Atoms in Strong Magnetic Fields: Quantum Mechanical Treatment and Applications in Astrophysics and Quantum Chaos

ISBN-13: 9783642788222 / Angielski / Miękka / 2011 / 309 str.

Hanns Ruder; G. Nter Wunner; Heinz Herold

Opis

In this book we summarize the essential results of our efforts over the years to calculate energies, wave functions, and electromagnetic transitions of atoms as functions of the magnetic field strength from laboratory fields up to neutron star magnetic fields. Motivated by the observational evidence of huge magnetic 5 fields with strengths up to 10 T in the vicinity of white dwarf stars and of up 9 to 10 T in the vicinity of neutron stars the authors, together with coworkers and candidates for doctor and diploma degrees, have investigated this, fasci nating quantum mechanical problem more or less continuously since 1978. The extensive tables and figures in the appendices represent the most complete data set to date in this field of research. For practical use all numbers are available by "anonymous ftp" over Internet. The first direct measurement of a neutron star magnetic field by Trum per and his group, who observed a cyclotron feature at about 50 ke V in the spectrum of the X-ray pulsar Hercules X-I corresponding to a field strength of 8 several 10 T, stimulated investigations of atoms within the framework of the adiabatic approximation, which is well justified for such field strengths. This method and its results are discussed in Chaps. 3, 5, and 6."

Spis treści

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.

O autorze

Prof. Dr. Hanns Ruder war bis zu seiner Emeritierung 1996 Professor für Theoretische Astrophysik an der Universität Tübingen. 2006 erhielt er die Medaille für Naturwissenschaftliche Publizistik von der Deutschen Physikalischen Gesellschaft.