The Spectrum of Atomic Hydrogen: Advances

The following sections are included:

• EDITOR’S INTRODUCTION

• LIST OF AUTHORS AND THEIR AFFILIATIONS

• CONTENTS

ATOMIC spectra furnish material for testing theories of atomic structure. Since hydrogen is the simplest kind of atom, the interpretation of its spectrum has been of the greatest interest to theorists, particularly since all but the most recent theories can be applied with mathematical rigour to the two-body problem which the hydrogen atom presents…

The following sections are included:

• The atomic and the molecular spectrum

• Atomic hydrogen

• Wood’s discharge tubes

• The ‘ring’ discharge

• Electron bombardment

The following sections are included:

• Balmer’s formula

• Bohr’s analysis

• Experimental tests

• Hydrogen-like spectra

• High series members and the continuum

IT had been known for over twenty-five years before Bohr’s theory that the Balmer lines were not single, but appeared to be close doublets under instruments of high resolving power There was, however, considerable disagreement as to the separation between the doublet peaks. It was particularly important to the early spectroscopists to know whether the doublet separation remained constant throughout the Balmer series, or whether it gradually decreased, since this is an important distinction in alkali spectra between the sharp and diffuse series on the one hand, and the principal series on the other. In fact, each Balmer line is a blend of sharp, principal and diffuse doublets. Complete resolution even in the most favourable case of H_α has not yet been achieved.

PASCHEN’S study [102] of the lines of ionized helium, and, in particular, of the line 4686 Å (n = 4→ n = 3) was claimed to provide striking experimental support for Sommerfeld’s theory. The fine structure of the Balmer series, as far as it was resolved at that time, also supported the theory, and further weighty evidence came from measurements of X-ray fine structure. In the following sections we shall briefly review these lines of argument.

The following sections are included:

• Wave and matrix mechanics

• Quantum mechanics

• Relativity

• Electron spin

• Spin and relativity corrections to the energy levels

• Pauli spin matrices-two-valued wave functions

• The Dirac theory of the electron

• The Dirac theory of the hydrogen atom

• The Breit interaction

• Corrections to the Dirac theory

• Intensities: new quantum theory

The following sections are included:

• The H_α line
  • The wavelength
  • The interval v₁₂
  • The interval v₂₃
  • Relative intensities of the components

• The ionized helium line 4686Å

• Conclusion

THE selection rules of the new quantum theory allow electric dipole transitions between levels of the same n but since the probability of spontaneous transition depends on the cube of the frequency such transitions in hydrogen are exceedingly improbable. Stimulated transitions, on the other hand, may take place under quite small alternating electric fields of the appropriate frequency. Absorption and emission of energy by the atom are equally probable, so that a change in an assembly of atoms may only be detected if the two states between which transitions are taking place are unequally populated at the outset…

THE confirmation by Lamb and Retherford of the inadequacy of the Dirac theory stimulated a re-examination of a theoretical problem to which only a very incomplete solution had so far been found: the problem of the interaction between charged particles and the electromagnetic field. We shall briefly refer to the problem as it presented itself in classical physics, and then (following Weisskopf [135]) notice the further difficulties which the quantum theory introduces. Finally we shall see how these difficulties have been circumvented by the new quantum electrodynamics, and how a small correction is thereby introduced to the energy levels predicted by Dirac’s theory. The new theory, however, is not a complete and logically satisfactory solution to the problems we shall state: a difficulty of principle remains now, as formerly.

DEVIATIONS from the Dirac theory have now been found in the levels n = 1,2 and 3 of deuterium, n = 2 of tritium, and n = 2, 3 and 4 of He⁺ by optical spectroscopy. Shifts in the level n = 3 of hydrogen and n = 2 of He⁺ have been measured by radio-frequency spectroscopy.

IT is well known that hyperfine structure in spectra arises from the interaction of nuclear magnetic dipoles and the magnetic field due to the electron cloud. In the case of hydrogen the interaction energy is appreciably greater than the natural width of the energy levels only in the case of the ground level and the abnormally narrow (metastable) 2²S_½ level. The hyperfine structure of both these levels has been measured with great precision by atomic beam magnetic resonance methods. The ground level in particular has been repeatedly examined by this technique, and also by the method of paramagnetic absorption of microwaves.

Calculation of the hyperfine structure requires knowledge of the magnetic moment of the proton. If this were a Dirac particle, its moment would be eh/4πMc (one nuclear magneton), which stands in conflict with the value 2.79275 nuclear magnetons measured by a variety of methods. This experimental value, used in the simplest hyperfine structure formula, leads to substantial agreement between experiment and theory. Even so, there remains a discrepancy of about 0.1 per cent, which is greatly in excess of the experimental errors. This discrepancy is closely related to the interactions which give rise to the Lamb shift, as we shall now see.

THE system comprised of one electron and one positron can exist in bound states for times sufficiently long to allow the measurement of energy differences between them. Positronium*, as this substance is called, thus allows a further test of the theory of the two-particle atom. Details of the theory were worked out before there was experimental proof of the existence of positronium.

The following sections are included:

• Conventional Laboratory Spectroscopy: Gas Discharges: Spontaneous Emission

• Radiofrequency Spectroscopy: Atomic Beams: Lamb’s experiment

• Radiofrequency Spectroscopy: Hyperfine Structure of the Ground State

• Optical Spectroscopy: the Laser Era
  • Saturated absorption spectroscopy
  • Two-photon spectroscopy
  • Polarization spectroscopy
  • Cross-over resonances
  • Interaction times: the Ramsey technique: cooling

• Optical Pumping: Ground States

• Fluorescence Spectroscopy: Excited States
  • Optical-radiofrequency double resonance
  • Level-crossing spectroscopy
  • Anticrossing spectroscopy

• Beam Foil Spectroscopy

• Production of Hydrogenic Atoms
  • Traditional methods
  • Cold hydrogen beams
  • Fast hydrogen beams
  • Hydrogenic ions
  • Positronium (e⁺e⁻)
  • Muonium (μ⁺e⁻

• REFERENCES

The following sections are included:

• Introduction

• Quantum Electrodynamics

• Magnetic Moment Anomaly

• Bound Interaction Picture QED

• Self-Energy

• Vacuum Polarization

• Higher Order Radiative Corrections

• Finite Nuclear Size Effects

• Nuclear Recoil Corrections

• Lamb Shift in Hydrogenlike Atoms

• Hyperfine Structure

• Helium Energy Levels

• REFERENCES

The following sections are included:

• Introduction

• Theory of Spontaneous Transitions

• Theory of Quenching Radiation Assymmetries
  • Basic formalism
  • Hyperfine structure effects for weak quenching fields
  • The Lamb shift anisotropy
  • E1-E1 damping interference
  • E1-M1 interference
  • The total quench rate

• Quantum Beats
  • Introduction
  • Theory of field-induced quantum beats
  • The two-state approximation
  • Comparison with experiment

• Two-photon Transitions
  • Introduction
  • Theory of two-photon transitions
  • Computational methods and results
  • Other two-photon processes
  • Static field quenching as a two-photon process

• The Electroweak Interaction Parity Non-Conservation in Atomic Physics
  • Introduction
  • Some basic concepts of weak interactions and their currents
  • The electron - nucleon weak interaction
  • Coupling constants in the standard electroweak model
  • Calculation of matrix elements
  • Bibliography on weak interactions

• APPENDIX Hydrogenic Perturbation Theory and the Stark Effect
  • Higher order perturbation corrections
  • Intermediate state summations

• Acknowledgements

• REFERENCES

The following sections are included:

• Introduction

• Hyperfine Structure
  • Hydrogen ground state interval
  • The hydrogen maser
  • The hyperfine anomaly δ
  • Comparison of 1S and 2S hyperfine intervals
  • Measurement of the ground state interval in ³He⁺
  • Muonium ground state interval
  • Measurement of muonium ground state interval
  • Positronium ground state interval

• Fine Structure and Lamb Shift
  • Energy levels
  • The Lamb shift interval
  • The 2P fine structure interval
  • The slow beam Lamb shift measurements
  • Fast beam rf Lamb shift measurements
  • Lamb shift measurements using static electric fields
  • Present status of the Lamb shift
  • Measurements of other n = 2 intervals: the fine structure constant

• Weak Interactions
  • Theory
  • General principles of parity measurements
  • Experiments to measure parity violation

• Acknowledgement

• REFERENCES

The following sections are included:

• Before The Laser Era
  • Helium+; resolution of the fine structure
  • The Rydberg constant: renewed interest
  • Student laboratories

• Precision Laser Spectroscopy: First Round of Experiments
  • Precision laser spectroscopy

• Precision Laser Spectroscopy: Later Work
  • Levels of accuracy; units and standards of measurement
  • Objectives of experiments and reduction of measurements
  • Design of experiment
  • Determinations of the Rydberg constant
  • The 1S-2S transition

• Experimental Results: Comparison with Theory
  • The Rydberg constant
  • The 1S-2S transition
  • Spectroscopic isotope shift
  • Indications for future measurements

• Acknowledgments

• REFERENCES

The following sections are included:

• Introduction

• Light Sources
  • Gas discharges
  • Laser-produced plasmas
  • Ion sources
  • Recoil ions
  • Fast ion beams

• More or Less Classical Spectroscopy: n = 1 Lamb Shift

• Application of Constant External Fields: Quench Experiments

• Application of Oscillating External Fields: Resonance Experiments

• Conclusion

• REFERENCES

The following sections are included:

• Introduction

• Elementary Considerations
  • Coupling constants — orders of magnitude
  • The atomic spectrum in external fields—the three gross regimes
  • Orders of magnitude and further remarks
  • The failure of traditional methods

• Basic Aspects of Experiments
  • The choice of the atomic species and optical state selection
  • Atomic beam experiments
  • Vapor phase experiments
  • Other experimental techniques
  • The production of fields
  • About the future

• Electric Field Structure of One-Electron Rydberg Atoms
  • Historical survey
  • The electric field structure of the hydrogen atom
  • One-electron Rydberg atoms in electric fields—the role of non-Coulombic corrections
  • Experimental manifestations in Rydberg atoms
  • Conclusions

• Magnetic Field Structure of One-Electron Rydberg Atoms — the Diamagnetic Behavior
  • Historical survey
  • The magnetic structure of atoms — standard analysis of a non-separable problem
  • The diamagnetic behavior from experiments

• Elementary Views on the Symmetries of the Coulomb Interaction
  • The overview from classical mechanics
  • The symmetry group of the orbital Coulomb problem
  • The Coulomb dynamical group

• The Low Field Regimes and Breaking the Coulomb Symmetry
  • Rydberg atoms in crossed E, B fields — the low field Pauli quantization
  • The atom in a magnetic field — the low field diamagnetic behavior
  • Stark effect for quasi-hydrogenic species

• The Strong Mixing Regimes and the Coulomb Dynamical Group
  • The magnetic problem and coupled-oscillators dynamics
  • The symmetries in the magnetic problem
  • Classical chaos and its quantum analog in the magnetic problem
  • Conclusions

• Conclusions

• Acknowledgements

• REFERENCES

The following sections are included:

• Introduction

• Positronium Formation Methods
  • Fast positrons
  • Slow positrons
  • Positronium Mass
  • Positronium Charge
  • Annihilation Rates
  • Positronium Energy Levels

• REFERENCES

The following sections are included:

• Introduction

• Nonrelativistic Approximation
  • Free electrons
  • Atoms

• Approximations for High and Low Temperatures

• The n = 2 Lamb Shift

• Hyperfine Structure

• Experiment

• REFERENCES

The following sections are included:

• The Atomic Constants, Physical Theory, and the Base Units of Measurement

• The Rydberg Constant

• The Fine Structure Constant
  • Experimental study of fine structure in hydrogen
  • Fine structure in helium
  • Hyperfine structure
  • The Josephson effect
  • Muonium hyperfine structure
  • The electron and the positron: the g-2 anomaly
  • Muons: the g-2 anomaly
  • he quantized Hall effect
  • The values of α

• The Electron-to-Proton Mass Ratio

• CODATA

• REFERENCES

• SUPPLEMENTARY REFERENCES

• SUBJECT INDEX