Nuclear Physics

Cover Contents Preface About the Author Acknowledgements Chapter 1: The Birth of the Nucleus 1.1 Background 1.2 Geiger and Marsden's Alpha Scattering Experiment 1.3 Rutherford's Model of Nuclear Atom 1.4 Rutherford's Scattering Formula 1.4.1 A ssumptions Made by Rutherford 1.4.2 The Concept of Cross-section 1.5 Nuclear Atom 1.5.1 Fundamental Properties of a Nucleus 1.6 Electron Cannot be a Constituent of the Nucleus 1.6.1 Nuclear Statistics 1.6.2 Compton and de-Broglie Wave Lengths of Electron 1.6.3 Uncertainty in the Momentum of Electron 1.6.4 Magnitude of Magnetic Dipole Moment of the Nucleus 1.6.5 Angular Momentum of the Odd A Nuclei 1.6.6 Nuclei that May Emit both β+ and β- Particles 1.6.7 Beta-Neutrino Pair 1.7 The Nucleus Today Chapter 2: Basic Properties of the Nucleus and Their Determination 2.1 Determination of Nuclear Charge 2.1.1 X-ray Attenuation 2.1.2 M oseley's Law for the Frequency of the Characteristic X-ray K-lines 2.1.3 Scattering of α Particles 2.2 Determination of Nuclear Mass 2.2.1 Mass Spectroscopy 2.2.2 Accelerator Mass Spectrometry (AMS) 2.2.3 Nuclear Mass from Reaction and Decay Data 2.3 Determination of Nuclear Radius 2.3.1 Elastic Scattering of Fast Electrons By Nuclei 2.3.2 Coulomb Energy Difference between Mirror Isobars 2.3.3 Anomalous Scattering of α Particles 2.3.4 Nuclear Radius from the Life Time of α Emitters 2.4 Nuclear Angular Momentum, Magnetic Dipole Moment, and Electric Quadrupole Moment 2.4.1 Angular Momentum 2.4.2 Magnetic Dipole Moment (μ) 2.4.3 Electric Quadrupole Moment Q 2.5 Determination of Nuclear Angular Momentum I 2.5.1 Nuclear Angular Momentum from the Multiplicity of the Hyper Multiplet 2.5.2 Interval Rule for Hyperfine Multiplets 2.5.3 Hyperfine Structure and External Magnetic Field 2.5.4 Rotational Band Spectra of Homonuclear Diatomic Molecule 2.6 Determination of Nuclear Magnetic Moment 2.6.1 Molecular Beam Resonance 2.6.2 Nuclear Magnetic Resonance Induction Method 2.6.3 Paramagnetic Resonance Method 2.7 Determination of the Nuclear Quadrupole Moment Q 2.7.1 The Shift in the Energy of Hyperfine Structure 2.7.2 The Hyperfine Structure of Molecular Rotational Spectra Chapter 3: Force between Nucleons 3.1 Introduction 3.2 Inadequacy of Classical Forces 3.3 Two-body Nucleon–Nucleon Force 3.3.1 Separation Energy of the Last Nucleon in Light Nuclei 3.3.2 Energy Levels of Mirror Nuclei 3.3.3 Difference in the Binding Energies of 31H and 32He 3.3.4 Study of Deuteron Properties 3.3.5 Nucleon–Nucleon Scattering 3.3.6 Constant Density of Nuclear Matter: Exchange Forces 3.4 Mediation of Nuclear Field 3.4.1 Virtual Mesons 3.4.2 Yukawa Particle: π -meson 3.5 Spin–Orbit Dependence of Nuclear Force 3.6 Nucleon–Nucleon Potential 3.6.1 Local and Global Nuclear Potentials 3.7 Quark and Gluon Chapter 4: Quantum Mechanical Analysis of Some Nuclear Systems 4.1 Deuteron and Its Properties 4.2 Schrödinger Equations for a System of Two Spinless Particles in Spherical Polar Coordinates 4.3 Simple Quantum Mechanical Description of Deuteron 4.3.1 Bound, Just Bound and Un-bound States 4.3.2 Spin Dependence of Nuclear Force 4.3.3 Tensor Nature of Nuclear Force 4.3.4 Radius of Deuteron 4.4 Quantum Mechanical Approach to Nucleon–Nucleon Scattering 4.4.1 Neutron–proton Elastic Scattering 4.4.2 Triplet and Singlet Cross-sections 4.4.3 Solving Schrödinger Equations for Scattering Problem 4.4.4 Zero Energy Limit and Scattering Length 4.4.5 Shape Independence and Effective Range Theory 4.4.6 Proton–Proton Elastic Scattering at Low Energies 4.4.7 n–p and p–p Elastic Scattering at High Energies 4.5 One-dimensional Rectangular Barrier Transmission Chapter 5: Characteristics of Stable Nuclei and Nuclear Models 5.1 Systematic Trends in Stable and Long-lived Nuclides 5.2 Shell Model 5.2.1 Spin–Orbit Coupling 5.2.2 Prediction of the Spin and the Parity of the Nucleus 5.2.3 Quadrupole Moment and Shell Model 5.2.4 Prediction of Low-lying Excited States 5.2.5 Prediction of Magnetic Moment: Schmidt Lines 5.3 Liquid Drop Model 5.3.1 Basis of the Liquid Drop Model: Similarity Between a Liquid Drop and the Nucleus 5.3.2 Differences Between a Liquid Drop and a Nucleus 5.3.3 Weizsacker's Semi-empirical Mass or Binding Energy Formula 5.3.4 Liquid Drop Model and Nuclear Fission 5.4 Collective Models of the Nucleus 5.4.1 Rotational Bands 5.4.2 Vibrational States 5.4.3 Rotating Nuclei 5.5 Fermi Gas Model of the Nucleus 5.5.1 Average Kinetic Energy per Nucleon 5.5.2 Total Kinetic Energy of a Nucleus Chapter 6: Radioactive Decay 6.1 Nuclear Stability 6.2 Radioactive Decay Chain 6.3 Two-step Decay 6.4 Activation Analysis 6.4.1 Carbon-14 Dating 6.5 The α decay 6.5.1 The α Decay Energy or Q-value 6.5.2 Characteristics of a Particle Spectrum 6.5.3 Theory of α Decay 6.6 The β decay 6.6.1 Decay Energy or Q -value 6.6.2 Characteristics of β Particle Spectrum 6.6.3 Simple Theory of β Decay 6.6.4 The Density of States dN/dE0 6.6.5 The Matrix Element 6.6.6 Fermi–Kurie Plot 6.6.7 The Comparative Half-life and log10(ft)-value 6.6.8 Allowed and Forbidden β Transitions 6.7 The Electron Capture Decay (EC) 6.8 Non-conservation of Parity in β Decay 6.8.1 Why more β particles are emitted in opposite direction to spin J of 60Co nucleus? 6.9 The Neutrino and Its Rest Mass 6.9.1 Neutrino Helicity 6.9.2 Two Types of Neutrinos 6.10 Gamma (γ ) Decay 6.10.1 Multipolarity of γ rays 6.10.2 Isomeric Transitions 6.10.3 Internal (or Inner) conversion (IC) 6.11 Resonance Fluorescence of γ Rays 6.11.1 The Red Shift 6.11.2 Applications of Resonance Fluorescence Chapter 7: Nuclear Radiations and Detectors 7.1 Attenuation Coefficients 7.2 Energy Loss by Electromagnetic Radiation 7.2.1 Photo Electric Effect 7.2.2 The Compton Scattering 7.2.3 Pair Production 7.2.4 γ Ray Energy Loss by Nuclear Reactions 7.3 Energy Loss by Heavy Charged Particles 7.3.1 Maximum Energy Transfer to Electron 7.3.2 The Stopping Power 7.3.3 Bragg's Curve 7.3.4 Formation of Ion-pairs 7.3.5 Range of Heavy Charged Particles 7.3.6 Bremsstrahlung and Cerenkov Radiation Losses For Heavy Charged Particles 7.4 Energy Loss by Light Charged Particles 7.4.1 Energy Loss of Electron by Ionization and Excitation of Target Atoms 7.4.2 Radiative Energy Loss 7.4.3 Energy Loss by Cerenkov Radiations 7.5 Energy Loss by Un-charged Nuclear Particles 7.5.1 Energy Loss by Neutrons 7.5.2 Energy Loss by Neutrino 7.6 Nuclear Detectors 7.6.1 Gas-filled Detectors 7.6.2 Scintillation Detector and Spectrometer 7.6.3 Semi-conductor Detectors 7.7 Some Special Detectors 7.7.1 Anti-Compton Shield 7.7.2 Phoswich Detector 7.7.3 Position Sensitive Single and Multiwire Proportional Counters (MWPC) 7.8 Detection of Neutron 7.9 Detection of Neutrino 7.9.1 Chemical Method 7.9.2 Cerenkov-ring Detectors 7.9.3 Indian Initiative for Neutrino Studies 7.10 Solid-state Nuclear Track Detectors (SSNTD) 7.10.1 Mechanism of Track Formation 7.11 Choosing a Detector Chapter 8: Nuclear Reactions 8.1 Quantities Conserved in a Nuclear Reaction 8.1.1 Conservation of Total Charge (or of Proton Number Z ) 8.1.2 Conservation of the Total Number of Nucleons 8.1.3 Conservation of Total Angular Momentum 8.1.4 Conservation of Parity 8.1.5 Conservation of Statistics 8.1.6 Conservation of Isospin and the Third Component of Isospin 8.1.7 Conservation of Linear Momentum 8.1.8 Conservation of Total Energy 8.2 Quantities that are not Conserved in Nuclear Reactions 8.3 The Q Equation 8.3.1 Exoergic Reactions 8.3.2 Endoergic Reactions 8.3.3 Relativistic Q Equation 8.4 The Partial Wave Analysis of Nuclear Reaction Cross-section 8.5 Reaction Mechanism 8.5.1 Compound Nuclear Reaction (or CN) Mechanism: Reactions Leading to Continuum 8.5.2 Cross-section for the Formation of the Compound Nucleus σC (Ec, σ) 8.5.3 Decay of the Compound Nucleus and the Branching Ratio Gc (Ec, β) 8.5.4 Special Feature of Continuum Reactions 8.5.5 Thermodynamic Approach to Continuum Reactions 8.5.6 Reaction and Scattering in Resonance Region 8.6 Test of the Compound Reaction Mechanism: Excitation Functions and Ghoshal's Experiment 8.6.1 Stacked Foil Activation Technique 8.7 Pre-equilibrium (or Pre-compound) Emission in Statistical Nuclear Reactions 8.8 Heavy Ion (HI) Reactions 8.8.1 Complete and Incomplete Fusion of Heavy Ions 8.8.2 Fusion–Fission and Other Reactions 8.9 Optical Model Approach to Nuclear Reactions 8.10 Direct Reaction Mechanism 8.11 Interaction of Electromagnetic Radiations with the Nucleus 8.11.1 Coulomb Excitation 8.11.2 Photo-disintegration and Giant Resonance Excitations 8.12 Nuclear Reactions Using Radioactive Ion Beams 8.13 Nuclear Reactions Responsible for Nucleosynthesis 8.13.1 Primordial Nucleosynthesis 8.13.2 Elemental Synthesis in Stars 8.13.3 Synthesis of Heavier Elements Chapter 9: Particle Accelerators 9.1 Electrostatic Accelerators 9.1.1 Cockcroft–Walton Accelerator 9.1.2 Van de Graaff Generator 9.1.3 Tandem Van de Graff 9.2 The Cyclotron 9.2.1 Superconducting Cyclotron 9.2.2 Focusing of Particles in a Cyclotron: Weak Focusing 9.2.3 Isochrone- and Synchrocyclotron 9.2.4 Azimuthally Varying Field (AVF) or Thomas Focusing or Sector Field Focusing 9.3 Linear Accelerator (Linac) 9.3.1 Acceleration of Electrons Using Linac 9.4 The Betatron 9.4.1 Betatron Condition for Acceleration 9.5 The Synchrotron 9.5.1 Electron Synchrotron 9.5.2 Proton Synchrotron 9.5.3 Alternate Gradient Focusing 9.6 Particle Collider Machines 9.7 Some Internationally Important Accelerators 9.7.1 Large Hadron Collider (LHC) 9.7.2 Fermi Lab Tavatron 9.7.3 CERN Super Proton Synchrotron (SPS) 9.7.4 Relativistic Heavy Ion Collider at BNL 9.7.5 RIKEN-RIBF 9.7.6 SLAC – Stanford University Linear Accelerator Chapter 10: Nuclear Energy 10.1 Energy from Nuclear Fission 10.1.1 Materials and Reactions Important from Fission Point of View 10.2 Fission Chain Reaction 10.3 Nuclear Fission Power Reactor 10.3.1 Properties of a Good Moderator 10.3.2 Properties of the Control Material 10.3.3 The Neutron Multiplication Factor k 10.4 The Delayed Neutrons 10.5 Controlling Reactor Power or Reactivity: Important Role of Delayed Neutrons 10.6 Essential Elements of a Reactor 10.7 Classification of Fission Reactors 10.7.1 Modern Technologies 10.8 Problems Associated with Fission Reactors 10.8.1 Core Meltdown 10.8.2 Production of Weapon-Grade Fissile Material 10.8.3 Radioactive Nuclear Waste 10.8.4 Limited Supply of Uranium Fuel 10.9 Fast and Thermal Breeder Reactors 10.9.1 What is a Breeder Reactor? 10.10 Advantages of Fission Energy 10.10.1 Non-polluting Source of Energy 10.10.2 Fuel Economy 10.10.3 Land Requirement, Installation Time and Cost 10.11 Accelerator-driven Energy Amplifier 10.12 India's Three-stage Program for Harnessing Nuclear Energy 10.13 Possibilities of Controlled Fusion 10.13.1 Nuclear Reactions Important for Fusion 10.13.2 Requirements for Sustained Fusion 10.13.3 Magnetic Confinement 10.13.4 Inertial Confinement 10.14 Global Status of Nuclear Energy 10.15 Heavy and Super Heavy (SHE) Elements: Transuranic/Actinide and Trans-actinide Nuclides 10.15.1 Super Heavy Elements 10.16 Nuclear Weapons 10.16.1 Neutron Bomb 10.16.2 Cobalt Bomb Chapter 11: Fundamentals of Elementary Particles 11.1 Elementary Particles 11.1.1 Leptons, Mesons, Baryons, and hadrons 11.1.2 Particle and Antiparticle 11.1.3 Principle of Cross-symmetry 11.1.4 Conservation of Baryon Number 11.1.5 The Strange Particles and the Law of Associate Production 11.2 The Eight-fold Way 11.3 Quark Model of Hadrons 11.3.1 Quark Model and Pauli's Exclusion Principle 11.4 New Quarks 11.5 Intermediate Vector Bosons 11.6 Gluons 11.7 Standard Model 11.8 Higg's Field and Higg's Particle 11.9 Conservation Laws 11.9.1 Conservation of Baryon Number B 11.9.2 Conservation of Lepton Numbers: Neutrino Oscillations 11.9.3 Conservation of Strangeness Quantum Number 11.9.4 Conservation of Isospin and the Third Component of Isospin 11.10 The Fundamental Forces of Nature 11.10.1 Cabibbo–Kobayashi–Maskowa (CKM) Matrix 11.11 Nucleon Resonances and Hyperons 11.11.1 Hyperons 11.11.2 Anti-matter Puzzle and CP Violation 11.12 Discovery of Muon and π-Meson 11.12.1 The Yukawa Particle? 11.12.2 The Final Confirmation 11.13 Measurement of the Spin and Parity of Pions 11.13.1 Measurement of the Spin of π-meson 11.13.2 Parity of Pions 11.14 The CPT or Lüders–Pauli Theorem 11.14.1 The Implication 11.14.2 Non Conservation of Parity (P-violation) 11.14.3 CP Invariance in Nuclear Weak Interactions 11.14.4 Breaking of CP Symmetry 11.14.5 The Status of K0, K0, K01, and K02 11.14.6 Breaking of CP Symmetry in Nuclear Weak Interactions 11.15 Units in Particle Physics: The Natural Units 11.16 Introduction to Feynman's Diagrams Chapter 12: Cosmic Rays 12.1 Discovery of Cosmic Rays 12.1.1 Cosmic Rays as High Energy γ Rays 12.1.2 Cosmic Rays as Charged Particles 12.2 The East–West Asymmetry 12.3 The Latitude and Longitude Effects 12.4 Some Important Detector Setups Used in the Study of Cosmic Rays 12.5 Primary Cosmic Rays 12.5.1 Composition of Primary Cosmic Rays 12.5.2 Energy Distribution of Particles in Primary Cosmic Rays 12.6 Passage of Primary Cosmic Rays Through the Atmosphere 12.6.1 The 'Soft' and the 'Hard' Components of Local Cosmic Rays 12.6.2 Discovery of Positron 12.6.3 Rossi's Experiment on the Softness of Vertical and Slant Cosmic Rays 12.7 Cosmic Ray Showers 12.7.1 Rossi Transition Curve 12.7.2 Extensive Air Showers (EAS) 12.8 Generation of Showers 12.8.1 Bhabha–Heitler Cascade Theory of Electron Showers 12.8.2 The Hard Component of Local Cosmic Rays 12.8.3 Interaction of Primary Cosmic Rays and Extensive Air Showers 12.9 Source of Cosmic Rays and the Mechanism of Acceleration of Cosmic Ray Particles 12.10 How Cosmic Rays Affect Us? 12.10.1 Production of Radio Isotope in the Atmosphere 12.10.2 Depletion of Ozone Layer 12.10.3 Malfunctioning of Electronics 12.10.4 Radiation Dose 12.10.5 Effect on Global Weather Solutions to Numerical Problems Index Nuclear Physics provides a clear and concise introduction to the subject. Fundamentals aside, the book reviews the evolution of thesubject from its emergence to its present-day advancements and critically examines the future directions of nuclear and particle physics. The book brings together the essence of nuclear, particle and cosmic ray physics, serving as an ideal text for undergraduate students