Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics
Подождите немного. Документ загружается.
Detailed Contents 1427
3 Group Theory for Atomic Shells
Brian R. Judd ..................................................................... 75
3.1 Generators ................................................................ 75
3.1.1 Group Elements ................................................... 75
3.1.2 Conditions on the Structure Constants .......................... 76
3.1.3 Cartan–Weyl Form ................................................ 76
3.1.4 Atomic Operators as Generators ................................. 76
3.2 Classification of Lie Algebras ............................................ 76
3.2.1 Introduction ....................................................... 76
3.2.2 The Semisimple Lie Algebras ..................................... 76
3.3 Irreducible Representations ............................................. 77
3.3.1 Labels .............................................................. 77
3.3.2 Dimensions ........................................................ 77
3.3.3 Casimir’s Operator ................................................ 77
3.4 Branching Rules .......................................................... 78
3.4.1 Introduction ....................................................... 78
3.4.2 U
(n) ⊃ SU(n) ...................................................... 78
3.4.3 Canonical Reductions ............................................ 79
3.4.4 Other Reductions ................................................. 79
3.5 Kronecker Products ....................................................... 79
3.5.1 Outer Products of Tableaux ...................................... 79
3.5.2 Other Outer Products ............................................. 80
3.5.3 Plethysms ......................................................... 80
3.6 Atomic States ............................................................. 80
3.6.1 Shell Structure .................................................... 80
3.6.2 Automorphisms of SO(8) ......................................... 81
3.6.3 Hydrogen and Hydrogen-Like Atoms ........................... 81
3.7 The Generalized Wigner–Eckart Theorem .............................. 82
3.7.1 Operators .......................................................... 82
3.7.2 The Theorem ...................................................... 82
3.7.3 Calculation of the Isoscalar Factors ............................. 82
3.7.4 Generalizations of Angular Momentum Theory ................ 83
3.8 Checks ..................................................................... 83
References ........................................................................ 84
4
Dynamical Groups
Josef Paldus ....................................................................... 87
4.1 Noncompact Dynamical Groups ......................................... 87
4.1.1 Realizations of so(2,1) ............................................ 88
4.1.2 Hydrogenic Realization of so(4,2) ............................... 88
4.2 Hamiltonian Transformation and Simple Applications ................ 90
4.2.1 N-Dimensional Isotropic Harmonic Oscillator .................. 90
4.2.2 N-Dimensional Hydrogenic Atom ............................... 91
4.2.3 Perturbed Hydrogenic Systems .................................. 91
4.3 Compact Dynamical Groups .............................................. 92
4.3.1 Unitary Group and Its Representations ......................... 92
4.3.2 Orthogonal Group O(n) and Its Representations ............... 93
Detailed Cont.
1428 Detailed Contents
4.3.3 Clifford Algebras and Spinor Representations .................. 94
4.3.4 Bosonic and Fermionic Realizations of U(n) .................... 94
4.3.5 Vibron Model ...................................................... 95
4.3.6 Many-Electron Correlation Problem ............................. 96
4.3.7 Clifford Algebra Unitary Group Approach ....................... 97
4.3.8 Spin-Dependent Operators ...................................... 97
References ........................................................................ 98
5
Perturbation Theory
Josef Paldus ....................................................................... 101
5.1 Matrix Perturbation Theory (PT) ......................................... 101
5.1.1 Basic Concepts .................................................... 101
5.1.2 Level-Shift Operators ............................................. 102
5.1.3 General Formalism ............................................... 102
5.1.4 Nondegenerate Case .............................................. 103
5.2 Time-Independent Perturbation Theory ............................... 103
5.2.1 General Formulation ............................................. 103
5.2.2 Brillouin–Wigner and Rayleigh–Schrödinger PT (RSPT) ........ 104
5.2.3 Bracketing Theorem and RSPT ................................... 104
5.3 Fermionic Many-Body Perturbation Theory (MBPT) .................... 105
5.3.1 Time Independent Wick’s Theorem ............................. 105
5.3.2 Normal Product Form of PT ...................................... 105
5.3.3 Møller–Plesset and Epstein–Nesbet PT ......................... 106
5.3.4 Diagrammatic MBPT .............................................. 107
5.3.5 Vacuum and Wave Function Diagrams .......................... 107
5.3.6 Hartree–Fock Diagrams .......................................... 108
5.3.7 Linked and Connected Cluster Theorems ....................... 108
5.3.8 Coupled Cluster Theory ........................................... 109
5.4 Time-Dependent Perturbation Theory .................................. 111
5.4.1 Evolution Operator PT Expansion ................................ 111
5.4.2 Gell–Mann and Low Formula .................................... 111
5.4.3 Potential Scattering and Quantum Dynamics .................. 111
5.4.4 Born Series ........................................................ 112
5.4.5 Variation of Constants Method .................................. 112
References ........................................................................ 113
6
Second Quantization
Brian R. Judd ..................................................................... 115
6.1 Basic Properties ........................................................... 115
6.1.1 Definitions ........................................................ 115
6.1.2 Representation of States ......................................... 115
6.1.3 Representation of Operators ..................................... 116
6.2 Tensors .................................................................... 116
6.2.1 Construction ....................................................... 116
6.2.2 Coupled Forms .................................................... 116
6.2.3 Coefficients of Fractional Parentage ............................ 117
Detailed Cont.
Detailed Contents 1429
6.3 Quasispin .................................................................. 117
6.3.1 Fermions .......................................................... 117
6.3.2 Bosons ............................................................. 118
6.3.3 Triple Tensors ..................................................... 118
6.3.4 Conjugation ....................................................... 118
6.3.5 Dependence on Electron Number ............................... 119
6.3.6 The Half-filled Shell .............................................. 119
6.4 Complementarity ......................................................... 119
6.4.1 Spin–Quasispin Interchange ..................................... 119
6.4.2 Matrix Elements .................................................. 119
6.5 Quasiparticles ............................................................. 120
References ........................................................................ 121
7
Density Matrices
Klaus Bartschat ................................................................... 123
7.1 Basic Formulae ........................................................... 123
7.1.1 Pure States ........................................................ 123
7.1.2 Mixed States ...................................................... 124
7.1.3 Expectation Values ............................................... 124
7.1.4 The Liouville Equation ............................................ 124
7.1.5 Systems in Thermal Equilibrium ................................. 125
7.1.6 Relaxation Processes ............................................. 125
7.2 Spin and Light Polarizations ............................................. 125
7.2.1 Spin-Polarized Electrons ......................................... 125
7.2.2 Light Polarization ................................................. 125
7.3 Atomic Collisions ......................................................... 126
7.3.1 Scattering Amplitudes ............................................ 126
7.3.2 Reduced Density Matrices ........................................ 126
7.4 Irreducible Tensor Operators ............................................ 127
7.4.1 Definition ......................................................... 127
7.4.2 Transformation Properties ....................................... 127
7.4.3 Symmetry Properties of State Multipoles ....................... 128
7.4.4 Orientation and Alignment ...................................... 128
7.4.5 Coupled Systems .................................................. 129
7.5 Time Evolution of State Multipoles ...................................... 129
7.5.1 Perturbation Coefficients ......................................... 129
7.5.2 Quantum Beats ................................................... 129
7.5.3 Time Integration over Quantum Beats .......................... 130
7.6 Examples .................................................................. 130
7.6.1 Generalized STU-parameters .................................... 130
7.6.2 Radiation from Excited States: Stokes Parameters ............. 131
7.7 Summary .................................................................. 133
References ........................................................................ 133
8
Computational Techniques
David R. Schultz, Michael R. Strayer ............................................ 135
8.1 Representation of Functions ............................................ 135
Detailed Cont.
1430 Detailed Contents
8.1.1 Interpolation ...................................................... 135
8.1.2 Fitting ............................................................. 137
8.1.3 Fourier Analysis ................................................... 139
8.1.4 Approximating Integrals ......................................... 139
8.1.5 Approximating Derivatives ....................................... 140
8.2 Differential and Integral Equations ..................................... 141
8.2.1 Ordinary Differential Equations ................................. 141
8.2.2 Differencing Algorithms for Partial Differential Equations .... 143
8.2.3 Variational Methods .............................................. 144
8.2.4 Finite Elements ................................................... 144
8.2.5 Integral Equations ................................................ 146
8.3 Computational Linear Algebra ........................................... 148
8.4 Monte Carlo Methods ..................................................... 149
8.4.1 Random Numbers ................................................ 149
8.4.2 Distributions of Random Numbers .............................. 150
8.4.3 Monte Carlo Integration .......................................... 151
References ........................................................................ 151
9
Hydrogenic Wave Functions
Robert N. Hill ..................................................................... 153
9.1 Schrödinger Equation .................................................... 153
9.1.1 Spherical Coordinates ............................................ 153
9.1.2 Parabolic Coordinates ............................................ 154
9.1.3 Momentum Space ................................................ 156
9.2 Dirac Equation ............................................................ 157
9.3 The Coulomb Green’s Function .......................................... 159
9.3.1 The Green’s Function for the Schrödinger Equation ........... 159
9.3.2 The Green’s Function for the Dirac Equation ................... 161
9.4 Special Functions ......................................................... 162
9.4.1 Confluent Hypergeometric Functions ........................... 162
9.4.2 Laguerre Polynomials ............................................ 166
9.4.3 Gegenbauer Polynomials ........................................ 169
9.4.4 Legendre Functions ............................................... 169
References ........................................................................ 170
Part B Atoms
10 Atomic Spectroscopy
William C. Martin, Wolfgang L. Wiese .......................................... 175
10.1 Frequency, Wavenumber, Wavelength ................................. 176
10.2 Atomic States, Shells, and Configurations .............................. 176
10.3 Hydrogen and Hydrogen-Like Ions ..................................... 176
10.4 Alkalis and Alkali-Like Spectra .......................................... 177
10.5 Helium and Helium-Like Ions; LS Coupling ............................ 177
10.6 Hierarchy of Atomic Structure in LS Coupling .......................... 177
10.7 Allowed Terms or Levels for Equivalent Electrons ...................... 178
Detailed Cont.
Detailed Contents 1431
10.7.1 LS Coupling ...................................................... 178
10.7.2 jj Coupling ....................................................... 178
10.8 Notations for Different Coupling Schemes .............................. 179
10.8.1 LS Coupling (Russell–Saunders Coupling) ..................... 179
10.8.2 jj Coupling of Equivalent Electrons ............................ 180
10.8.3 J
1
j or J
1
J
2
Coupling ............................................... 180
10.8.4 J
1
l or J
1
L
2
Coupling (J
1
K Coupling) .............................. 180
10.8.5 LS
1
Coupling (LK Coupling) ...................................... 181
10.8.6 Coupling Schemes and Term Symbols ......................... 181
10.9 Eigenvector Composition of Levels ...................................... 181
10.10 Ground Levels and Ionization Energies for the Neutral Atoms ....... 182
10.11 Zeeman Effect ............................................................. 183
10.12 Term Series, Quantum Defects, and Spectral-Line Series ............. 184
10.13 Sequences ................................................................. 185
10.13.1 Isoelectronic Sequence ........................................ 185
10.13.2 Isoionic, Isonuclear, and Homologous Sequences .......... 185
10.14 Spectral Wavelength Ranges, Dispersion of Air ........................ 185
10.15 Wavelength (Frequency) Standards ..................................... 186
10.16 Spectral Lines: Selection Rules, Intensities, Transition Probabilities,
f Values, and Line Strengths ............................................ 186
10.16.1 Emission Intensities (Transition Probabilities) .............. 186
10.16.2 Absorption f Values ........................................... 186
10.16.3 Line Strengths .................................................. 186
10.16.4 Relationships Between A, f,andS ........................... 187
10.16.5 Relationships Between Line and Multiplet Values .......... 192
10.16.6 Relative Strengths for Lines of Multiplets in LS Coupling ... 193
10.17 Atomic Lifetimes .......................................................... 194
10.18 Regularities and Scaling ................................................. 194
10.18.1 Transitions in Hydrogenic (One-Electron) Species .......... 194
10.18.2 Systematic Trends and Regularities in Atoms and Ions
with Two or More Electrons ................................... 194
10.19 Spectral Line Shapes, Widths, and Shifts ............................... 195
10.19.1 Doppler Broadening ........................................... 195
10.19.2 Pressure Broadening .......................................... 195
10.20 Spectral Continuum Radiation .......................................... 196
10.20.1 Hydrogenic Species ............................................ 196
10.20.2 Many-Electron Systems ....................................... 196
10.21 Sources of Spectroscopic Data ........................................... 197
References ........................................................................ 197
11
High Precision Calculations for Helium
Gordon W. F. Drake ............................................................... 199
11.1 The Three-Body Schrödinger Equation ................................. 199
11.1.1 Formal Mathematical Properties ............................... 200
11.2 Computational Methods ................................................. 200
11.2.1 Variational Methods ............................................ 200
11.2.2 Construction of Basis Sets ...................................... 201
Detailed Cont.
1432 Detailed Contents
11.2.3 Calculation of Matrix Elements ................................. 202
11.2.4 Other Computational Methods ................................. 205
11.3 Variational Eigenvalues .................................................. 205
11.3.1 Expectation Values of Operators and Sum Rules ............. 205
11.4 Total Energies ............................................................. 208
11.4.1 Quantum Defect Extrapolations ................................ 211
11.4.2 Asymptotic Expansions ......................................... 213
11.5 Radiative Transitions ..................................................... 215
11.5.1 Basic Formulation ............................................... 215
11.5.2 Oscillator Strength Table ........................................ 216
11.6 Future Perspectives ....................................................... 218
References ........................................................................ 218
12
Atomic Multipoles
William E. Baylis .................................................................. 221
12.1 Polarization and Multipoles ............................................. 222
12.2 The Density Matrix in Liouville Space ................................... 222
12.3 Diagonal Representation: State Populations ........................... 224
12.4 Interaction with Light .................................................... 224
12.5 Extensions ................................................................ 225
References ........................................................................ 226
13
Atoms in Strong Fields
S. Pedro Goldman, Mark M. Cassar ............................................. 227
13.1 Electron in a Uniform Magnetic Field ................................... 227
13.1.1 Nonrelativistic Theory ........................................... 227
13.1.2 Relativistic Theory ............................................... 228
13.2 Atoms in Uniform Magnetic Fields ...................................... 228
13.2.1 Anomalous Zeeman Effect ...................................... 228
13.2.2 Normal Zeeman Effect .......................................... 229
13.2.3 Paschen–Back Effect ............................................ 229
13.3 Atoms in Very Strong Magnetic Fields ................................... 230
13.4 Atoms in Electric Fields .................................................. 231
13.4.1 Stark Ionization ................................................. 231
13.4.2 Linear Stark Effect ............................................... 231
13.4.3 Quadratic Stark Effect ........................................... 232
13.4.4 Other Stark Corrections ......................................... 232
13.5 Recent Developments .................................................... 233
References ........................................................................ 234
14
Rydberg Atoms
Thomas F. Gallagher ............................................................. 235
14.1 Wave Functions and Quantum Defect Theory .......................... 235
14.2 Optical Excitation and Radiative Lifetimes ............................. 237
14.3 Electric Fields ............................................................. 238
14.4 Magnetic Fields ........................................................... 241
14.5 Microwave Fields ......................................................... 242
Detailed Cont.
Detailed Contents 1433
14.6 Collisions .................................................................. 243
14.7 Autoionizing Rydberg States ............................................. 244
References ........................................................................ 245
15
Rydberg Atoms in Strong Static Fields
Thomas Bartsch, Turgay Uzer .................................................... 247
15.1 Scaled-Energy Spectroscopy ............................................. 248
15.2 Closed-Orbit Theory ...................................................... 248
15.3 Classical and Quantum Chaos ........................................... 249
15.3.1 Magnetic Field ................................................... 249
15.3.2 Parallel Electric and Magnetic Fields .......................... 250
15.3.3 Crossed Electric and Magnetic Fields .......................... 250
15.4 Nuclear-Mass Effects ..................................................... 251
References ........................................................................ 251
16
Hyperfine Structure
Guy T. Emery ...................................................................... 253
16.1 Splittings and Intensities ................................................ 254
16.1.1 Angular Momentum Coupling .................................. 254
16.1.2 Energy Splittings ................................................ 254
16.1.3 Intensities ....................................................... 255
16.2 Isotope Shifts ............................................................. 256
16.2.1 Normal Mass Shift ............................................... 256
16.2.2 Specific Mass Shift ............................................... 256
16.2.3 Field Shift ........................................................ 256
16.2.4 Separation of Mass Shift and Field Shift ...................... 257
16.3 Hyperfine Structure ...................................................... 258
16.3.1 Electric Multipoles ............................................... 258
16.3.2 Magnetic Multipoles ............................................ 258
16.3.3 Hyperfine Anomalies ............................................ 259
References ........................................................................ 259
17
Precision Oscillator Strength and Lifetime Measurements
Lorenzo J. Curtis .................................................................. 261
17.1 Oscillator Strengths ....................................................... 262
17.1.1 Absorption and Dispersion Measurements .................... 262
17.1.2 Emission Measurements ........................................ 263
17.1.3 Combined Absorption, Emission and Lifetime
Measurements ................................................... 263
17.1.4 Branching Ratios in Highly Ionized Atoms .................... 264
17.2 Lifetimes .................................................................. 264
17.2.1 The Hanle Effect ................................................. 265
17.2.2 Time-Resolved Decay Measurements .......................... 265
17.2.3 Other Methods ................................................... 267
17.2.4 Multiplexed Detection .......................................... 267
References ........................................................................ 268
Detailed Cont.
1434 Detailed Contents
18 Spectroscopy of Ions Using Fast Beams and Ion Traps
Eric H. Pinnington, Elmar Träbert ............................................... 269
18.1 Spectroscopy Using Fast Ion Beams ..................................... 269
18.1.1 Beam–Foil Spectroscopy ........................................ 269
18.1.2 Beam-Gas Spectroscopy ........................................ 270
18.1.3 Beam-Laser Spectroscopy ...................................... 271
18.1.4 Other Techniques of Ion-Beam Spectroscopy ................. 272
18.2 Spectroscopy Using Ion Traps ............................................ 272
18.2.1 Electron Beam Ion Traps ........................................ 273
18.2.2 Heavy-Ion Storage Rings ....................................... 275
References ........................................................................ 277
19
Line Shapes and Radiation Transfer
Alan Gallagher .................................................................... 279
19.1 Collisional Line Shapes ................................................... 279
19.1.1 Voigt Line Shape ................................................ 279
19.1.2 Interaction Potentials ........................................... 280
19.1.3 Classical Oscillator Approximation ............................. 280
19.1.4 Impact Approximation .......................................... 281
19.1.5 Examples: Line Core ............................................. 282
19.1.6
∆ and γ
c
Characteristics ........................................ 284
19.1.7 Quasistatic Approximation ..................................... 284
19.1.8 Satellites ......................................................... 285
19.1.9 Bound States and Other Quantum Effects ..................... 286
19.1.10 Einstein A and B Coefficients ................................. 286
19.2 Radiation Trapping ....................................................... 287
19.2.1 Holstein–Biberman Theory ..................................... 287
19.2.2 Additional Factors ............................................... 289
19.2.3 Measurements ................................................... 290
References ........................................................................ 292
20
Thomas–Fermi and Other Density-Functional Theories
John D. Morgan III ................................................................ 295
20.1 Thomas–Fermi Theoryand Its Extensions ............................... 296
20.1.1 Thomas–Fermi Theory .......................................... 296
20.1.2 Thomas–Fermi–von Weizsäcker Theory ....................... 298
20.1.3 Thomas–Fermi–Dirac Theory ................................... 299
20.1.4 Thomas–Fermi–von Weizsäcker–Dirac Theory ................ 299
20.1.5 Thomas–Fermi Theory with Different Spin Densities ......... 300
20.2 Nonrelativistic Energies of Heavy Atoms ................................ 300
20.3 General Density Functional Theory ...................................... 301
20.3.1 The Hohenberg–Kohn Theorem for the One-Electron
Density ........................................................... 301
20.3.2 The Kohn–Sham Method for Including Exchange
and Correlation Corrections .................................... 302
20.3.3 Density Functional Theory for Excited States .................. 303
Detailed Cont.
Detailed Contents 1435
20.3.4 Relativistic and Quantum Field Theoretic Density Functional
Theory ............................................................ 303
20.4 Recent Developments .................................................... 303
References ........................................................................ 304
21
Atomic Structure: Multiconfiguration Hartree–Fock Theories
Charlotte F. Fischer ............................................................... 307
21.1 Hamiltonians: Schrödinger and Breit–Pauli ........................... 307
21.2 Wave Functions: LS and LSJ Coupling ................................... 308
21.3 Variational Principle ..................................................... 309
21.4 Hartree–Fock Theory ..................................................... 309
21.4.1 Diagonal Energy Parameters and Koopmans’ Theorem ...... 311
21.4.2 The Fixed-Core Hartree–Fock Approximation ................. 311
21.4.3 Brillouin’s Theorem ............................................. 311
21.4.4 Properties of Hartree–Fock Functions ......................... 312
21.5 Multiconfiguration Hartree–Fock Theory ............................... 313
21.5.1 Z-Dependent Theory ............................................ 313
21.5.2 The MCHF Approximation ....................................... 314
21.5.3 Systematic Methods ............................................. 315
21.5.4 Excited States .................................................... 316
21.5.5 Autoionizing States ............................................. 316
21.6 Configuration Interaction Methods ..................................... 316
21.7 Atomic Properties ......................................................... 318
21.7.1 Isotope Effects ................................................... 318
21.7.2 Hyperfine Effects ................................................ 319
21.7.3 Metastable States and Lifetimes ............................... 320
21.7.4 Transition Probabilities ......................................... 321
21.7.5 Electron Affinities ............................................... 321
21.8 Summary .................................................................. 322
References ........................................................................ 322
22
Relativistic Atomic Structure
Ian P. Grant ....................................................................... 325
22.1 Mathematical Preliminaries ............................................. 326
22.1.1 Relativistic Notation: Minkowski Space-Time ................. 326
22.1.2 Lorentz Transformations ........................................ 326
22.1.3 Classification of Lorentz Transformations ..................... 326
22.1.4 Contravariant and Covariant Vectors .......................... 327
22.1.5 Poincaré Transformations ...................................... 327
22.2 Dirac’s Equation .......................................................... 328
22.2.1 Characterization of Dirac States ................................ 328
22.2.2 The Charge-Current 4-Vector ................................... 328
22.3 QED: Relativistic Atomic and Molecular Structure ...................... 329
22.3.1 The QED Equations of Motion ................................... 329
22.3.2 The Quantized Electron–Positron Field ........................ 329
22.3.3 Quantized Electromagnetic Field ............................... 330
22.3.4 QED Perturbation Theory ........................................ 331
Detailed Cont.
1436 Detailed Contents
22.3.5 Propagators ...................................................... 333
22.3.6 Effective Interaction of Electrons .............................. 333
22.4 Many-Body Theory For Atoms ........................................... 334
22.4.1 Effective Hamiltonians .......................................... 335
22.4.2 Nonrelativistic Limit: Breit–Pauli Hamiltonian ............... 335
22.4.3 Perturbation Theory: Nondegenerate Case .................... 335
22.4.4 Perturbation Theory: Open-Shell Case ......................... 336
22.4.5 Perturbation Theory: Algorithms ............................... 337
22.5 Spherical Symmetry ...................................................... 337
22.5.1 Eigenstates of Angular Momentum ............................ 337
22.5.2 Eigenstates of Dirac Hamiltonian in Spherical Coordinates .. 338
22.5.3 Radial Amplitudes ............................................... 340
22.5.4 Square Integrable Solutions .................................... 341
22.5.5 Hydrogenic Solutions ........................................... 342
22.5.6 The Free Electron Problem in Spherical Coordinates ......... 343
22.6 Numerical Approximation of Central Field Dirac Equations ........... 344
22.6.1 Finite Differences ............................................... 344
22.6.2 Expansion Methods ............................................. 345
22.6.3 Catalogue of Basis Sets for Atomic Calculations ............... 347
22.7 Many-Body Calculations ................................................. 350
22.7.1 Atomic States .................................................... 350
22.7.2 Slater Determinants ............................................. 350
22.7.3 Configurational States .......................................... 350
22.7.4 CSF Expansion ................................................... 350
22.7.5 Matrix Element Construction ................................... 350
22.7.6 Dirac–Hartree–Fock and Other Theories ...................... 351
22.7.7 Radiative Corrections ........................................... 353
22.7.8 Radiative Processes ............................................. 353
22.8 Recent Developments .................................................... 354
22.8.1 Technical Advances ............................................. 354
22.8.2 Software for Relativistic Atomic Structure and Properties ... 354
References ........................................................................ 355
23
Many-Body Theory of Atomic Structure and Processes
Miron Ya. Amusia ................................................................. 359
23.1 Diagrammatic Technique ................................................ 360
23.1.1 Basic Elements .................................................. 360
23.1.2 Construction Principles for Diagrams .......................... 360
23.1.3 Correspondence Rules .......................................... 362
23.1.4 Higher-Order Corrections and Summation of Sequences .... 363
23.2 Calculation of Atomic Properties ........................................ 365
23.2.1 Electron Correlations in Ground State Properties ............. 365
23.2.2 Characteristics of One-Particle States ......................... 366
23.2.3 Electron Scattering .............................................. 367
23.2.4 Two-Electron and Two-Vacancy States ........................ 369
23.2.5 Electron–Vacancy States ........................................ 370
Detailed Cont.