The Theory of Atomic Structure and Spectra

Couverture
University of California Press, 25 sept. 1981 - 650 pages
Both the interpretation of atomic spectra and the application of atomic spectroscopy to current problems in astrophysics, laser physics, and thermonuclear plasmas require a thorough knowledge of the Slater-Condon theory of atomic structure and spectra. This book gathers together aspects of the theory that are widely scattered in the literature and augments them to produce a coherent set of closed-form equations suitable both for computer calculations on cases of arbitrary complexity and for hand calculations for very simple cases.
 

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Table des matières

EXPERIMENTAL BACKGROUND AND BASIC CONCEPTS
xiii
12 Characteristic Spectra of Atoms and Ions
xvi
13 Isoelectronic Sequences
xviii
15 Energy Levels
2
16 Units for Energy Levels
3
17 Energy Level Diagrams
4
18 The Ritz Combination Principle Grotrian Diagrams
10
19 The Profiles of Spectrum Lines
11
119 Unit Tensor Operators
308
1110 Double Tensor Operators
311
1111 SpinOrbit Matrix Elements OneElectron Configurations
313
1112 Direct Coulomb Matrix Elements TwoElectron Configurations
314
1113 Exchange Coulomb Matrix Elements TwoElectron Configurations
315
1115 Summary
318
ENERGY LEVEL STRUCTURE COMPLEX CONFIGURATIONS
319
Equivalent Electrons
320

110 Wavelength Range and Accuracy
18
111 Empirical Spectrum Analysis
19
112 The Role of Theory
21
ANGULARMOMENTUM PROPERTIES OF WAVEFUNCTIONS
27
22 AngularMomentum Operators
28
23 Eigenvalues of AngularMomentum Operators
29
24 Stepup and Stepdown Operators
32
25 Orbital Angular Momentum
33
26 The Addition Theorem of Spherical Harmonics
38
27 Electron Spin
43
28 Addition of Two Angular Momenta
44
29 The Vector Model
47
211 Coupling Schemes LS Coupling
50
212 Notation for AngularMomentum States
52
213 Parity
55
214 Parity and AngularMomentum Selection Rules
56
215 Appendix
58
ONEELECTRON ATOMS
61
32 Centralfield Problems
62
33 Analytical Solution of the Radical Equation
64
34 Numerical Solution of the Radical Equation
66
35 Electron Probability Density
72
36 Energy Levels and Wavelengths
73
3 7 Relativistic Corrections
75
The Virial Theorem
82
The SpinOrbit Interaction
85
COMPLEX ATOMSTHE VECTOR MODEL
87
42 The Matrix Method
88
43 The CentralField Model
91
44 Product Wavefunctions
92
45 Antisymmetrization Determinantal Functions
93
46 Coupling of Antisymmetrized Wavefunctions
96
47 Electron Configurations
97
48 Equivalent Electrons Closed Subshells
100
49 Permitted LS Terms for Equivalent Electrons
102
410 Configurations with Several Open Subshells
103
411 ConfigurationAverage Energies
106
412 Relative Energies of Configurations
107
413 The Periodic System
109
414 Variation of Ionization Energy with 𝐙
114
415 Level Structure under LSCoupling Conditions
116
416 Hunds Rule
118
417 𝐣𝐣 Coupling
119
418 Pair Coupling
122
𝐒𝒊 𝐈 3pns
125
420 Other Coupling Schemes
128
422 Statistical Weights Complex Atoms
130
423 Quantitative Calcualtion of Level Structures
132
THE 3𝒏𝐣 SYMBOLS
136
52 The 6𝐣 Symbol
141
53 The 9𝐣 Symbol
144
54 Graphical Methods
146
CONFIGURATIONAVERAGE ENERGIES
150
62 OneElectron and TotalAtom Binding Energies
154
63 Ionization Energy and OneElectron Binding Energies
162
64 Numerical Example
165
RADIAL WAVE EQUATIONS
170
72 The HartreeFock Equations
172
73 The Classical Potential Energy
175
74 The Exchange Potential Energy
177
75 Solution of the HartreeFock Equations
178
76 Complications and Instabilities
179
77 HomogeneousEquation LocalPotential Methods
184
78 The ThomasFermi TF and ThomasFermiDirac TFD Methods
185
79 The Parametric Potential Method
187
710 The Hartree Method H
188
712 The HartreeplusStatisticalExchange MethodHX
191
713 The HartreeSlater Method HS
193
714 Relativistic Corrections
194
715 Correlation Corrections
196
The ThomasFermi and ThomasFermiDirac Atoms
200
Small𝒓 Solution for the HXR Method
206
RADIAL WAVEFUNCTIONS AND RADIAL INTEGRALS
208
82 Comparison Methods
212
83 Accuracy of Computed ConfigurationAverage Energies
213
84 Relativistic Effects
217
85 Variation with the Principal Quantum Number
218
86 Variation with 𝐙 of OneElectron Binding Energies
223
87 Variation with 𝐙 of Coulomb and SpinOrbit Integrals
230
COUPLED ANTISYMMETRIC BASIS FUNCTIONS
234
92 Recoupling of Three Angular Momenta
239
93 Transformations Between Coupling Schemes
242
94 Antisymmetrization Difficulties for Equivalent Electrons
244
95 Coefficients of Fractional Parentage
249
96 Coefficients of Fractional Grandparentage
253
97 The Seniority Number
255
98 Antisymmetrized Functions for an Arbitrary Configuration
259
99 SingleConfiguration Matrix Elements of Symmetric Operators
261
910 Uncoupling of Spectator Subshells
264
VectorCoupling Coefficients
265
ENERGY LEVEL STRUCTURE SIMPLE CONFIGURATIONS
270
102 Effects of Closed Subshells
272
103 OneElectron Configurations
273
104 TwoElectron Configurations SpinOrbit Matrix Elements
274
105 TwoElectron Configurations Coulomb Matrix Elements
276
106 Intermediate Coupling
282
107 Eigenvector Purities
285
109 Pair Coupling
290
THE ALGEBRA OF IRREDUCIBLE TENSOR OPERATORS
295
112 Racah Algebra
296
113 Irreducible Tensor Operators
297
114 The WignerEckart Theorem
299
115 Matrix Elements of the Product of Two Operators
302
116 Tensor Product of Two Tensor Operators
303
117 Uncoupling Formulae for Reduced Matrix Elements
305
118 Scalar Product of Two Tensor Operators
306
Direct Electrons
323
Exchange Integral
325
125 SpinOrbit Matrix Elements
327
f³sd²
329
SpinOrbit Effects under Near2𝕾 Coupling Conditions
331
Configurations 𝒍𝚠
333
Configurations 𝒍₂𝚠¹𝒍₂
338
MoreComplex Configurations
348
CenterofGravity Relations
349
CONFIGURATION INTERACTION
350
132 Wavefunction Orthogonality
353
133 TwoElectron Configurations
358
134 SingleConfigurationLike Interactions
360
135 RydbergSeries Interactions
361
136 OneElectron Configurations
363
137 Brillouins Theorem
364
138 Arbitrary Configuration Interactions
365
139 Matrix Elements of Symmetric Operators
367
1310 Coulomb Matrix Elements General Case
370
1311 OneElectron Matrix Elements General Case
382
RADIATIVE TRANSITIONS E1
387
142 Electric Dipole Radiation Classical
390
143 Electric Dipole Radiation Quantum Mechanical
392
144 Selection Rules Electric Dipole Radiation
394
146 Oscillator Strengths
396
147 Theoretical Calculation of Line Strengths
397
148 Selection Rules and Relative Intensities for LS Coupling
398
149 OneElectron Configurations The Radial Dipole Integral
402
1410 Transitions Involving an Electron in Singly Occupied Subshells
404
1411 Line Strengths for General Transition Arrays
409
1412 SelectionRule Violations
413
1413 Line Strength Sum Rules
414
1414 Oscillator Strength Sum Rules
416
1415 Cancellation Effects
424
1416 Experimental Measurement of Oscillator Strengths
426
1417 Systematics of Oscillator Strengths
428
1418 Radiative Decay in LowDensity Plasmas
432
RADIATIVE TRANSITIONS M1 AND E2
434
152 Electric Quadrupole Radiation E2
437
153 Interference Between M1 and E2 Radiation
441
154 Examples of Forbidden Transitions
442
NUMERICAL CALCULATION OF ENERGY LEVELS AND SPECTRA
448
162 𝐴𝑏 𝐼𝑛𝑖𝑡𝑖𝑜 Calculations
453
163 LestSquares Calculations
457
164 Basic LeastSquares Calculations
460
165 Modifications of the Basic Method
465
166 Phase of the ConfigurationInteraction Parameters
469
168 LSDependent HartreeFock Calculations
473
169 Highly Excited Configurations
475
EXTERNAL FIELDS AND NUCLEAR EFFECTS
477
172 Matrix Elements of the MagneticEnergy 𝐎𝐩𝐞𝐫𝐚𝐭𝐨𝐫
478
173 The WeakField Limit
480
174 WeakField Zeeman Patterns
484
175 Strong Magnetic Fields The PaschenBack Effect
486
176 Intermediate Magnetic Fields
489
177 The Stark Effect
490
178 Isotope Shifts
497
179 Hyperfine Structure
498
CONTINUUM STATES IONIZATION AND RECOMBINATION
504
182 OneElection Contiuum Basis 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧𝐬
507
183 Normalization of the Radial Function
508
184 The Energy Dimensions of Pₓ𝗂
513
185 Relation Between Radial Integrals for Discrete 𝐚𝐧𝐝 𝐂𝐨𝐧𝐭𝐢𝐧𝐮𝐦𝐦 𝐒𝐭𝐚𝐭𝐞𝐬
514
186 Photoionization
515
187 Interaction of Discrete State with a Single 𝐂𝐨𝐧𝐭𝐢𝐧𝐮𝐦𝐦 Authorization
518
188 PseudoDiscrete Treatment of Continuum Problems
527
189 Ionization Equilibrium
536
1810 Radiative Recombination
539
1811 Dielectronic Recombination
541
1812 Generalized Oscillator Strengths
555
1813 PlaneWaveBorn Collision Strengths
559
HIGHLY IONIZED ATOMS
562
192 EnergyLevel Structures
565
193 Configuration Interactions
570
194 Radial Multipole Integrals
572
195 Spectra
573
196 XRay Sprectra
575
197 Comparison of Highly Ionization and XRay Spectra
576
198 Autoionization adn Dielectronic Recombination
581
199 InnerSubshell Excitations
582
1911 Iron Kₐ Diagnostics
585
201 Lanthanide Configurations
590
202 Level Structure General Remarks
592
203 LowLevel Structures and Coupling Conditions
595
204 Spectra
596
205 Aids to Empirical Spectrum Analysis
598
206 Ions
602
207 Actinides
604
208 Transition Elements
605
STATISTICAL DISTRIBUTIONS
608
212 Opacities of Thick Plasmas
609
213 Energy Distribution of Levels of a Configuration
610
214 Wavelength and OscillatorStrength Distributions Within a Transition Array
617
Physical Constants Units and Conversion Factors
624
Conversion Between Vacuum and Air Wavelengths
626
3𝐣 Symbols
627
6𝐣 Symbols
638
OneElectron and TotalAtom Energies
657
Basis Functions Matrix Elements and Racah Algebra
660
Matrix Elements of Spherical Harmonics
669
Coefficients of Fractional Parentage U𝑘V𝑘ˡ
671
Relative Line Strengths Within an LS Multiplet
686
Bibliography
694
Name Index
701
Subject Index
709
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À propos de l'auteur (1981)

Robert D. Cowan was a staff member at the Los Alamos Scientific Laboratory.

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