Table of Contents

Theoretical Approaches to the Energy Levels of Loosely Bound Systems     1
Nonrelativistic Electron in the Coulomb Field     1
Dirac Electron in the Coulomb Field     3
Bethe-Salpeter Equation and the Effective Dirac Equation     5
Nonrelativistic Quantum Electrodynamics     10
References     11
General Features of the Hydrogen Energy Levels     13
Classification of Corrections     13
Physical Origin of the Lamb Shift     15
Natural Magnitudes of Corrections to the Lamb Shift     17
References     18
External Field Approximation     19
Leading Relativistic Corrections with Exact Mass Dependence     19
Radiative Corrections of Order [alpha superscript n](Z[alpha])[superscript 4]m     22
Leading Contribution to the Lamb Shift     22
Radiative Corrections of Order [alpha superscript 2](Z[alpha])[superscript 4]m     27
Corrections of Order [alpha superscript 3](Z[alpha])[superscript 4]m     29
Total Correction of Order [alpha superscript n](Z[alpha])[superscript 4]m     31
Heavy Particle Polarization Contributions of Order [alpha](Z[alpha])[superscript 4]m     32
Radiative Corrections of Order [alpha superscript n](Z[alpha])[superscript 5]m     36
Skeleton Integral Approach to Calculations of Radiative Corrections     36
Radiative Corrections of Order [alpha](Z[alpha])[superscript 5]m     38
Corrections of Order [alpha superscript 2](Z[alpha])[superscript 5]m     40
Corrections of Order [alpha superscript 3](Z[alpha])[superscript 5]m     47
Radiative Corrections of Order [alpha superscript n](Z[alpha])[superscript 6]m     48
Radiative Corrections of Order [alpha](Z[alpha])[superscript 6]m     48
Corrections of Order [alpha superscript 2](Z[alpha])[superscript 6]m     58
Radiative Corrections of Order [alpha](Z[alpha])[superscript 7]m and of Higher Orders     68
Corrections Induced by the Radiative Insertions in the Electron Line     68
Corrections Induced by the Radiative Insertions in the Coulomb Lines     73
Corrections of Order [alpha superscript 2](Z[alpha])[superscript 7]m     76
References     77
Essentially Two-Particle Recoil Corrections     81
Recoil Corrections of Order (Z[alpha])[superscript 5](m/M)m     81
Coulomb-Coulomb Term     83
Transverse-Transverse Term     85
Transverse-Coulomb Term     87
Recoil Corrections of Order (Z[alpha])[superscript 6](m/M)m     89
The Braun Formula     89
Lower Order Recoil Corrections and the Braun Formula     92
Recoil Correction of Order (Z[alpha])[superscript 6](m/M)[superscript n]m to the S Levels     93
Higher Order in Mass Ratio Recoil Correction of Order (Z[alpha])[superscript 6](m/M)m to the S Levels     94
Recoil Correction of Order (Z[alpha])[superscript 7](m/M) to the Non-S Levels     95
Recoil Correction of Order (Z[alpha])[superscript 6](m/M)m     94
References     98
Radiative-Recoil Corrections     99
Corrections of Order [alpha](Z[alpha])[superscript 6](m/M)m     99
Corrections Generated by the Radiative Insertions in the Electron Line     99
Corrections Generated by the Polarization Insertions in the Photon Lines     101
Corrections Generated by the Radiative Insertions in the Proton Line     103
Corrections of Order [alpha](Z[alpha])[superscript 5](m/M)m     105
References     107
Nuclear Size and Structure Corrections     109
Main Proton Size Contribution     109
Spin One-Half Nuclei     111
Nuclei with Other Spins     112
Empirical Nuclear Form Factor and the Contributions to the Lamb Shift     113
Nuclear Size and Structure Corrections of Order (Z[alpha])[superscript 5]m     114
Nuclear Size Corrections of Order (Z[alpha])[superscript 5]m     114
Nuclear Polarizability Contribution of Order (Z[alpha])[superscript 5]m to S-Levels     117
Nuclear Size and Structure Corrections of Order (Z[alpha])[superscript 6]m     121
Nuclear Polarizability Contribution to P-Levels     121
Nuclear Size Correction of Order (Z[alpha])[superscript 6]m     122
Radiative Corrections to the Finite Size Effect     124
Radiative Correction of Order [alpha](Z[alpha])[superscript 5]m[Greather than]r[superscript 2 Greather than][Character not reproducible] to the Finite Size Effect     124
Higher Order Radiative Corrections to the Finite Size Effect     127
Weak Interaction Contribution     127
References     129
Lamb Shift in Light Muonic Atoms     131
Closed Electron-Loop Contributions of Order [alpha superscript n](Z[alpha])[superscript 2]m     133
Diagrams with One External Coulomb Line     133
Diagrams with Two External Coulomb Lines     137
Relativistic Corrections to the Leading Polarization Contribution with Exact Mass Dependence     138
Higher Order Electron-Loop Polarization Contributions     141
Wichmann-Kroll Electron-Loop Contribution of Order [alpha](Z[alpha])[superscript 4]m     141
Light by Light Electron-Loop Contribution of Order [alpha superscript 2](Z[alpha])[superscript 3]m     143
Diagrams with Radiative Photon and Electron-Loop Polarization Insertion in the Coulomb Photon. Contribution of Order [alpha superscript 2](Z[alpha])[superscript 4]m     144
Electron-Loop Polarization Insertion in the Radiative Photon. Contribution of Order [alpha superscript 2](Z[alpha])[superscript 4]m     145
Insertion of One Electron and One Muon Loops in the same Coulomb Photon. Contribution of Order [alpha superscript 2](Z[alpha])[superscript 2](m[subscript e]/m)[superscript 2]m     146
Hadron Loop Contributions     148
Hadronic Vacuum Polarization Contribution of Order [alpha](Z[alpha])[superscript 4]m     148
Hadronic Vacuum Polarization Contribution of Order [alpha](Z[alpha])[superscript 5]m     149
Contribution of Order [alpha superscript 2](Z[alpha])[superscript 4]m Induced by Insertion of the Hadron Polarization in the Radiative Photon     149
Insertion of One Electron and One Hadron Loops in the Same Coulomb Photon     150
Standard Radiative, Recoil and Radiative-Recoil Corrections     150
Nuclear Size and Structure Corrections     151
Nuclear Size and Structure Corrections of Order (Z[alpha])[superscript 5]m     151
Nuclear Size and Structure Corrections of Order (Z[alpha])[superscript 6]m     153
Radiative Corrections to the Nuclear Finite Size Effect      153
Radiative Corrections to Nuclear Polarizability Contribution     155
References     158
Physical Origin of the Hyperfine Splitting and the Main Nonrelativistic Contribution     161
References     164
Nonrecoil Corrections to HFS     165
Relativistic (Binding) Corrections to HFS     165
Electron Anomalous Magnetic Moment Contributions (Corrections of Order [alpha superscript n]E[subscript F])     167
Radiative Corrections of Order [alpha superscript n](Z[alpha])E[subscript F]     169
Corrections of Order [alpha](Z[alpha])E[subscript F]     169
Corrections of Order [alpha superscript 2](Z[alpha])E[subscript F]     173
Corrections of Order [alpha superscript 3](Z[alpha])E[subscript F]     179
Radiative Corrections of Order [alpha superscript n](Z[alpha])[superscript 2]E[subscript F]     180
Corrections of Order [alpha](Z[alpha])[superscript 2]E[subscript F]     180
Corrections of Order [alpha superscript 2](Z[alpha])[superscript 2]E[subscript F]     184
Radiative Corrections of Order [alpha](Z[alpha])[superscript 3]E[subscript F] and of Higher Orders     185
Corrections of Order [alpha](Z[alpha])[superscript 3]E[subscript F]     187
Corrections of Order [alpha superscript 2](Z[alpha])[superscript 3]E[subscript F] and of Higher Orders in [alpha]      190
References     190
Essentially Two-Body Corrections to HFS     193
Recoil Corrections to HFS     193
Leading Recoil Correction     193
Recoil Correction of Relative Order (Z[alpha])[superscript 2](m/M)     195
Higher Order in Mass Ratio Recoil Correction of Relative Order (Z[alpha])[superscript 2]     197
Recoil Corrections of Order (Z[alpha])[superscript 3](m/M)E[subscript F]     197
Radiative-Recoil Corrections to HFS     198
Corrections of Order [alpha](Z[alpha])(m/M)E[subscript F] and (Z[superscript 2][alpha])(Z[alpha])(m/M)E[subscript F]     198
Electron-Line Logarithmic Contributions of Order [alpha](Z[alpha])(m/M)E[subscript F]     200
Electron-Line Nonlogarithmic Contributions of Order [alpha](Z[alpha])(m/M)E[subscript F]     201
Muon-Line Contribution of Order (Z[superscript 2][alpha])(Z[alpha])(m/M)E[subscript F]     202
Leading Photon-Line Double Logarithmic Contribution of Order [alpha](Z[alpha])(m/M)E[subscript F]     203
Photon-Line Single-Logarithmic and Nonlogarithmic Contributions of Order [alpha](Z[alpha])(m/M)E[subscript F]     204
Heavy Particle Polarization Contributions of Order [alpha](Z[alpha])E[subscript F]     205
Leading Logarithmic Contributions of Order [alpha superscript 2](Z[alpha])(m/M)E[subscript F]      206
Leading Four-Loop Contribution of Order [alpha superscript 3](Z[alpha])(m/M)E[superscript F]     209
Corrections of Order [alpha](Z[alpha])(m/M)[subscript n]E[subscript F]     209
Corrections of Orders [alpha](Z[alpha])[superscript 2](m/M)E[subscript F] and Z[superscript 2][alpha](Z[alpha])[superscript 2](m/M)E[subscript F]     210
Weak Interaction Contribution     211
References     213
Hyperfine Splitting in Hydrogen     217
Nuclear Size, Recoil and Structure Corrections of Orders (Z[alpha])E[subscript F] and (Z[alpha])[superscript 2]E[subscript F]     218
Corrections of Order (Z[alpha])E[subscript F]     218
Recoil Corrections of Order (Z[alpha])[superscript 2](m/M)E[subscript F]     226
Correction of Order (Z[alpha])[superscript 2]m[superscript 2]r[superscript 2]E[subscript F]     226
Correction of Order (Z[alpha])[superscript 3](m/[Lambda])E[subscript F]     227
Radiative Corrections to Nuclear Size and Recoil Effects     227
Radiative-Recoil Corrections of Order [alpha](Z[alpha])(m/[Lambda])E[subscript F]     227
Radiative-Recoil Corrections of Order [alpha](Z[alpha])(m/M)E[subscript F]     228
Heavy Particle Polarization Contributions     229
Weak Interaction Contribution     229
References     231
Notes on Phenomenology     233
Lamb Shifts of the Energy Levels     233
Values of Some Physical Constants     233
Theoretical Accuracy of S-State Lamb Shifts     234
Theoretical Accuracy of P-State Lamb Shifts     235
Theoretical Accuracy of the Interval [Delta subscript n] = n[superscript 3]L(nS) - L(1S)     235
Classic Lamb Shift 2S[Fraction 12] - 2P[Fraction 12]     236
1S Lamb Shift and the Rydberg Constant     238
Isotope Shift     245
Lamb Shift in Helium Ion He[superscript +]     246
1S - 2S Transition in Muonium     247
Light Muonic Atoms     248
Hyperfine Splitting     250
Hyperfine Splitting in Hydrogen     250
Hyperfine Splitting in Deuterium     251
Hyperfine Splitting in Muonium     252
Theoretical Perspectives     254
References     255
Index     259