A Student's Guide to Atomic Physics

This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics. Cover Half-title Periodic table figure Series information Title page Copyright information Table of contents Preface List of symbols Quantum Numbers Part I Fundamental Principles 1 Preliminary Concepts 1.1 Quantized Energy States in Atoms 1.2 Ionization States and Spectroscopic Notation 1.3 Ground States and Excited States 1.4 Atomic Spectroscopy 1.5 Spectroscopic Energy Units and Atomic Databases 1.6 Energy Scales in Atoms Exercises 2 Hydrogen 2.1 The Bohr Model of Hydrogen 2.2 The Quantum Mechanics of the Hydrogen Atom 2.2.1 The Schrödinger Equation 2.2.2 Separation of Variables 2.2.3 The Angular Solution and the Spherical Harmonics 2.2.4 The Radial Wave Functions 2.2.5 The Full-Wave Function and Energy 2.3 Degeneracy and Spin 2.4 Hydrogen-Like Atoms Exercises 3 Radiative Transitions 3.1 Classical Theories of Radiating Dipoles 3.2 Quantum Theory of Radiative Transitions 3.3 Electric Dipole (E1) Transitions 3.4 Selection Rules for E1 Transitions 3.5 Higher-Order Transitions 3.6 Radiative Lifetimes 3.7 The Width and Shape of Spectral Lines 3.8 Natural Broadening 3.9 Collision (Pressure) Broadening 3.10 Doppler Broadening 3.11 Voigt Line Shapes 3.12 Converting between Line Widths in Frequency and Wavelength Units Exercises 4 The Shell Model and Alkali Spectra 4.1 The Central-Field Approximation 4.2 The Shell Model and the Periodic Table 4.3 Justification of the Shell Model 4.4 Experimental Evidence for the Shell Model 4.4.1 The Periodic Table of Elements 4.4.2 Ionization Potentials and Atomic Radii 4.4.3 X-Ray Spectra 4.5 Alkali Metals Exercises 5 Angular Momentum 5.1 Conservation of Angular Momentum 5.2 Types of Angular Momentum 5.2.1 Orbital Angular Momentum 5.2.2 Spin Angular Momentum 5.3 Addition of Angular Momentum 5.4 Spin-Orbit Coupling 5.5 Angular Momentum Coupling in Single-Electron Atoms 5.6 Angular Momentum Coupling in Multi-Electron Atoms 5.7 LS Coupling 5.8 Electric-Dipole Selection Rules in the LS Coupling Limit 5.9 Hund’s Rules 5.10 jj Coupling Exercises 6 Helium and Exchange Symmetry 6.1 Exchange Symmetry 6.2 Helium Wave Functions 6.3 The Pauli Exclusion Principle 6.3.1 Slater Determinants 6.4 The Hamiltonian for Helium 6.5 The Helium Term Diagram 6.6 Optical Spectra of Divalent Metals Exercises 7 Fine Structure and Nuclear Effects 7.1 Orbital Magnetic Dipoles 7.2 Spin Magnetism 7.3 Spin-Orbit Coupling 7.3.1 Spin-Orbit Coupling in the Bohr Model 7.3.2 Spin-Orbit Coupling Beyond the Bohr Model 7.3.3 Scaling of Spin-Orbit Coupling with Z 7.4 Evaluation of the Spin-Orbit Energy for Hydrogen 7.5 Spin-Orbit Coupling in Alkali Atoms 7.6 Spin-Orbit Coupling in Many-Electron Atoms 7.7 Fine Structure in X-Ray Spectra 7.8 Nuclear Effects in Atoms 7.8.1 Isotope Shifts 7.8.2 Hyperfine Structure Exercises 8 External Fields: The Zeeman and Stark Effects 8.1 Magnetic Fields 8.1.1 The Normal Zeeman Effect 8.1.2 The Anomalous Zeeman Effect 8.1.3 The Paschen–Back Effect 8.2 The Concept of ``Good'' Quantum Numbers 8.3 Nuclear Effects 8.3.1 Magnetic Field Effects for Hyperfine Levels 8.3.2 Nuclear Magnetic Resonance 8.4 Electric Fields 8.4.1 The Quadratic Stark Effect 8.4.2 The Linear Stark Effect Exercises Part II Applications of Atomic Physics 9 Stimulated Emission and Lasers 9.1 Stimulated Emission 9.2 Population Inversion 9.3 Optical Amplification 9.4 Principles of Laser Oscillation 9.5 Four-Level Lasers 9.6 The Helium–Neon Laser 9.7 Three-Level Lasers 9.8 Classification of Lasers Exercises 10 Cold Atoms 10.1 Introduction 10.2 Gas Temperatures 10.3 Doppler Cooling 10.3.1 The Laser-Cooling Process 10.3.2 The Doppler-Limit Temperature 10.4 Optical Molasses and Magneto-Optical Traps 10.5 Experimental Considerations 10.6 Cooling below the Doppler Limit 10.7 Bose–Einstein Condensation 10.7.1 Atomic Bosons 10.7.2 The Condensation Temperature 10.7.3 Experimental Techniques for Atomic BEC Exercises 11 Atomic Physics Applied to the Solid State 11.1 Solid-State Spectroscopy 11.1.1 Selection Rules 11.1.2 Linewidths 11.2 Semiconductors 11.2.1 Electronic States 11.2.2 Interband Transitions 11.2.3 Light-Emitting Diodes 11.2.4 Semiconductor Diode Lasers 11.2.5 Photodiodes 11.3 Solid-State Hydrogenic Systems 11.3.1 Impurity States in Semiconductors 11.3.2 Excitons 11.4 Quantum-Confined Semiconductor Structures 11.4.1 The Quantum-Confined Stark Effect 11.4.2 Quantum Dots 11.5 Ions Doped in Crystals 11.5.1 Transition Metals 11.5.2 Rare Earths Exercises 12 Atomic Physics in Astronomy 12.1 Astrophysical Environments 12.2 Astrophysical Spectra 12.2.1 General Features 12.2.2 Forbidden Transitions 12.2.3 Spectral Regions 12.2.4 Doppler Shifts 12.3 Information Gained from Analysis of Astrophysical Spectra 12.4 Hydrogen Spectra 12.4.1 Optical Frequency Transitions 12.4.2 Radio-Frequency Transitions 12.4.3 Radio-Frequency Spectra of Rydberg Atoms 12.5 Helium Spectra Exercises Appendix A The Reduced Mass Appendix B Mathematical Solutions for the Hydrogen Schrödinger Equation Appendix C Helium Energy Integrals Appendix D Perturbation Theory of the Stark Effect Appendix E Laser Dynamics References Index Fundamental constants