Atoms in Strong Magnetic Fields: Quantum Mechanical Treatment and Applications in Astrophysics and Quantum Chaos
Atoms in Strong Magnetic Fields: Quantum Mechanical Treatment and Applications in Astrophysics and Quantum Chaos
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发表时间：
1994-10
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通讯作者：
H. Ruder
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作者：
H. Ruder
1.导论。-1.1致密宇宙物体的磁场。-1.2历史回顾。-1.3记号和缩写。-2.均匀磁场中相互作用的带电粒子。-2.1 N体问题。-2.2未带电两体问题。-2.2.1质心和相对坐标下的哈密顿和波函数。-2.2.2分类，非相互作用情况下的量子数和简并。-2.2.3谐相互作用的精确解。-2.3库仑问题的标度性质。-2.3.1一般情况K？0。-2.3.2特殊情况K=0。-2.3.3核电荷(Z)标度。-3.磁化库仑问题的解决方法。-3.1一般考虑。-3.1.1磁场强度的特征域。-3.1.2波函数和多组态方程的展开。-3.1.3低场高场对应。-3.2数值处理。-3.2.1类Hartree-Fock方法。-3.2.2类耦合通道方法。-3.2.3对角化方法。-4.低激发态的结果。-4.1能量值。-4.2氢原子的波长。-4.3氢原子的波函数。-4.3.1电子的空间概率分布的图形表示。-4.3.2图形表示电子的空间几率分布。-5.绝热近似下任意激发态的能量。-5.1有效势的渐近性质。-5.2数值结果及其精度。-6.电磁跃迁概率。-6.1一般表达式。-6.2有限质子质量对跃迁矩阵元的影响。-6.3结果。-6.4绝热近似下电磁跃迁的表达式。-6.4.1偶极强度。-6.4.2选择规则。-6.4.3求和规则。-6.4.4渐近公式-6.4.5结果及讨论-7.静止线及白矮星光谱-7.1静止线-7.2选定磁白矮星的光谱-7.2.1 Gw+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磁力表白矮星。-7.4未来的工作。-8。相对论效应，核质量效应，和朗道激发态。-8.1自旋-轨道耦合。-8.2有限质子质量和垂直于磁场的运动的影响。-8.3朗道激发态。-9.任意强度磁场中的类氦原子。-9.1对应图。-9.1.1单电子问题简评。-9.1.2磁场中的两电子系统。-9.1.3 1/Z=0的对应。-9.1.4单电子问题的对应一般情况。-9.2解的方法。-9.2.1中低场强(Z？1)的Hartree-Fock方法。-9.2.2高场强(Z？1)的Hartree-Fock方法。-9.3偶极强度，振子强度和跃迁几率。-9.3.1球形反卫星的选择规则。-9.3.2圆柱反卫星的选择规则。-9.4双电子问题的结果。-9.4.1用单组态反卫星计算的能级。-9.4.2组态混合的影响。-9.4.3不同方法获得的能量值的比较。-9.4.4波长，偶极强度，振子强度，和跃迁几率。-10.高激发态。-10.1结果。-10.1.1能级。-10.1.2跃迁几率和与实验的比较。-10.2量子力学中存在混沌吗？-10.2.1导言。-10.2.2氢原子里德堡态的微波电离。-10.2.3能级序列的统计分析。-10.2.4磁场中氢原子的有序和混沌。-10.2.5氢原子的能级统计磁场。-10.2.6混沌中的共振--周期轨道的作用。-10.2.7波函数的“伤疤”。-展望。-A1。能量值-A1.1能量值表格-A1.2能量值数字-A2。波长。-A2.1波长图。-A2.2固定波长表。-A2.3固定波长图。-A3。电磁跃迁概率。-A3.1波长、偶极强度、振荡器强度和跃迁速率。-A3.2绝热近似下的振子强度和跃迁概率。-A3.3静止跃迁的偶极强度。-A4。氦和类氦原子。-A4.1能量值表。-A4.2波长、偶极强度、振荡器强度和跃迁速率。-参考文献。
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.