Theory of Light Hydrogenic Bound States
by Eides, Michael I.; Grotch, Howard; Shelyuto, Valery A.Format: Hardcover
Pub. Date: 2006-11-15
Publisher(s): Springer Verlag
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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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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