Atoms in Strong Magnetic Fields

1. Introduction.- 1.1 Magnetic Fields of Compact Cosmic Objects.- 1.2 Historical Review.- 1.3 Notations and Abbreviations.- 2. Interacting Charged Particles in Uniform Magnetic Fields.- 2.1 The N-Body Problem.- 2.2 The Uncharged Two-Body Problem.- 2.2.1 Hamiltonian and Wave Functions in Centre-of-Mass and Relative Coordinates.- 2.2.2 Classification, Quantum Numbers and Degeneracy in the Non-Interacting Case.- 2.2.3 Exact Solution for Harmonic Interaction.- 2.3 Scaling Properties of the Coulomb Problem.- 2.3.1 The General Case K ? 0.- 2.3.2 The Special Case K = 0.- 2.3.3 Nuclear Charge (Z) Scaling.- 3. Methods of Solution for the Magnetized Coulomb Problem.- 3.1 General Considerations.- 3.1.1 Characteristic Domains of the Magnetic Field Strength.- 3.1.2 Expansions of the Wave Functions and Multiconfiguration Equations.- 3.1.3 Low-Field High-Field Correspondence.- 3.2 Numerical Treatment.- 3.2.1 Hartree-Fock-Like Methods.- 3.2.2 Coupled-Channels-Like Methods.- 3.2.3 Diagonalization Methods.- 4. Results for Low-Lying States.- 4.1 Energy Values.- 4.2 Wavelengths of the Hydrogen Atom.- 4.3 Wave Functions of the Hydrogen Atom.- 4.3.1 Graphic Representation of the Spatial Probability Distribution of the Electron.- 4.3.2 Pictorial Representation of the Spatial Probability Distribution of the Electron.- 5. Energies for Arbitrarily Excited States in Adiabatic Approximation.- 5.1 Asymptotic Property of the Effective Potentials.- 5.2 Numerical Results and Their Accuracy.- 6. Electromagnetic Transition Probabilities.- 6.1 The General Expressions.- 6.2 Effects of the Finite Proton Mass on the Transition Matrix Element.- 6.3 Results.- 6.4 Expressions for Electromagnetic Transitions in Adiabatic Approximation.- 6.4.1 Dipole Strengths.- 6.4.2 Selection Rules.- 6.4.3 Sum Rules.- 6.4.4 Asymptotic Formulae.- 6.4.5 Results and Discussion.- 7. Stationary Lines and White Dwarf Spectra.- 7.1 Stationary Lines.- 7.2 Spectra of Selected Magnetic White Dwarfs.- 7.2.1 Grw+70°8247.- 7.2.2 PG 1031+234.- 7.2.3 SBS 1349+5434.- 7.2.4 PG 1015+014.- 7.2.5 G227–35.- 7.2.6 MR Serpentis.- 7.2.7 LB 11146 (PG 0945+245).- 7.3 Table of Magnetic White Dwarfs.- 7.4 Future Work.- 8. Relativistic Effects, Nuclear Mass Effects, and Landau-Excited States.- 8.1 Spin-Orbit Coupling.- 8.2 Effects of the Finite Proton Mass and of Motion Perpendicular to the Magnetic Field.- 8.3 Landau-Excited States.- 9. Helium-Like Atoms in Magnetic Fields of Arbitrary Strengths.- 9.1 Correspondence Diagrams.- 9.1.1 Short Review of the One-Electron Problem.- 9.1.2 The Two-Electron System in a Magnetic Field.- 9.1.3 The Correspondence for 1/Z = 0.- 9.1.4 The Correspondence for the General Case.- 9.2 Method of Solution.- 9.2.1 The Hartree-Fock Method for Low to Intermediate Field Strengths (?Z ? 1).- 9.2.2 The Hartree-Fock Method for High Field Strengths (?Z ? 1).- 9.3 Dipole Strengths, Oscillator Strengths, and Transition Probabilities.- 9.3.1 Selection Rules for the Spherical Ansatz.- 9.3.2 Selection Rules for the Cylindrical Ansatz.- 9.4 Results for the Two-Electron Problem.- 9.4.1 Energy Levels Calculated with a Single-Configuration Ansatz.- 9.4.2 Influence of Configuration Mixing.- 9.4.3 Comparison of Energy Values Obtained by Different Methods.- 9.4.4 Wavelengths, Dipole Strengths, Oscillator Strengths, and Transition Probabilities.- 10. Highly Excited States.- 10.1 Results.- 10.1.1 Energy Levels.- 10.1.2 Transition Probabilities and Comparison with Experiments.- 10.2 Is There Chaos in Quantum Mechanics?.- 10.2.1 Introduction.- 10.2.2 Microwave Ionisation of Rydberg States of the Hydrogen Atom.- 10.2.3 Statistical Analysis of Energy-Level Sequences.- 10.2.4 Order and Chaos in the Hydrogen Atom in a Magnetic Field.- 10.2.5 Level Statistics for the Hydrogen Atom in Magnetic Fields.- 10.2.6 Resonances in Chaos — the Role of Periodic Orbits.- 10.2.7 “Scarring” of Wave Functions.- Outlook.- A1. Energy Values.- A1.1 Tables of the Energy Values.- A1.2 Figures of the Energy Values.- A2. Wavelengths.- A2.1 Figures of the Wavelengths.- A2.2 Tables of Stationary Wavelengths.- A2.3 Figures of Stationary Wavelengths.- A3. Electromagnetic Transition Probabilities.- A3.1 Wavelengths, Dipole Strengths, Oscillator Strengths, and Transition Rates.- A3.2 Oscillator Strengths and Transition Probabilities in Adiabatic Approximation.- A3.3 Dipole Strengths of Stationary Transitions.- A4. Helium and Helium-Like Atoms.- A4.1 Tables of the Energy Values.- A4.2 Wavelengths, Dipole Strengths, Oscillator Strengths, and Transition Rates.- References.