Modern Atomic and Nuclear Physics

The following sections are included:

• ABOUT THE AUTHORS

• CONTENTS

• PREFACE

Physics is the discipline of science that concerns itself with the study of the most general laws of matter and energy and the fundamental structure of matter. The branch of atomic physics aims primarily at the study of that structure at what is called the atomic scale—a term for sizes between those of molecules and the nuclei of atoms. Figure 1.1 gives us a perspective on the dimensions of our universe from clusters of galaxies to the nucleus of the atom. While the concept of atoms has a history of more than 2000 years, atomic physics as we know it today is a discipline that began to form in the present century and parallels the development of modern physics…

The following sections are included:

• SPECIAL RELATIVITY

• GENERAL RELATIVITY

• APPENDIX lA FOUR-VECTOR NOTATION

• PROBLEMS

The following sections are included:

• THE BACKGROUND
  • The Discovery of the Electron
  • The Charge and Mass of the Electron
  • Avogadro's Constant
  • The Size of Atoms

• THE EMERGENCE OF THE RUTHERFORD MODEL

• RUTHERFORD SCATTERING FORMULA
  • The Derivation of the Coulomb Scattering Formula
  • The Derivation of Rutherford's Formula

• THE EXPERIMENTAL VERIFICATION OF THE RUTHERFORD FORMULA
  • Geiger–Marsden Experiment
  • Rutherford Formula for Small Angles
  • The Estimation of the Nuclear Size
  • Rutherford Formula at θ = 180°

• SUMMARY OF THE SIGNIFICANCES AND DIFFICULTIES OF A NUCLEAR MODEL
  • The Significances
  • The Difficulties
  • Quantifying a Difficulty with Rutherford's Model

• APPENDIX 2A CENTRAL FORCES

• APPENDIX 2B ELECTRIC UNITS

• APPENDIX 2C THE DERIVATION OF RUTHERFORD'S FORMULA IN THE LABORATORY SYSTEM

• PROBLEMS

The following sections are included:

• BACKGROUND
  • Evidence of the Quantum Hypothesis I: Blackbody Radiation
  • Evidence of the Quantum Hypothesis II: Photoelectric Effect
  • Spectrum of Light

• THE BOHR MODEL
  • Classical Orbits with Stationary State Conditions
  • Frequency Condition
  • Quantization of Angular Momentum
  • Numerical Calculational Methods

• EXPERIMENTAL EVIDENCE I: SPECTRA
  • Spectrum of Hydrogen
  • Spectra of Hydrogenlike Ions
  • The Existence of Deuterium
  • Note I: Nonquantized Orbits
  • Note II: Rydberg Atoms

• EXPERIMENTAL EVIDENCE II: FRANCK–HERTZ EXPERIMENT
  • Basic Idea
  • Franck–Hertz Experiment
  • Improved Franck–Hertz Experiment
  • Concluding Remarks

• EXTENSION: BOHR–SOMMERFELD MODEL
  • Extension of Quantization
  • Elliptical Orbits
  • Relativistic Corrections
  • Comparison with Experiments

• SUMMARY

• PROBLEMS

The following sections are included:

• MAGNETIC MOMENT PRODUCED BY THE ELECTRON ORBITAL MOTION IN AN ATOM
  • Classical Expression
  • The Quantization Condition

• THE STERN–GERLACH EXPERIMENT

• THE HYPOTHESIS OF ELECTRON SPIN
  • The Hypothesis of Electron Spin
  • Landé g-Factor
  • Expression of the g-Factor for a Single Electron
  • Interpretation of the Stern–Gerlach Experiment

• DOUBLET LINES OF ALKALI METALS
  • Fine Structure in the Spectral Lines of Alkali Metals: Qualitative Considerations
  • Spin–Orbit Interaction: Quantitative Consideration of Fine Structure
  • Note: Estimation of the Internal Magnetic Field of an Atom

• THE ZEEMAN EFFECT
  • The Normal Zeeman Effect
  • The Polarization Character of the Zeeman Spectrum
  • The Anomalous Zeeman Effect
  • Supplementary Note 1: Grotrian Diagrams
  • Supplementary Note 2: Paschen–Back Effect
  • Conclusions

• SUMMARY OF THE HYDROGEN ENERGY SPECTRUM

• SUMMARY

• APPENDIX 4A DIPOLE MOMENT

• APPENDIX 4B MAGNETIC RESONANCE

• PROBLEMS

The following sections are included:

• THE SPECTRA AND ENERGY LEVELS OF HELIUM

• THE COUPLING OF THE TWO ELECTRONS
  • Electron Configurations
  • L–S and j–j Couplings
  • Coupting Rule for Two Angular Moments
  • Selection Rules
  • From Electron Configurations to Atomic States

• THE PAULI EXCLUSION PRINCIPLE
  • Historical Review
  • Exclusion Principle
  • Examples
  • The Resultant States for Equivalent Electrons

• THE PERIODIC TABLE OF THE ELEMENTS
  • The Periodicity of the Properties of the Elements
  • The Number of Electrons in the Shells
  • The Energies of the Electron Configurations—The Order of the Shells
  • Atomic Ground States
  • Explanation for the Variation of Ionization Energy

• SUMMARY

• PROBLEMS

The following sections are included:

• THE DISCOVERY OF X-RAYS AND THEIR WAVE NATURE
  • The Discovery of X-Rays
  • X-Ray Tube
  • The Wave Nature of X-Rays
  • The Polarization of X-Rays
  • The Diffraction of X-Rays
  • A Further Derivation of Bragg's Relation

• MECHANISMS FOR PRODUCING X-RAYS
  • X-Ray Emission Spectra
  • Continuous Spectrum—Bremsstrahlung
  • Characteristic Radiation—Transitions of the Inner Shell Electrons
  • The Labeling of Characteristic X-Ray Radiation
  • Auger Electrons
  • Synchrotron Radiation

• COMPTON SCATTERING
  • Classical Considerations
  • The Quantum Explanation
  • The Physical Meaning
  • Compton Scattering and the Fundamental Constants
  • Note 1: Compton Profile
  • Note 2: Inverse Compton Effect
  • Note 3: The Photon Theory of Light

• THE ABSORPTION OF X-RAYS
  • Two Kinds of Interactions
  • The Interactions Between Photons and Matter
  • The Absorption of X-Rays
  • The Absorption Limit
  • Extended X-Ray Absorption Fine Structure (EXAFS)
  • Photoelectron Spectroscopy

• SUMMARY
  • Important Formulas
  • Important Concepts
  • The Experimental Measurements of Some Physical Quantities
  • Nobel Prizes Relating to the Studies of X-Rays

• PROBLEMS

The following sections are included:

• THE DIFFICULTY OF THE BOHR THEORY

• WAVE–PARTICLE DUALISM
  • The Wave and the Particle in Classical Physics
  • Wave–Particle Dualism of Light
  • The de Broglie Hypothesis
  • Davisson–Germer Experiment
  • de Broglie Waves and Quantum States
  • A Particle in a Rigid Box
  • A Wave and the Property of Nonlocalization

• UNCERTAINTY RELATIONS
  • Simple Derivation of the Uncertainty Principle
  • Examples of the Application of the Uncertainty Relations
  • Principle of Complementarity

• THE WAVEFUNCTION AND ITS STATISTICAL EXPLANATION
  • The Wave–Particle Dualism and the Concept of Probability
  • Double-Slit Interference Experiment
  • Superposition of States Principle
  • The Explanation of the Interference Experiment
  • Further Comments

• SUMMARY

• APPENDIX 7A THE SYMMETRY OF THE WAVEFUNCTION AND THE PAULI EXCLUSION PRINCIPLE

• APPENDIX 7B EINSTEIN'S A AND B COEFFICIENTS

• APPENDIX 7C SELECTION RULES FOR TRANSITIONS

• APPENDIX 7D THE PRINCIPLES OF LASERS

• PROBLEMS

The following sections are included:

• SCHRÖDINGER EQUATION
  • The Establishment of the Schrödinger Equation
  • The Schrödinger Equation of a Stationary State
  • Examples

• AVERAGE VALUE AND OPERATOR
  • Average Values
  • The Introduction of Operators
  • Eigenvalue and Eigenequation

• THE SOLUTION OF THE SCHRÖDINGER EQUATION OF THE HYDROGEN ATOM
  • Schrödinger Equation in a Central Force Field
  • The Motion of Electrons in a Coulomb Field
  • Comments

• APPENDIX 8A HARMONIC OSCILLATOR SOLUTION

• PROBLEMS

The following sections are included:

• THE NUCLEUS OF THE ATOM
  • Introduction
  • Atomic Center: The Nucleus
  • Constituents of the Nucleus
  • Chart of the Nuclides

• NUCLEAR GROUND STATE PROPERTIES
  • Nuclear Shapes and Densities
  • Nuclear Masses: “1 + 1 ≠ 2”
  • Binding Energy
  • Semi-empirical Mass Formula
  • A More Complete Mass Formula

• NUCLEAR GROUND STATE SPINS AND MOMENTS
  • Nuclear Spin
  • Magnetic Dipole Moment
  • The Electric Quadrupole Moment

• SUMMARY

• PROBLEMS

The following sections are included:

• RADIOACTIVE DECAY LAWS
  • The Exponential Decay Law
  • The Half-Life
  • The Mean Life
  • λ Is a Characteristic Parameter of a Radioactive Nuclide
  • Activity
  • Measurement of a Long Half-Life
  • Simple Cascade Decay
  • Isotope Production

• ALPHA, PROTON, HEAVY CLUSTER AND SPONTANEOUS FISSION DECAYS
  • The Necessary Condition for α Decay
  • α Decay Energies and Energy Level Diagrams
  • α Decay Mechanism and Half-Life
  • Some Important Historical Events in α Studies
  • Proton Radioactivity and Proton Decay
  • Spontaneous Fission and Cluster Radioactivities

• BETA DECAY
  • The Puzzle of β Decay
  • The Neutrino Hypothesis
  • β⁻ Decay
  • β⁺ Decay
  • Orbital Electron Capture (EC)
  • The Other Decay Modes Associated with β Decay

• GAMMA DECAY, INTERNAL CONVERSION AND PAIR PRODUCTION
  • Gamma Decay
  • Internal Conversion
  • Internal Pair Creation
  • Isomeric Transitions
  • Mössbauer Effect
  • Brief Summary of the Properties of α, β, and γ Radiations in Radioactive Decays and Their Interactions in Matter

• SUMMARY

• APPENDIX l0A THEORY OF BETA DECAY

• PROBLEMS

The following sections are included:

• NUCLEAR FORCES
  • General Characteristics
  • Meson Theory of the Nuclear Force

• NUCLEAR MODELS
  • Fermi Gas Model
  • Nuclear Shell Model
  • The Collective Model

• TOWARD A UNIFIED MODEL DESCRIPTION OF NUCLEI
  • Nuclear Shape Coexistence in the Region below Z = 82
  • New Islands of Superdeformation Associated with New Deformed Magic Numbers
  • Nuclei at High Angular Momentum
  • New Facilities to Meet New Challenges

• SUMMARY

• PROBLEMS

The following sections are included:

• INTRODUCTION TO NUCLEAR INTERACTIONS AND REACTIONS
  • Overview
  • Several Famous Early Nuclear Reactions

• REACTION KINEMATICS
  • The Q Value Equation
  • Coulomb Barrier and Coulomb Excitation
  • Examples of the Application of the Q Value Equation
  • Reaction Cross-Section

• COULOMB EXCITATION, COMPOUND NUCLEUS REACTIONS, AND OTHER REACTIONS
  • Coulomb Excitation
  • Compound Nuclear Reactions
  • Other Types of Reactions

• FISSION AND FUSION: ATOMIC ENERGY UTILIZATION
  • The Fission Discovery
  • Fission Mechanism
  • Spontaneous Fission (SF)
  • Fission Energy and Its Applications
  • Fusion of Light Nuclei
  • Solar Energy—Gravitational Confinement Fusion
  • The Hydrogen Bomb—Inertial Confinement Fusion
  • Controllable Fusion Reactor – Magnetic Confinement

• SOME SELECTED APPLICATIONS OF NUCLEAR PHYSICS

• SUMMARY

• PROBLEMS

The following sections are included:

• INTRODUCTION

• MAGNETIC DIPOLE HYPERFINE INTERACTION
  • General Expression
  • Magnetic Dipole Hyperfine Interaction of a Single-Electron Atom
  • Magnetic Hyperfine Structure of a Hydrogen Atom
  • Magnetic Hyperfine Interaction for Many-Electron Atoms
  • Determination of the Nuclear Spin from Magnetic Hyperfine Structure
  • Nuclear Level Splitting by the Magnetic Hyperfine Interaction

• ELECTRIC QUADRUPOLE HYPERFINE INTERACTION
  • General Expression
  • An Example of a Quadrupole Hyperfine Shift of Atomic Energy Levels
  • Nuclear Energy Level Shift by Quadrupole Hyperfine Interaction

• ISOTOPE SHIFT
  • Isotope Shift from the Mass Effect
  • Isotope Shift from the Volume Effect
  • Isomer Shift of the Atomic Energy Levels
  • Examples of Isotope and Isomer Shifts of Atomic Energy Levels
  • The Isomer Shift of the Nuclear Energy Levels
  • The Hyperfine Structure Anomaly of Isotopes: Bohr–Weisskopf Effect
  • Isotopic Separation by Lasers
  • Study of the Isotope Shift by Muonic Atoms

• SUMMARY

• PROBLEMS

The following sections are included:

• TOWARD A DEEPER STRATUM
  • Dimension and Energy
  • High-energy Particle Sources
  • Characteristics of High-energy Physics
  • Historical Review

• PARTICLE FAMILIES AND INTERACTIONS
  • Particle Families
  • Interactions
  • Resonances

• CONSERVATION RULES
  • Baryon Number, Lepton Number, and Isospin Conservation
  • Meson Number Conservation
  • Strangeness Conservation
  • Violation of Parity and Time Reversal and CPT Conservation
  • Charm, Bottom and Top Conservation
  • Summary: Conservation Laws and Interactions

• THE QUARK MODEL
  • Internal Structure of Hadrons
  • Quark Model
  • New Synthesis of Particle and Nuclear Physics
  • Grand Unified Theories
  • Summary and Perspectives

• PROBLEMS

The following sections are included:

• APPENDIX I ION BEAM ANALYSIS

• APPENDIX II TABLE OF ISOTOPES

• APPENDIX III THE 2006 VALUES OF THE PHYSICAL CONSTANTS RECOMMENDED BY CODATA

• APPENDIX IV TABLES OF ATOMIC-ELECTRON BINDING ENERGIES AND X-RAY ENERGIES AND INTENSITIES

• INDEX