
3.8. Coupling Elements Vuv 67
Appendix. Eigenvalues and Eigenvectors of Three- and Four-State Systems 72
Notes 76
Chapter 4 Multiple-Quantum Transitions 78
4.1. The Quantized Radiofrequency Field 78
4.2. Remarks on Dipole Coupling 85
4.3. The Two-Level Atom (Again) 87
4.4. Coherent Field States 91
4.5. Triple-Quantum Transitions 93
4.6. Crossings and Anticrossings 94
4.7 Resolvent Operator Solution 99
4.8 One- and Three-Photon Lineshapes 106
Appendix 4A: Semiclassical Theory of Multiphoton Transitions 111
Appendix 4B: Resolvents, Propagators, and Green's Functions 113
Notes 115
Chapter 5 The Decay of Coupled States 117
5.1. Perspectives on Radiation Damping 117
5.2. The Quantized Optical Field 118
5.3. State Amplitudes and Radiative Decay Rates 122
5.4. Emission Lineshapes 127
Notes 138
Chapter 6 Optical Detection Theory 139
6.1. The Process of Detection 139
6.2. The Optical Detection Function 143
6.3. The Efficiency Matrix 147
6.4. The Optical Signal 153
Notes 158
Chapter 7 State Selection and Lineshape Resolution 160
7.1. The Use of Sequential Fields 160
7.2. Parallel Oscillating Fields 162
7.3. Nonparallel Oscillating Fields 170
Notes 172
Chapter 8 Elements of Experimental Design and Application 173
8.1. General Description 173
8.2. Ion Production and Extraction 175
8.3. Ion Acceleration and Focusing 179
8.4. Excited Atom Production 184
8.5. The Radiofrequency System 187
8.6. Optical Detection 196
8.7. Spectroscopy 197
8.8. Electron Capture and Atom Formation 206
Appendix 8A: The Paraxial Ray Equation for Ions 214
Appendix 8B: Effect of Standing Waves on a Resonance Lineshape 215
Appendix 8C: Phenomenological Model of the RF Chamber 219
Notes 222
Index 225

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"This book is a personal account of how physicists understand, and go about understanding, atomic structures and interactions with electromagnetic fields. It is a story because the book has an overriding vision. Subjects are not simply thrown together, but instead flow smoothly; it is like sitting and talking physics with a trusted mentor.... Silverman achieves his goal and provides a timeless view of the major ideas and techniques of atomic physics."—Jim McClymer, University of Maine

"The author guides us on a grand tour of probing the atomic structure and behavior by means of oscillating fields with radio frequencies (rf). In the course of the tour, he presents systematically the basic principles and quantum mechanical frameworks in a way instructive and helpful in understanding spectroscopic rf-line shape analysis. This book will be useful not only to spectroscopists as a quick review of theories in the field but also to those interested more generally in application of quantum mechanics in beam-field interactions. The book is extremely well written and well organized. I believe a wide class of readers will benefit from this book."—Akira Inomata, State University of New York at Albany

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