Theory of Light Hydrogenic Bound States

by Eides, Michael I.; Grotch, Howard; Shelyuto, Valery A.

• ISBN13: 9783540452690
• ISBN10: 3540452699
• eBook ISBN(s): 9783540452706
• Format: Hardcover
• Copyright: 2006-11-15
• Publisher: Springer Verlag
• More Book Details
• Purchase Benefits

Summary

The book describes the modern theory of light hydrogen-like systems, and the discussion is based on quantum electrodynamics. In particular, Green's functions, relativistic bound-state equations and Feynman diagrams are extensively used. New theoretical approaches are described and explained. The book contains derivation of many theoretical results obtained in recent years. A complete set of all theoretical results for the energy levels of hydrogen-like bound states, as well as comparison with experiment, is presented.

Table of Contents

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