Modern Nuclear Physics - From Fundamentals to Frontiers

Description

This textbook is a unique and ambitious primer of nuclear physics, which introduces recent theoretical and experimental progresses starting from basics in fundamental quantum mechanics. The highlight is to offer an overview of nuclear structure phenomena relevant to recent key findings such as unstable halo nuclei, superheavy elements, neutron stars, nucleosynthesis, the standard model, lattice quantum chromodynamics (LQCD), and chiral effective theory. An additional attraction is that general properties of nuclei are comprehensively explained from both the theoretical and experimental viewpoints. The book begins with the conceptual and mathematical basics of quantum mechanics, and goes into the main point of nuclear physics – nuclear structure, radioactive ion beam physics, and nuclear reactions. The last chapters devote interdisciplinary topics in association with astrophysics and particle physics. A number of illustrations and exercises with complete solutions are given. Each chapter is comprehensively written starting from fundamentals to gradually reach modern aspects of nuclear physics with the objective to provide an effective description of the cutting edge in the field. Preface Contents About the Authors 1 Concepts of Quantum Mechanics from a Nuclear Physics Viewpoint 1.1 Genesis of Quantum Physics 1.2 Spin and Isospin Quantum Numbers 1.2.1 The Spin 1.2.2 The Stern–Gerlach Experiment 1.2.3 The Isospin 1.3 Quantum Entanglement 1.4 The Schrödinger Equation and Its Physical Meaning 1.5 Solving the Schrödinger Equation in One Dimension 1.6 Quantum Tunnelling and Probability of Wave Function 1.7 Uncertainty Relation 1.8 The Dirac Equation 1.8.1 Relativistic Kinematics and Dirac Equation 1.8.2 Continuity Equation of Dirac Wave Function 1.8.3 Negative Energy and Spin of the Dirac Wave Function 1.8.4 Spin of Dirac Particle 1.9 Symmetries and Symmetry Breaking in the Nucleus 1.9.1 Explicit and Spontaneous Symmetry Breaking 1.9.2 The Chiral Symmetry of QCD References 2 Nuclear Forces 2.1 Fundamental Interactions 2.2 Energy Resolution and Effective Theories 2.3 Nuclear Forces 2.4 Meson Theory for Nucleon-Nucleon Interactions 2.5 NN Potentials and Phase Shifts 2.5.1 Symmmetry Requirement on NN Interactions 2.6 Many-Body Interactions 2.7 QCD and Chiral Effective Field Theory (ChEFT) 2.7.1 QCD and NN Interaction 2.7.2 Chirality 2.7.3 ChEFT and NN and Many-Body Interactions References 3 Nuclear Structure Theory 3.1 Preamble 3.2 A Bird's-Eye View of Nuclear Theory 3.3 The Deuteron 3.4 Effective Interactions for Nuclear Many-Body Problems 3.5 Nuclear Mean Field 3.5.1 Slater Determinant and the Second Quantization 3.5.2 The Mean-Field Potential 3.6 Energy Density Functionals (EDF) 3.6.1 Hartree–Fock Models 3.6.2 Relativistic Mean Field (RMF) Model 3.6.3 Pairing Interactions and BCS/Bogolyubov Approximation 3.6.4 Tamm-Dancoff and Random Phase Approximations 3.7 Beyond the Mean Field Approaches 3.7.1 Particle-Vibration Coupling (PVC) Model 3.7.2 Second RPA 3.7.3 Generator Coordinate Method (GCM) 3.8 Many-Body Shell Model Wave Function 3.9 The Monte Carlo and No-Core Shell Models 3.9.1 Shell Model Monte Carlo (SMMC) 3.10 Anti-symmetrized Molecular Dynamics and Fermionic Molecular Dynamics 3.11 Ab Initio Approaches 3.11.1 Unitary Correlation Operator Method (UCOM) 3.11.2 Similarity Renormalization Group (SRG) 3.11.3 No-Core Shell Model (NCSM) 3.11.4 Variational Monte Carlo (VMC) and Green's Function Monte Carlo (GFMC) Approaches 3.11.5 Coupled Cluster Method 3.11.6 Self-consistent Green's Function (SCGF) Approach 3.11.7 Nuclear Lattice Effective Field Theory (NLEFT) Simulation References 4 Nuclear Observables and Measurement Techniques 4.1 Masses 4.1.1 Definitions 4.1.2 The Liquid-Drop Model 4.1.3 Overview of Measurement Techniques 4.1.4 Time of Flight 4.1.5 Storage Rings 4.1.6 Time-of-flight Ion-Cyclotron-Resonance (ICR) 4.1.7 Phase-Imaging Method 4.2 Beta Decay Strength and Half-Life 4.2.1 The Discovery of the Weak Interaction 4.2.2 The Fermi β-decay Theory 4.2.3 Conservation Laws 4.2.4 Decay Probabilities and ft Values 4.2.5 Examples of β-decay Measurements 4.3 Charge and Matter Radii 4.3.1 Electron Elastic Scattering 4.3.2 Laser Spectroscopy 4.3.3 Reaction Cross Sections 4.3.4 Proton Elastic Scattering 4.3.5 Parity Violation Scattering 4.3.6 Coherent π0 Photoproduction 4.3.7 Comparison of Radii Extraction Techniques 4.4 Nuclear Moments 4.4.1 The Electric Quadrupole Moment 4.4.2 The Magnetic Dipole Moment 4.4.3 Hyperfine Structure 4.4.4 Magnetic and Quadrupole Nuclear Resonance 4.4.5 Time-Differential Perturbed Angular Distributions (TDPAD) 4.5 Particle Spectroscopy 4.5.1 Nucleon Transfer and the Missing-Mass Technique 4.5.2 Charged-Particle Detectors 4.5.3 Neutron Spectroscopy 4.6 Gamma-Ray Spectroscopy 4.6.1 General Propoerties of Electromagnetic Transitions in Nuclei 4.6.2 Electric and Magnetic Multipole Transitions 4.6.3 Transitions Probabilities 4.6.4 Weisskopf Estimates of Transition Rates 4.6.5 Photon-Matter Interactions 4.6.6 Gamma Detection and Resolving Power 4.6.7 In-Flight Spectroscopy 4.6.8 Short Lifetime Measurements References 5 Nuclear Shells 5.1 Experimental Evidence in Stable Nuclei 5.1.1 Masses 5.1.2 Charge Density Distributions 5.1.3 Charge Radii 5.1.4 Electric Quadrupole and Magnetic Dipole Moments 5.1.5 Spectroscopy and Transition Probabilities 5.1.6 Direct-Reaction Cross Sections 5.2 Superheavy Elements 5.2.1 Relativistic Limit to the Existence of Chemical Elements 5.3 Hypernuclei 5.3.1 Classification of Hyperons 5.3.2 Production of Hypernuclei 5.3.3 Extending the Study of Baryon-Baryon Interactions to Hyperons 5.3.4 Femtoscopy: A Tool to Investigate YN and YY Interactions 5.4 Non Observability of Nuclear Shells 5.5 Correlations Beyond the Shell-Model Picture References 6 Radioactive-Ion-Beam Physics 6.1 Radioactive-ion-beam Production 6.1.1 The Primary Beam: Ion Sources and Acceleration Systems 6.1.2 The ISOL Method 6.1.3 The In-Flight Method 6.2 Density Distributions of Nuclei Near Drip Lines 6.2.1 Halo Nuclei 6.2.2 Neutron Skins 6.2.3 Neutron Droplets 6.3 Evolution of Nuclear Shells 6.3.1 Observations 6.3.2 Mean Field Approach for Shell Evolution 6.3.3 Shell Model Approach: Monopole Interaction and Tensor Force 6.3.4 3N Force and Shell Evolution 6.4 Island of Inversion 6.5 Di-neutron Correlations and Nuclear Superfluidity 6.5.1 Pairing Correlations 6.5.2 Three-Body Model and Borromian Nuclei 6.5.3 Di-neutron Correlations in 11Li and Three-Body Model 6.5.4 Soft Dipole Excitation in 11Li 6.5.5 Two Neutron Correlations in 26O 6.6 Isoscalar Spin-Triplet Pairing 6.6.1 Wigner Energy in the Mass Formula 6.6.2 Isoscalar Pairing and Magnetic Dipole Transitions 6.6.3 Pair Transfer Reactions and Pairing Correlations 6.7 Clusters in Neutron-Rich Nuclei 6.7.1 Molecular Orbit and Linear-Chain Configuration 6.7.2 Oscillation of Cluster States References 7 Deformation and Rotation 7.1 Deformation of Molecules and Nuclei 7.1.1 Diatomic Molecule and Deuteron 7.1.2 Harmonic Vibration and Particle-Vibration Coupling Hamiltonian 7.1.3 Vibrational One-Body Potential and Separable Two-Body Interaction 7.2 Nuclear Deformation 7.2.1 Parameterizations for Deformation/Nomenclatura 7.2.2 Rotational Spectrum 7.2.3 Quadrupole Deformation Across the Nuclear Chart 7.3 Deformed Single-Particle States 7.3.1 Elliott SU(3) Model 7.3.2 Deformed Harmonic Oscillator Model 7.3.3 Nilsson Model for Deformed Single-Particle States 7.4 Strutinsky's Shell Correction Method to Liquid Drop Model 7.5 Measuring Shapes 7.5.1 Electric and Magnetic Moments 7.5.2 Coulomb Excitation 7.6 Backbending Phenomenon in Moment of Inertia 7.7 Shape Coexistence 7.8 Superdeformation and Hyperdeformation 7.8.1 Shell Structure of Deformed Single-Particle Potential and Super- and Hyperdeformation 7.8.2 Superdeformed Band in 152Dy 7.8.3 Superdeformed Band in 40Ca and Theoretical Models 7.9 Octupole Deformation 7.10 Appendix 7.10.1 Clebsch–Gordan Coefficient and Wigner–Eckart Theorem 7.10.2 Spherical Harmonics and Spherical Bessel Functions References 8 Nuclear Reactions 8.1 Diversity of Reaction Mechanisms 8.2 Direct Reactions 8.2.1 General Formalism 8.2.2 T Matrix and Plane Wave Born Approximation (PWBA) 8.2.3 Scattering Amplitude and Cross Sections 8.2.4 S Matrix and Scattering Amplitude 8.2.5 Scattering Length and Effective Range 8.2.6 Optical Model 8.2.7 Optical Potentials 8.3 Born Approximation 8.3.1 Plane Wave Born Approximation (PWBA) 8.3.2 Distorted Wave Born Approximation (DWBA) 8.4 Applications of Direct Reaction Theory 8.4.1 Proton Elastic Scattering 8.4.2 Inelastic Scattering 8.5 Nucleon Transfer Reactions 8.5.1 One Nucleon Transfer Reactions and Spectroscopic Factors 8.5.2 Quasi-free Scattering 8.5.3 Heavy-Ion Induced Inclusive Nucleon Removal Reactions at Intermediate Energy 8.5.4 Eikonal Approximation and S Matrices 8.6 Compound Nuclear Reactions 8.6.1 Resonant Scattering of Neutrons 8.6.2 Statistical Distributions of Resonance Energies 8.7 Fusion, Energy from the Stars 8.7.1 Producing Energy by Fusion 8.8 Fission 8.8.1 Brief History 8.8.2 Models for Fission 8.8.3 Energy Production from Fission 8.8.4 New Generation Reactors References 9 Neutron Stars and Nucleosynthesis 9.1 The Nuclear Equation of State (EoS) 9.2 Incompressibility and Giant Monopole Resonances 9.3 Symmetry Energy and Terrestrial Experiments 9.3.1 Electric Dipole Polarizability and Neutron Skin 9.3.2 Symmetry Energy and Mass Formula 9.4 Summary of Constraints on Symmetry Energy 9.5 Neutron Stars 9.5.1 Tolman–Oppenheimer–Volkoff Equation 9.5.2 Ligo–Virgo Neutron Star Merger Observation and NICER Experiment 9.5.3 Hyperon Puzzle 9.5.4 Crust of Neutron Star 9.6 Nucleosynthesis 9.6.1 Solar System Abundances 9.6.2 Big Bang Nucleosynthesis 9.6.3 Stellar Nucleosynthesis 9.7 Neutron Capture Nucleosynthesis 9.7.1 Neutron Capture Cross Section 9.7.2 s-Process, r-Process and Supernova Explosion References 10 Nuclear Physics and Standard Model of Elementary Particles 10.1 Standard Model 10.1.1 Overview 10.1.2 Confinement and Experimental Evidence of Quarks 10.1.3 Gauge Bosons 10.2 Lattice Quantum Chromodynamics 10.2.1 Framework 10.2.2 Expectation Value of Observables 10.2.3 Algorithms 10.2.4 Masses 10.2.5 NN Potentials 10.3 Cabibbo–Kobayashi–Maskawa Matrix and Superallowed β Decay 10.4 Neutrinos 10.4.1 Flavors and Masses 10.4.2 Search for a 4th Neutrino 10.4.3 Double Beta Decay 10.5 Non-zero Electric Dipole Moment and Octupole Deformation 10.6 Appendix 10.6.1 Dirac γ Matrices 10.6.2 Grassmann Algebra 10.6.3 Gauge Theory and Wilson Action 10.6.4 Correlation Function References