Atomic Structure and Lifetimes: A Conceptual Approach

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Physical constants and useful interrelations......Page 15
1.1 Atomic physics is more than quantum mechanics......Page 17
1.2 Trajectories versus probabilities......Page 18
1.3 Semiempirical parametrization......Page 21
2.1.1 Probabilistic formalism......Page 22
2.2.1 Conceptual inclusion of periodic processes......Page 23
2.3.1 Historical context......Page 24
2.3.3 Example: simple harmonic oscillator......Page 26
2.4 The Kepler problem......Page 27
2.4.2 Position probability densities......Page 28
2.4.3 Calculation of expectation values of radial moments......Page 30
2.4.4 The EBK quantization......Page 31
2.4.5 Position probability densities for these orbits......Page 33
2.4.6 Expectation values of rk......Page 34
2.4.7 Perturbations......Page 37
2.4.8 Relativistic corrections to the kinetic energy......Page 38
2.4.9 Relativistic corrections to the potential energy......Page 39
2.4.10 The core polarization model......Page 43
2.4.11 Gauss’s formulation of the perturbations of the planets......Page 44
2.4.12 Semiclassical self-consistent field (SCSCF)......Page 45
2.4.13 Relativistic formulation of angle-action integrals......Page 49
2.4.14 The EBK quantization......Page 51
2.4.15 Relativistic extension of SCSCF......Page 52
2.5 Semiclassical formulation of the decay meanlife......Page 53
2.5.1 The Wien model......Page 54
2.5.2 Connection with the quantum mechanical formulation......Page 56
3.1 Historical development......Page 58
3.2.1 The nonrelativistic two-body problem......Page 60
3.2.2 Relativistic nonseparability of the two-body problem......Page 61
3.3 The Rydberg formula and the Ritz parametrization......Page 63
3.3.1 Semiclassical derivation of the Rydberg–Ritz formula......Page 64
3.3.2 Use of the Rydberg–Ritz quantum defect parametrization of spectroscopic data......Page 66
3.4 The core polarization model......Page 70
3.5.1 Characterizing the regions of small and large r......Page 74
3.5.2 The regular and irregular doublet laws......Page 75
3.6 Screening parametrization of the fine structure......Page 77
3.6.1 Expansion of the Dirac-Sommerfeld formula......Page 78
3.6.2 Application to complex atoms......Page 80
3.6.3 Relative importance of higher-order terms......Page 82
3.7 Screening parametrization of transition rates......Page 83
3.7.1 Parametrizing line strengths......Page 84
3.7.2 Relativistic form of the hydrogenic line strength......Page 85
4.1 The Schrödinger approximation......Page 88
4.2 The intrinsic angular momentum and magnetic moment of the electron......Page 89
4.3 The Pauli spin matrices......Page 90
4.4 Internal magnetic fields......Page 92
4.5 Coupling approximations......Page 93
4.5.2 jj coupling......Page 94
4.6 Quantum mechanical vector coupling of angular momenta......Page 95
4.7 The connection between spin and statistics......Page 96
4.8 The Landé interval rule......Page 97
4.9.1 Zeeman effect......Page 98
4.9.2 Classical model for the Zeeman effect......Page 100
4.9.3 Paschen–Back effect......Page 101
4.9.4 Extremely strong fields......Page 103
Application......Page 104
5.1 Spectroscopic notation......Page 106
5.2 Two-valence-electron systems......Page 108
5.2.1 Solution of the unperturbed problem......Page 109
5.2.2 Consequences of exchange symmetry for equivalent electrons......Page 110
5.2.3 Electrostatic corrections: the Slater parameters......Page 111
5.2.4 Spin–orbit interaction......Page 113
5.2.5 Example: nsn\'p and nsn\'p configurations......Page 114
Hydrogenlike calculations for G1(nsnp)......Page 118
5.2.6 Example: the np2 and np4 configuration......Page 119
5.3.1 nsn\'p configurations......Page 123
5.4 Systems with three or more valence electrons......Page 125
5.5 Antisymmetrization of a multielectron system......Page 128
6 Electric dipole radiation......Page 129
6.1 Hierarchies in transition arrays......Page 130
6.1.1 Components......Page 131
6.1.2 Lines......Page 134
6.1.3 Multiplet values......Page 135
6.2 Ab initio calculations......Page 136
6.3.1 Velocity form of the transition moment......Page 139
6.3.3 The Thomas–Reiche–Kuhn sum rule......Page 140
6.4.1 Polarizabilities and oscillator strengths......Page 141
6.4.2 Determination of dipole polarizabilities from lifetime measurements......Page 142
6.5 Core polarization contributions to the E1 transition moment......Page 145
6.6 Cancellation......Page 147
7.1.1 Selection rules......Page 154
7.1.2 LS singlet–triplet mixing angles......Page 155
7.1.3 LS singlet–triplet mixing of the sp configuration......Page 156
Application: the Cd sequence......Page 157
7.1.4 Application in…transitions......Page 159
7.1.5 Extension to sp-sd transitions......Page 161
7.1.6 LS singlet–triplet mixing of the p2 configuration......Page 164
7.1.7 LS branching fractions for the ns2np2-ns2npn\'s transition array......Page 166
Application: Si, Ge, and Sn sequences......Page 168
7.2.1 jj mixing-angle formulation......Page 171
7.2.2 jj formulation of s2-sp transitions......Page 172
Application: the Hg sequence......Page 173
7.2.3 jj formulation of p2-sp transitions......Page 175
Application: the Pb sequence......Page 176
7.3 Gyromagnetic ratios in intermediate coupling......Page 177
8.1 M1 transitions......Page 180
8.2 M1 line strengths......Page 181
8.2.1 p and p5 configurations......Page 184
Application:  M1 rates in excited configurations of single-valence-electron ions......Page 186
8.2.2 Single–triplet mixing in sp or sp5 configurations......Page 187
Ni…and Ni… (more coronium)......Page 189
8.2.4 Doublet–quartet mixing in p3 configurations......Page 190
8.2.5 Use of screening parameter extrapolations of energy levels to obtain M1 rates......Page 192
9 Absorption of radiation......Page 195
9.1 Driven damped harmonic oscillator......Page 196
9.2 Doppler broadening......Page 198
9.3 Comparison of the Lorentzian and Gaussian functions......Page 199
9.4 Convolutions of lineshape functions......Page 200
9.4.2 Convolution of two Gaussians......Page 201
9.4.4 The inverse Lorentzian function......Page 202
9.5 Equivalent width......Page 203
9.5.2 Example: stellar temperature determination from relative absorption among levels in a given atom......Page 205
9.6 Atomic derivation of the Planck radiation law......Page 207
10 Time-resolved measurements......Page 210
10.1.1 Solution of the driven coupled linear rate equations......Page 211
10.1.2 Applications......Page 214
10.2 Adjusted normalization of decay curve (ANDC) method......Page 216
10.3 Differential lifetime measurements......Page 218
10.3.1 Radiative intercombination rates in the Be-like triplets......Page 219
10.3.2 Autoionization rates in doubly excited levels in Li-like quartet levels......Page 220
10.4 Hanle effect......Page 221
11.1 The origins of hyperfine structure observations......Page 223
11.2 Magnetic dipole moment of the nucleus......Page 224
11.2.1 Vector model formulation......Page 225
11.2.2 Application to hydrogen......Page 227
11.3 Electric quadrupole moment of the nucleus......Page 229
11.5 Isotope shifts......Page 231
11.5.2 Finite nuclear size......Page 232
11.6 Hyperfine quenching......Page 234
12.1 Rayleigh-Schrödinger perturbation theory......Page 236
12.2 The Dalgarno–Lewis operator......Page 238
12.3 Application: ground-state polarizabilities......Page 239
12.3.1 Formulation......Page 240
12.3.2 Convergence of the sum......Page 243
12.4 Nonadiabatic correlations......Page 244
12.5 Casimir–Polder retardation corrections......Page 245
12.6 Quadratic Stark effect......Page 246
12.7 Indices of refraction for inert gases......Page 247
13.1.1 Formulation......Page 250
13.1.2 Example: expectation values for a P state with coherently excited magnetic sublevels......Page 252
13.2 Stokes parameters......Page 254
13.2.1 Linear polarizer......Page 255
13.2.2 Retarding plate......Page 256
Circular polarizer......Page 257
Circular polarization analyzer......Page 258
13.3 Application to a measurement of elliptic polarization......Page 259
13.4.1 Cascade transfer of alignment and orientation in decay-curve measurements......Page 262
13.4.2 Cascade-free lifetime measurements utilizing anisotropies......Page 263
13.5 Quantum-beat spectroscopy......Page 264
13.6 Level crossing and optical double resonance spectroscopy......Page 267
References......Page 268
Index......Page 277