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Nuclear Physics in a Nutshell

Book Description

Nuclear Physics in a Nutshell provides a clear, concise, and up-to-date overview of the atomic nucleus and the theories that seek to explain it. Bringing together a systematic explanation of hadrons, nuclei, and stars for the first time in one volume, Carlos A. Bertulani provides the core material needed by graduate and advanced undergraduate students of physics to acquire a solid understanding of nuclear and particle science. Nuclear Physics in a Nutshell is the definitive new resource for anyone considering a career in this dynamic field.

The book opens by setting nuclear physics in the context of elementary particle physics and then shows how simple models can provide an understanding of the properties of nuclei, both in their ground states and excited states, and also of the nature of nuclear reactions. It then describes: nuclear constituents and their characteristics; nuclear interactions; nuclear structure, including the liquid-drop model approach, and the nuclear shell model; and recent developments such as the nuclear mean-field and the nuclear physics of very light nuclei, nuclear reactions with unstable nuclear beams, and the role of nuclear physics in energy production and nucleosynthesis in stars.

Throughout, discussions of theory are reinforced with examples that provide applications, thus aiding students in their reading and analysis of current literature. Each chapter closes with problems, and appendixes address supporting technical topics.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Introduction
    1. 0.1 What is Nuclear Physics?
    2. 0.2 This Book
  7. 1 Hadrons
    1. 1.1 Nucleons
    2. 1.2 Nuclear Forces
    3. 1.3 Pions
    4. 1.4 Antiparticles
    5. 1.5 Inversion and Parity
    6. 1.6 Isospin and Baryonic Number
    7. 1.7 Isospin Invariance
    8. 1.8 Magnetic Moment of the Nucleons
    9. 1.9 Strangeness and Hypercharge
    10. 1.10 Quantum Chromodynamics
    11. 1.11 Exercises
  8. 2 The Two-Nucleon System
    1. 2.1 Introduction
    2. 2.2 Electrostatic Multipoles
    3. 2.3 Magnetic Moment with Spin-orbit Coupling
    4. 2.4 Experimental Data for the Deuteron
    5. 2.5 A Square-well Model for the Deuteron
    6. 2.6 The Deuteron Wavefunction
      1. 2.6.1 Angular momentum coupling
      2. 2.6.2 Two particles of spin 1/2
      3. 2.6.3 Total wavefunction
    7. 2.7 Particles in the Continuum: Scattering
    8. 2.8 Partial Wave Expansion
    9. 2.9 Low Energy Scattering
    10. 2.10 Effective Range Theory
    11. 2.11 Proton-Proton Scattering
    12. 2.12 Neutron-Neutron Scattering
    13. 2.13 High Energy Scattering
    14. 2.14 Laboratory and Center of Mass Systems
    15. 2.15 Exercises
  9. 3 The Nucleon-Nucleon Interaction
    1. 3.1 Introduction
    2. 3.2 Phenomenological Potentials
    3. 3.3 Local Potentials
      1. 3.3.1 Nonlocal potential
    4. 3.4 Meson Exchange Potentials
      1. 3.4.1 Yukawa and Van der Waals potentials
      2. 3.4.2 Field theory picture
      3. 3.4.3 Short range part of the NN interaction
      4. 3.4.4 Chiral symmetry
      5. 3.4.5 Generalized boson exchange
      6. 3.4.6 Beyond boson exchange
    5. 3.5 Effective Field Theories
    6. 3.6 Exercises
  10. 4 General Properties of Nuclei
    1. 4.1 Introduction
    2. 4.2 Nuclear Radii
    3. 4.3 Binding Energies
    4. 4.4 Total Angular Momentum of the Nucleus
    5. 4.5 Multipole Moments
    6. 4.6 Magnetic Dipole Moment
    7. 4.7 Electric Quadrupole Moment
    8. 4.8 Excited States of Nuclei
    9. 4.9 Nuclear Stability
    10. 4.10 Exercises
  11. 5 Nuclear Models
    1. 5.1 Introduction
    2. 5.2 The Liquid Drop Model
    3. 5.3 The Fermi Gas Model
    4. 5.4 The Shell Model
    5. 5.5 Residual Interaction
    6. 5.6 Nuclear Vibrations
    7. 5.7 Nuclear Deformation
    8. 5.8 The Nilsson Model
    9. 5.9 The Rotational Model
    10. 5.10 Microscopic Theories
      1. 5.10.1 Hartree-Fock theory
      2. 5.10.2 The Skyrme interaction
      3. 5.10.3 Relativistic mean field theory
    11. 5.11 Exercises
  12. 6 Radioactivity
    1. 6.1 Introduction
    2. 6.2 Multiple Decays—Decay Chain
    3. 6.3 Preparation of a Radioactive Sample
    4. 6.4 Secular Equilibrium
    5. 6.5 Natural Radioactive Series
    6. 6.6 Radiation Units
    7. 6.7 Radioactive Dating
    8. 6.8 Properties of Unstable States—Level Width
    9. 6.9 Transition Probability—Golden Rule
    10. 6.10 Exercises
  13. 7 Alpha-Decay
    1. 7.1 Introduction
    2. 7.2 Theory of α-Decay
    3. 7.3 Angular Momentum and Parity in α-Decay
    4. 7.4 Exercises
  14. 8 Beta-Decay
    1. 8.1 Introduction
    2. 8.2 Energy Released in β-Decay
    3. 8.3 Fermi Theory
    4. 8.4 The Decay Constant—The Log ft Value
    5. 8.5 Gamow-Teller Transitions
    6. 8.6 Selection Rules
    7. 8.7 Parity Nonconservation in β-Decay
      1. 8.7.1 Double β-Decay
    8. 8.8 Electron Capture
    9. 8.9 Exercises
  15. 9 Gamma-Decay
    1. 9.1 Introduction
    2. 9.2 Quantization of Electromagnetic Fields
      1. 9.2.1 Fields and gauge invariance
      2. 9.2.2 Normal modes
      3. 9.2.3 Photons
    3. 9.3 Interaction of Radiation with Matter
      1. 9.3.1 Radiation probability
      2. 9.3.2 Long wavelength approximation
    4. 9.4 Quantum and Classical Transition Rates
    5. 9.5 Selection Rules
    6. 9.6 Estimate of the Disintegration Constants
    7. 9.7 Isomeric States
    8. 9.8 Internal Conversion
    9. 9.9 Resonant Absorption—The Mössbauer Effect
    10. 9.10 Exercises
  16. 10 Nuclear Reactions—I
    1. 10.1 Introduction
    2. 10.2 Conservation Laws
    3. 10.3 Kinematics of Nuclear Reactions
    4. 10.4 Scattering and Reaction Cross Sections
    5. 10.5 Resonances
    6. 10.6 Compound Nucleus
    7. 10.7 Mean Free Path of a Nucleon in Nuclei
    8. 10.8 Empirical Optical Potential
    9. 10.9 Compound Nucleus Formation
    10. 10.10 Compound Nucleus Decay
    11. 10.11 Exercises
  17. 11 Nuclear Reactions—II
    1. 11.1 Direct Reactions
      1. 11.1.1 Theory of direct reactions
    2. 11.2 Validation of the Shell Model
    3. 11.3 Photonuclear Reactions
      1. 11.3.1 Cross sections
      2. 11.3.2 Sum rules
      3. 11.3.3 Giant resonances
    4. 11.4 Coulomb Excitation
    5. 11.5 Fission
    6. 11.6 Mass Distribution of Fission Fragments
    7. 11.7 Neutrons Emitted in Fission
    8. 11.8 Cross Sections for Fission
    9. 11.9 Energy Distribution in Fission
    10. 11.10 Isomeric Fission
    11. 11.11 Exercises
  18. 12 Nuclear Astrophysics
    1. 12.1 Introduction
    2. 12.2 Astronomical Observations
      1. 12.2.1 The Milky Way
      2. 12.2.2 Dark matter
      3. 12.2.3 Luminosity and Hubble’s law
    3. 12.3 The Big Bang
    4. 12.4 Stellar Evolution
      1. 12.4.1 Stars burn slowly
      2. 12.4.2 Gamow peak and astrophysical S-factor
    5. 12.5 The Sun
      1. 12.5.1 Deuterium formation
      2. 12.5.2 Deuterium burning
      3. 12.5.3 3He burning
      4. 12.5.4 Reactions involving 7Be
    6. 12.6 The CNO Cycle
      1. 12.6.1 Hot CNO and rp process
    7. 12.7 Helium Burning
    8. 12.8 Red Giants
    9. 12.9 Advanced Burning Stages
      1. 12.9.1 Carbon burning
      2. 12.9.2 Neon burning
      3. 12.9.3 Oxygen burning
      4. 12.9.4 Silicon burning
    10. 12.10 Synthesis of Heaviest Elements
    11. 12.11 White Dwarfs and Neutron Stars
    12. 12.12 Supernova Explosions
    13. 12.13 Nuclear Reaction Models
      1. 12.13.1 Microscopic models
      2. 12.13.2 Potential and DWBA models
      3. 12.13.3 Parameter fit
      4. 12.13.4 Statistical models
    14. 12.14 Exercises
  19. 13 Rare Nuclear Isotopes
    1. 13.1 Introduction
    2. 13.2 Light Exotic Nuclei
      1. 13.2.1 Halo nuclei
      2. 13.2.2 Borromean nuclei
    3. 13.3 Superheavy Elements
    4. 13.4 Exercises
  20. Appendix A Angular Momentum
    1. A.1 Orbital Momentum
    2. A.2 Spherical Functions
    3. A.3 Generation of Rotations
    4. A.4 Orbital Rotations
    5. A.5 Spin
    6. A.6 Ladder Operators
    7. A.7 Angular Momentum Multiplets
    8. A.8 Multiplets as Irreducible Representations
    9. A.9 SU(2) Group and Spin 1/2
    10. A.10 Properties of Spherical Harmonics
      1. A.10.1 Explicit derivation
      2. A.10.2 Legendre polynomials
      3. A.10.3 Completeness
      4. A.10.4 Spherical functions as matrix elements of finite rotations
      5. A.10.5 Addition theorem
  21. Appendix B Angular Momentum Coupling
    1. B.1 Tensor Operators
      1. B.1.1 Transformation of operators
      2. B.1.2 Scalars and vectors
      3. B.1.3 Tensors of rank 2
      4. B.1.4 Introduction to selection rules
    2. B.2 Angular Momentum Coupling
      1. B.2.1 Two subsystems
      2. B.2.2 Decomposition of reducible representations
      3. B.2.3 Tensor operators and selection rules revisited
      4. B.2.4 Vector coupling of angular momenta
      5. B.2.5 Wigner-Eckart theorem
      6. B.2.6 Vector Model
  22. Appendix C Symmetries
    1. C.1 Time Reversal
    2. C.2 Spin Transformation and Kramer’s Theorem
    3. C.3 Time-conjugate Orbits
    4. C.4 Two-component Neutrino and Fundamental Symmetries
    5. C.5 Charge Conjugation
    6. C.6 Electric Dipole Moment
    7. C.7 CPT -Invariance
  23. Appendix D Relativistic Quantum Mechanics
    1. D.1 Lagrangians
      1. D.1.1 Covariance
    2. D.2 Electromagnetic Field
    3. D.3 Relativistic Equations
      1. D.3.1 Particle at rest
      2. D.3.2 Covariant form: γ matrices
    4. D.4 Probability and Current
    5. D.5 Wavefunction Transformation
      1. D.5.1 Bilinear Covariants
      2. D.5.2 Parity
    6. D.6 Plane Waves
      1. D.6.1 Summary of plane wave spinor properties
      2. D.6.2 Projection operators
    7. D.7 Plane Wave Expansion
    8. D.8 Electromagnetic Interaction
    9. D.9 Pauli Equation
      1. D.9.1 Spin-orbit and Darwin terms
  24. Appendix E Useful Constants and Conversion Factors
    1. E.1 Constants
    2. E.2 Masses
    3. E.3 Conversion Factors
  25. References
  26. Index