Atomic collisions and spectra

Title page......Page 1
Copyright page......Page 2
CONTENTS......Page 3
Preface......Page 7
1.1 Introduction......Page 9
1.2 Experimental Aspects......Page 11
1.3 Atomic Complex: Input and Exit Channels......Page 16
1.4 Symmetries......Page 18
1.5 A One-Dimensional Illustration......Page 20
1.6 Outline of Later Chapters......Page 22
Problems......Page 26
References......Page 28
Part A. PERTURBATION TREATMENTS......Page 31
2.2 Basic Theory......Page 33
2.3 Macroscopic Analysis......Page 35
2.4 General Properties of the Spectrum......Page 39
2.5 Discrete Spectrum......Page 41
2.6 Partial Oscillator Strengths......Page 43
2.7 Specific Features......Page 44
Problems......Page 48
References......Page 49
3.2 The Born Approximation......Page 50
3.3 Construction of the Wave Function......Page 52
3.5 Momentum Transfer and Form Factors......Page 54
3.6 Total Cross Section......Page 59
Problems......Page 64
References......Page 65
Part B. SINGLE-CHANNEL PHENOMENA......Page 67
4.2 Partial Wave Expansion......Page 69
4.3 Scattering Wave Functions......Page 71
4.4 Time Delay......Page 74
4.5 Collision Parameters and Matrices......Page 76
4.6 Collision Cross Section......Page 77
4.7 Calculation of Phase Shifts: Example of a Spherical Well......Page 78
4.8 Phenomena at Near-Zero Energy......Page 79
4.9 Bound-State Levels......Page 85
4.10 Levinson's Theorem......Page 86
4.11 General Aspect of Threshold Behavior......Page 87
References......Page 88
5.1 Introduction......Page 89
5.2 Alternative Pairs of Base Functions......Page 90
5.3 Jost Functions......Page 92
5.4 Parameters of Short-Range Interactions......Page 97
5.5 Threshold Behavior: Resonances......Page 100
5.6 Negative Energies: Spectrum of Bound-State Levels......Page 101
5.7 Normalization of Wave Functions......Page 104
5.8 The Phase Parameter $\beta(\epsilon)$ in (5.27)......Page 108
5.9 Spin-Orbit Coupling and Relativistic Effects......Page 109
5.10 Phase - Amplitude Treatments......Page 110
5.11 Indentification of Irregular Wave Functions......Page 115
Problems......Page 116
References......Page 117
6.2 Direct Integration......Page 119
6.3 Configuration Mixing......Page 122
6.4 $R$-Matrix Treatment......Page 130
6.5 Variational Approaches......Page 133
6.6 Close-Coupling Equations......Page 136
6.7 Reduction of Integrodifferential Equations to a Coupled Differential System......Page 140
6.8 Variational Principles for Scattering......Page 141
6.9 Polarization Field......Page 143
Problems......Page 144
References......Page 145
Part C. MULTICHANNEL PHENOMENA......Page 147
7.1 Introduction......Page 149
7.2 Two Degenerate Channels: Spin Exchange in $e$ + H Collisions......Page 152
7.3 Collision Parameters......Page 160
7.4 Electron-Fluorine Interaction at Low Energy......Page 165
7.5 Photoabsorption of H$_2$......Page 178
7.6 Semiempirical Analysis of $e$ + Ne$^+$......Page 189
7.7 Spin Polarization of Photoelectrons......Page 193
7.8 Alternative Base Pairs in Multichannel Problems......Page 194
7.9 Cross Sections in the Laboratory Frame......Page 196
7.10 Angular Distribution of Collision Fragments......Page 199
Problems......Page 204
References......Page 205
8.1 Introduction......Page 206
8.2 Resonances in Elastic Scattering......Page 208
8.3 Resonances in the Two-Channel Photoabsorption of H$_2$......Page 211
8.4 Multichannel Treatment......Page 222
8.5 Semiempirical Analysis of Multichannel Photoabsorption: Argon and Other Spectra......Page 228
8.6 Elimination of Open Channels......Page 238
8.7 Fragmentation Channels in External Fields......Page 245
Problems......Page 254
References......Page 255
9.1 Introduction......Page 256
9.2 Alternative Parametrizations......Page 257
9.3 Methods of Calculation......Page 267
9.4 Illustrative Examples......Page 286
References......Page 306
Part D. MULTIELECTRON EXCITATIONS......Page 307
10.1 Introduction......Page 309
10.2 Early Observations: Experimental and Theoretical......Page 311
10.3 Angular and Radial Correlations......Page 314
10.4 Analysis of the SchrGdinger Equation......Page 318
10.5 Low Doubly Excited States......Page 329
10.6 High Excitations and Double Ionization......Page 346
10.7 Extension to More Than Two Electrons......Page 357
References......Page 366
11.1 Introduction......Page 367
11.2 Correlations within Valence Shells: Survey of Phenomena......Page 368
11.3 Excitations in the Valence Shell of Alkaline Earths......Page 376
11.4 Correlations in the He$^-$ Complex......Page 385
11.5 Channel Crossing in Open Valence Shells......Page 393
References......Page 397
12.1 Discussion......Page 398
References......Page 401
Glossary of Symbols......Page 403
Index......Page 405