The Hydrogen Atom: Precision Physics of Simple Atomic Systems (Lecture Notes in Physics)

front-matter
	The Hydrogen Atom
	Foreword
	Preface
	Table of Contents
	List of Contributing Participants
Chapter 1
	1 Historica Remarks
	2 Precision Physics of Simple Atoms
	3 Studying the Simple Atoms
		3.1 Hydrogen and deuterium (see [6,7] and Part VI)
		3.2 Muonium and Positronium (see [12,13] and Part VII)
		3.3 Muonic Atoms and Nuclear Structure (see Part VIII)
		3.4 Nuclear-Structure Independent Differences
		3.5 Fine Structure in Helium (see [23] and Part VI)
		3.6 Few-Electron Ions (see [26,27] and Part XI)
		3.7 Medium-Z Physics (see [26,27] and Part XI)
		3.8 Higher-Order Corrections
		3.9 Bound State QED
		3.10 Exotic Atoms (see [35,36] and Part IX)
		3.11 Antihydrogen and CPT Violation (Part IX)
		3.12 Exotic Events
		3.13 Variation of Constants (Part X)
		3.14 Precision Frequency Metrology ([38] and Part X)
		3.15 Determination of Fundamental Constants ([39,40] and Part X)
	4 About This Publication
	Acknowledgements
	References
Chapter 2
	1 Introduction
	2 The Hydrogen 1S -2S Transition
		2.1 Hydrogen 1S -2S Two-Photon Spectroscopy in an Atomic Beam
		2.2 Theoretical Line Shape Model
		2.3 Optical Lamb Shift Measurements
		2.4 Absolute Measurements of the 1S -2S Transition Frequency in Atomic Hydrogen
		2.5 1S-2S Isotope Shift and the Deuteron Structure Radius
	3 Spectroscopy of the2S-nS and 2S-nD Transitions
		3.1 Method
		3.2 Optical Frequency Measurements in Paris
		3.3 Comparison of the 1S-3S and 2S-6 S/D Transitions
	4 Determination of the Rydberg Constant and Lamb Shifts
		4.1 Rydberg Constant
		4.2 Lamb Shifts
	5 Conclusion and Prospects
	References
Chapter 3
	1 Introduction
	2 Ultracold Hydrogen Research at MIT
		2.1 The Road to Bose-Einstein Condensation
		2.2 Two-Photon 1S-2S Spectroscopy
		2.3 Bose-Einstein Condensation
		2.4 High Resolution Spectroscopy in Ultracold Hydrogen
	Acknowledgments
	References
Chapter 4
	1 Introduction
	2 Principal Effects
	3 Nonrelativistic Wave Functions
		3.1 Recent Advances
	4 Asymptotic Expansions
	5 Relativistic Corrections
	6 Quantum Electrodynamic Corrections
		6.1 Electron-Nucleus Terms
		6.2 Electron-Electron Terms
		6.3 Higher Order Terms
	7 Comparison with Experiment
		7.1 Measurement of the Fine Structure Constant
		7.2 Applications to Lithium
	8 Concluding Remarks
	Acknowledgements
	References
Chapter 5
	1 Introduction
	2 Muonium Formation
	3 Ground State Hyperfine Structure
	4 1s-2s Energy Interval
	5 Connection to a New Measurement of the Muon Magnetic Anomaly
	6 Muonium-Antimuonium Conversion
	7 Long Term Future Possibilities
	8 Conclusions
	9 Acknowledgements
	References
Chapter 6
	1 Introduction
	2 Decay Rates
		
		
	3 Energy Level Intervals
		3.1 Ground State Interval
		3.2 Rydberg Interval
		3.3 Intervals in the n=2 and 3 excited states
	4 Summary and Conclusions
	References
Chapter 7
	1 Introduction
	2 Kerr-Lens Mode-Locked Lasers
	3 Femtosecond Frequency Combs
	4 Spectral Broadening by Self-Phase Modulation
	5 Photonic Crystal Fibers
	6 Phase-Locking the Frequency Comb
	7 Self-calibrated Optical Combs: Absolute Optical Frequencies
	8 Accuracy Tests of the fs Laser Comb Approach
	9 The Fine Structure Constant ±
	10 Conclusion
	Acknowledgement
	References
Chapter 8
	1 Introduction
	2 1998 Least Squares Adjustment
	3 Electron Magnetic Moment Anomaly
	4 Rydberg Constant
		4.1 Theory Relevant to the Rydberg Constant
		4.2 Self Energy
		4.3 Two-Photon Corrections
		4.4 Finite Nuclear Size
		4.5 Total Energy and Uncertainty
		4.6 Result of LSA for the Rydberg Constant
	5 Conclusion
	References
Chapter 9
	1 Introduction
	2 Electron Magnetic Moment Anomaly
	3 Muon Magnetic Moment Anomaly
	4 Improving the alpha^4 Term of the Electron g-2
	5 Concluding remarks
	Acknowledgments
	Appendix: VEGAS and Feynman Integral
	References
Chapter 10
	1 Introduction
	2 Fast-Beam Laser Resonance Technique
		2.1 Signal Formation
		2.2 Co-linear Geometry and Kinematic Compression
		2.3 Determination of the Beam Velocity: Doppler-tuned Spectroscopy with Co- and Counter-Propagating Laser Beams
		2.4 Wavefront Curvature Effects
		2.5 Alternatives to the Beam-Foil Technique
	3 Hydrogen-like Ions
		3.1 Lamb Shift
		3.2 Experimental Considerations
		3.3 Lamb Shift Measurements in F^8+, P^14+, S^15+ and Cl^16+
		3.4 Future Prospects for Laser Lamb Shift Measurements
		3.5 Ground-state Hyperfine Structure of High-Z Hydrogen-like Ions
	4 Helium-like Ions
		4.1 Experimental Considerations
		4.2 2^3 S_1 - 2^3 P_J Transitions in Li^+ ,Be^2+ and B^3+
		4.3 2^1 S_0 - 2^3 P_1, 2^3 P_0 Intercombination Transitions in N^5+
		4.4 2^3 P_J - 2^3 P_J\' Fine Structure Transitions in F^7+ and Mg^10+
		4.5 Future Prospects
	5 Conclusions
	Acknowledgments
	References
Chapter 11
	1 Introduction
	2 Summary of Theory
	3 Experiment
	4 Results
	5 Future Prospects
		5.1 Electron Mass
		5.2 Fine Structure Constant
		5.3 Electron Binding Energies
		5.4 Nuclear Magnetic Moments
		5.5 Lithium-like Ions
	Acknowledgements
	References
Chapter 12
	1 Introduction
	
		2.1 A_pi mu properties
		
		
	3 Ultrarelativistic positronium atoms (A_2e)
		3.1 Source of the ultrarelativistic A_2e and their quantum numbers
		3.2 Superpenetration of ultrarelativistic atoms
		3.3 Time-of-formation effects in production of ultrarelativistic A_2e
		3.4 Observation of ultrarelativistic positronium and measurement of the branching ratio for the pi°-mesons decay...
		3.5 Measurement of the total cross section for interaction of ultrarelativistic positronium atoms with carbon.
	
		
		
		4.3 Data processing
		4.4 Approximation procedure for the pi^+ pi^ - pair distribution A_2pi number obtaining
		
		4.6 A_piK as a source of model-independent data on piK S-wave scattering lengths
	Acknowledgements
	References
Chapter 13
	1 Introduction
	2 Unique Facets of Antiprotonic Helium
	3 Advanced Theories
	4 Laser Spectroscopy of Antiprotonic Helium
	5 Precise Determination of Transition Energies
	6 Chemical Physics Aspects
		6.1 State Dependent Lifetime Shortening
		6.2 Pressure Shifts of Resonance Lines
		6.3 Quenching with H_2 Admixtures
		6.4 Hydrogen-Assisted Inverse Resonances and Individual Quenching Rates
	7 Hyperfine Structure
	8 The Future
	References
Chapter 14
	1 Introduction
	2 Overview of Lamb Shift Calculations
	3 The Experimental Method
		3.1 The UV Ligh Source
		3.2 The Interaccion Region
		3.3 The He^+2S Ion Source and Beam
		3.4 Metastable Detection
		3.5 The Reference Laser System
		3.6 Detection of the Two-Photon Transition
	4 Conclusion
	5 Acknowledgments
	References
Chapter 15
	1 Helium and Fundamental Physics
	2 Fine Structure of the Helium 2^3 P Level: Experiments
		2.1 The Florence Experiment
		2.2 State of the Art of the 2^3 P Helium Splittings
	3 Hyperfine Iodine Transitions at 541 nm: a New Frequency Reference for Helium Spectroscopy
	4 Conclusions and Final Remarks
	Acknowledgments
	References
Chapter 16
	Conclusion
	References
Chapter 17
	1 Introduction
	2 Theory
		2.1 Non-recoil limit
	3 Present status of D21 theory
		3.1 Old theory and recent progress
		3.2 Our results
	4 Present status
	Acknowledgments
	References
Chapter 18
	1 Introduction
	2 Strategy of the calculation
	3 Basics of the program
	4 Results
	5 Acknowledgments
	References
Chapter 19
	1 Theory and results
	References
Chapter 20
	1 Atomic interferometer method
	2 Discussions
	References
Chapter 21
	1 Introduction
	2 Framework of the calculation
	3 Soft Scale Contributions
		3.1 Irreducible corrections
		3.2 Reducible Corrections
		3.3 Total soft scale contribution
	4 Hard Scale Contributions
		4.1 Radiative Recoil Correction
		4.2 Radiative Corrections
		4.3 Pure Recoil Correction
	5 Conclusion
	Acknowledgments
	Appendix
	References
Chapter 22
	1 Introduction
	2 NRQED
	3 The Matching Calculation
	4 The Bound State Calculation
	References
Chapter 23
	1 Introduction
	2 Calculational methods
		2.1 General discussion
		2.2 Quantum mechanics in d =3 -2epsilon dimensions
		2.3 Hard scale contributions
	3 Results
		3.1 Positronium spectroscopy
		3.2 Parapositronium decay to two photons
	4 Acknowledgments
	References
Chapter 24
	Introduction
	Analysis of Muonium Spectroscopy Data
	Results
	Other Tests of CPT
	References
Chapter 25
	1 Introduction
	2 Theoretical expressions for the energy levels
	3 Theoretical expressions for the annihilation rates
	4 Comparison between theory and experiment
		4.1 Spectroscopy
		4.2 Annihilation rates
	Acknowledgements
	Appendix
	References
Chapter 26
	1 Introduction
	2 Underlying Theory
	3 Results
	References
Chapter 27
	1 Introduction
	2 Muon Catalyzed Fusion
	3 A beam of muonic hydrogen atoms
	4 Resonant formation of muonic molecules dµt
	
	6 Future prospects
	Acknowledgements
	References
Chapter 28
	1 Introduction
	2 Theory for Delta_12 for muonic hydrogen and deuterium HFS structure.
		2.1 Vacuum polarization term Delta^VP
		2.2 Relativistic corrections
		2.3 Nuclear-structure effects
		2.4 Numerical results
	3 Experimental considerations
	Acknowledgments
	References
Chapter 29
	1 Introduction
	2 Long-Lived Metastable µp(2S)
		2.1 Measurement of the Initial Kinetic Energies of µp(1S) Atoms
		2.2 Direct Observation of Resonantly Quenched 2S States
	3 Laser Experiment
		3.1 High-Intensity Low-Energy Muon Beam Line
		3.2 Three-Stage Laser System for 6 µm Light
		3.3 X-Ray Detector
	4 Conclusions
	Acknowledgments
	References
Chapter 30
	1 Motivation for Experiments with Low Energy Neutral Antimatter
	2 Antihydrogen Formation
	3 The ATHENA Project
		3.1 The Changed Particle Traps in ATHENA
		3.2 First Capture of Antiprotons in the ATHENA Catching Trap
		3.3 The ATHENA Positron Accumulator
		3.4 Antihydrogen Detection
		3.5 Outlook
	References
Chapter 31
	1 Introduction
	2 Experiment
	3 Results
		3.1 Spin-averaged shifts and widths
		3.2 Hyperfine structure
	4 Summary and outlook
	References
Chapter 32
	1 Introduction
	2 Calibration using exotic atom X-rays
	3 Experimental set-up
	4 Charged Pion Mass
	5 Energy calibration of fluorescence X-rays
	6 Outlook
	References
Chapter 33
	1 Introduction
	2 Proposed Measurements of the Strong Interaction Shift and Width in Pionic Hydrogen
	2.1 Calibration Procedures
	References
Chapter 34
	1 Introduction
	2 Relativistic corrections. Radiative corrections. Asymptotic expansion in terms of alpha
	3 Results
	References
Chapter 35
	1 Introduction
	
	3 Laser Cooling and Shelving Spectroscopy
	References
Chapter 36
	1 Introduction
	2 Hyperfine Structure of pHe^+
		2.1 Observation of a Line Splitting in a Laser Transition
		2.2 Planned Two-Laser Microwave Triple Resonance Experiment
	3 Ground-State Hyperfine Structure of Antihydrogen
		3.1 General Remarks
		3.2 Hydrogen Hyperfine Structure and Related CPT Invariant Quantities
		3.3 Proposed Experimental Scenario to Measure the Ground-state Hyperfine Structure of Antihydrogen
	4 Conclusion and Summary
	References
Chapter 37
	1 Introduction
	2 High-Resolution Spectroscopy and Absolute Frequency Measurement of the Clock Transition
	3 Uncertainties of the Indium Standard
		3.1 Doppler Effect
		3.2 Electric Fields
		3.3 Magnetic Fields
		3.4 Ligh Shifts
	Acknowledgments
	References
Chapter 38
	1 Introduction
	2 Neutrality of matter: present knowledge
	3 Experimental method
	4 Discussion
	5 Conclusion
	6 Acknowledgement
	References
Chapter 39
	1 Introduction
	2 AtomicTheory
		
		2.2 Relativistic Many-Body Calculations
	3 Results of Observations
		3.1 Systematic Errors?
	Acknowledgments
	References
Chapter 40
	1 Introduction
	2 Laser Systems
	3 Frequency Chain
	4 Absolute Frequency Measurements
	5 Conclusion
	References
Chapter 41
	1 Introduction
	2 Electron Interaction in He-like Ions
		2.1 Coulomb-Coulomb Interaccion in he Case of Two-Electron Configurations
		2.2 Coulomb-Breit Interaction in he Case of Two-Electron Configurations
		2.3 Breit-Breit Interaction in he Case of Two-Electron Configurations
	3 Electron Interaction in Li-like Ions
		3.1 Coulomb-Coulomb Interaction in he Case of Three-Electron Configurations
		3.2 Coulomb-Breit Interaction in he Case of Three-Electron Configurations
		3.3 Breit-Breit Interaction in he Case of Three-Electron Configurations
	4 Analysis
	Appendix
	References
Chapter 42
	1 Introduction
	2 Pure Binding and Nuclear Effects
	
	4 QED Effects of Higher Orders
	5 Total Theoretical Value
	6 Acknowedgements
	References
Chapter 43
	1 Introduction
	2 Loop after loop irreducible SESE contribution
	3 Other SESE contributions
	Acknowledgements
	References
Chapter 44
	1 Introduction
	2 Theoretical contributions
		2.1 Deffinitions and notation
		2.2 One-loop contributions: self energy of the electron
		2.3 One-loop contributions: polarization of vacuum
		2.4 Wichmann-Kroll contributions
		2.5 Fitting of one-loop self energy contributions
		2.6 Two-loop contributions
		2.7 Three-loop contributions
		2.8 Pure recoil corrections
		2.9 Radiative-recoil corrections
		2.10 Finite-nuclear-size correction
	3 Summary
	Acknowledgments
	References
Chapter 45
	1 Introduction
	2 Theory
		2.1 Present status
		2.2 Comparison to the experiment
		2.3 Potential model
	3 Precise tests of the bound state QED
		3.1 Weak and strong theory
		3.2 Higher-order two-loop contributions
		3.3 Physics of medium Z
	4 Carbon and calcium experiments
		4.1 Carbon experiment and electron-to-proton mass ratio
		4.2 Calcium measurement: why it is getting interesting
	5 Summary
	Aknowledgements
	Appendix: Auxiliary data on the bound electron g factor measurements
	References
Chapter 46
	1 Introduction
	2 Theoretical Contributions to Hydrogenic Energy Levels
	3 Experiment
	4 Hydrogenic Systems for Calculable Standards
	Acknowledgements
	References
Chapter 47
	1 Introduction
	2 Storage Ring Laser Spectroscopy
	3 Experimental Procedure
	4 Results and Outlook
	References
Chapter 48
	1 Introduction
	2 Method
	3 Allowance for Doppler Shift
	4 Doppler-tuned Resonances
	5 Results
	6 Acknowledgments
	References
Chapter 49
	1 Introduction
	2 Survey Experiment
		2.1 Experimental Arrangement
		2.2 Procedure
		2.3 Results
	3 Ongoing Work
		3.1 Set-up using Two ^13C^16 O_2 Lasers and a 5°. Interaction Geometry
		3.2 Set-up using Transverse Geometry and a ^14C^16 O_2 Laser
	4 Conclusion
	5 Acknowledgments
	References
Chapter 50
	1 Introduction
	2 Experiment
		2.1 Calibration
		2.2 Clinometry
	3 Curved Crystal Theory and Systematic Shifts
		3.1 Depth Penetration
		3.2 Lateral Shifts
	4 Data Analysis and Error Sources
		4.1 Error Budget
	5 Results and Discussion
		5.1 Comparison to Theory
		5.2 Two-electron Lamb Shifts
		5.3 Previous Helium-like Vanadium Observations
	6 Coclusion
	References
Chapter 51
	1 Introduction
	2 Relativistic formula for the recoil correction
	3 Simple approach to the recoil effect in atoms
	4 Numerical results
		4.1 Hydrogenlike atoms
		4.2 Lithiumlike ions
	5 Coclusion
	Acknowledgments
	References
Chapter 52
	1 Introduction
	2 Experiment Setup
		2.1 Electron Beam Ion Traps
		2.2 High Resolution X-r y Spectroscopy
	3 Recent Results
		
		
	4 Future Directions
		4.1 Relative and Absolute Wavelength Measurements
		4.2 An Intercomparison Technique
	5 Conclusions
	References
Chapter 53
	1 Introduction
	2 The free eight-component two-fermion equation
	3 Introduction of the interaction in the 8-component equation
	4 Perturbation theory and results
	5 Concluding remarks
	References
Chapter 54
	1 Experiment and Theory
	2 Theoretical Methods for Highly-Charged Ions
	2.1 Overview of the Two-Time Green ’s Function Method
	2.2 Second-Order Calculations
	3 Conclusion and Outlook
	References
Chapter 55
	1 Introduction
	2 General formulation of method
	3 Analytical basis set for higher-order calculations of transition amplitudes
	4 Results and discussions
	5 Conclusions
	Acknowledgments
	References
Chapter 56
	1 Introduction
	2 Radiation Matrix Element Dependence on a Magnetic Field
	3 Diamagnetic Corrections to Matrix Elements of Transitions from Degenerate States
	4 Numerical Results or Lyman and Balmer Transitions
	5 Conclusion
	Refferences
Chapter 57
	1 The Current Status of the Theory
	2 Feynman Amplitudes for the g -2 and the Integration by Parts Identities
	3 Feynman Graphs, Subtopologies and Master Integrals
	References
Chapter 58
	1 Introduction
	2 Theory
		2.1 Basic Equations
		2.2 Solutions to Equations (15a)–(16b)
		2.3 Relativistic Dipole Dynamic Polarizabilities
	Acknowledgments
	References
Chapter 59
	Introduction
	1 Loop-after-loop contribution
	2 Combined self-energy vacuum-polarization diagram
	Conclusion
	Appendix I: Partial Wave Renormalization
	Appendix II: Potential expansion of the reducible Green function
	References
back-matter
	Author Index