Nuclear Structure

The following sections are included:

• PREFACE TO THE REISSUE OF NUCLEAR STRUCTURE (VOLUMES I AND II)

• PREFACE

• CONTENTS

The following sections are included:

• NUCLEAR CONSTITUTION
  • ILLUSTRATIVE EXAMPLES TO SECTION 1-1

• NUCLEAR SYMMETRY PROPERTIES ASSOCIATED WITH SPACE-TIME INVARIANCE
  • Continuous Transformations
  • Space Reflection
  • Time Reversal
  • ILLUSTRATIVE EXAMPLES TO SECTION 1-2

• ISOBARIC INVARIANCE
  • Isospin Symmetry
  • Extension of Isobaric Symmetry
  • ILLUSTRATIVE EXAMPLES TO SECTION 1-3

• INVARIANCE CONDITIONS FOR NUCLEAR FORCES
  • Velocity-Independent Forces
  • Velocity-Dependent Forces

• APPENDIX 1A Rotational Invariance
  • Angular Momentum Matrices
  • Coupling of Angular Momenta
  • Recoupling Coefficients
  • Rotation Matrices. 𝒟 Functions
  • Spherical Tensors and Reduced Matrix Elements
  • Transformation to Intrinsic Coordinate System
  • Transformation of Fields
  • Field Couplings and Expansion in Multipole Moments
  • Tensors in Isospace

• APPENDIX 1B Time Reversal
  • Single-Particle States
  • Many-Particle States (Bound Systems)
  • Collision Processes
  • Decay Processes

• APPENDIX 1C Permutation Symmetry
  • Symmetry Quantum Numbers (Partitions)
  • Symmetry Classification of Wave Functions in Occupation Number Space
  • Unitary Symmetry
  • ILLUSTRATIVE EXAMPLES TO APPENDIX 1C

The following sections are included:

• BULK PROPERTIES OF NUCLEI
  • Nuclear Size
  • Mean Free Path of Nucleons
  • Momentum Distribution (Fermi Gas Approximation)
  • Nuclear Binding Energies
  • Pairing Energy
  • Isospin Quantum Number
  • Nuclear Potential
  • Antisymmetrized Fermi Gas Wave Functions
  • Statistical Features of Excitation Spectrum
  • ILLUSTRATIVE EXAMPLES TO SECTION 2-1

• EVIDENCE FOR NUCLEAR SHELL STRUCTURE
  • Binding Energies
  • Excitation Energies of Even-Even Nuclei
  • Level Densities
  • ILLUSTRATIVE EXAMPLES TO SECTION 2-2

• NUCLEAR SPECIES AND ABUNDANCES
  • Nuclear Stability
  • Relative Abundances and Nucleogenesis
  • ILLUSTRATIVE EXAMPLES TO SECTION 2-3

• AVERAGE NUCLEAR POTENTIAL
  • Sequence of Single-Particle Levels. Spin-Orbit Coupling
  • Single-Particle Strength Function
  • Optical Potential
  • ILLUSTRATIVE EXAMPLES TO SECTION 2-4

• NUCLEONIC INTERACTIONS AND NUCLEAR POTENTIAL
  • Main Features of Nucleonic Interaction
  • Relation of Nuclear Potential to Nucleonic Interactions
  • Theory of Nuclear Matter
  • ILLUSTRATIVE EXAMPLES TO SECTION 2-5

• APPENDIX 2A Antisymmetrized Product States Creation and Annihilation Operators
  • Antisymmetric Wave Functions
  • Properties of Creation Operators for Fermions
  • One-Particle Operators
  • Two-Particle Operators
  • Particle Transfer Operators
  • x Representation
  • Density Matrices
  • Creation Operators for Bosons

• APPENDIX 2B Statistical Calculation of Level Densities
  • Level Density Function and its Laplace Transform
  • Inversion of Laplace Transform
  • Average Occupation Numbers for One-Particle States
  • Description of Spectrum in Terms of Quasiparticle Excitations
  • Thermodynamic Interpretation of Level Density Calculation
  • Calculation of Level Densities Specified by Additional Quantum Numbers

• APPENDIX 2C Fluctuations in Terms of Random Matrices
  • Random Distribution of Elements of Two-Dimensional Matrix
  • Distribution of Eigenvalues and Eigenvectors
  • Matrices of Large Dimensions

• APPENDIX 2D Model for Strength Function Phenomena
  • Choice of Representation
  • Diagonalization
  • Strength Function for Constant Matrix Elements
  • Time-Dependent Description of Coupling Process
  • Second Moment of Strength Function
  • Intermediate Coupling Stages
  • Evaluation of Strength Function for Nonconstant Matrix Elements

The spectra of nuclei consisting of closed shells with an additional single particle, or with a single hole, provide especially detailed and quantitative evidence on the nuclear independent-particle motion.

A closed shell contains (2J + 1) particles, each with an angular momentum J. Such a configuration forms only a single antisymmetric state (the Slater determinant). This state must then have total angular momentum J = 0, since any state of total angular momentum J possesses ( 2J + 1) degenerate substates. Moreover, the parity of the closed shell is even.

Thus, for a configuration of a single particle, in addition to closed shells, one expects a number of low-lying states having angular momentum and parity determined by the quantum numbers of the orbits available to the single particle. Additional properties, such as the moments involved in electromagnetic and β transitions and the matrix elements characterizing various nuclear reaction processes, provide further information regarding the adequacy of the singleparticle description of these states.

Configurations obtained by removing a particle from closed shells (singlehole configurations) are expected to have properties related in a simple manner to those of single-particle configurations.

The following sections are included:

• BIBLIOGRAPHY

• INDEX

The following sections are included:

• PREFACE TO THE REISSUE OF NUCLEAR STRUCTURE (VOLUMES I AND II)

• CONTENTS, VOLUME II

• CONTENTS, VOLUME I

• PREFACE

The following sections are included:

• OCCURRENCE OF COLLECTIVE ROTATIONAL MOTION IN QUANTAL SYSTEMS

• SYMMETRIES OF DEFORMATION. ROTATIONAL DEGREES OF FREEDOM
  • Degrees of Freedom Associated with Spatial Rotations
  • Consequences of Axial Symmetry
  • R Invariance
  • P and I Symmetry
  • Deformations Violating P or I Symmetry
  • Combinations of Rotation and Reflection Symmetries
  • Rotational Motion in Isospace

• ENERGY SPECTRA AND INTENSITY RELATIONS FOR AXIALLY SYMMETRIC NUCLEI
  • Rotational Energies
  • E2-Matrix Elements within Band
  • M1-Matrix Elements within Band
  • General Structure of Matrix Elements

• ILLUSTRATIVE EXAMPLES TO SECTION 4-3

• COUPLING BETWEEN ROTATIONAL AND INTRINSIC MOTION FOR AXIALLY SYMMETRIC NUCLEI

• ILLUSTRATIVE EXAMPLES TO SECTION 4-4

• ROTATIONAL SPECTRA FOR SYSTEMS WITHOUT AXIAL SYMMETRY
  • Symmetry Classification for Even A
  • Energy Spectra
  • Systems with Small Asymmetry
  • Symmetry Classification for Odd A
  • States with Large I

• ILLUSTRATIVE EXAMPLES TO SECTION 4-5

• APPENDIX 4A Particle-Rotor Model
  • The Coupled System
  • Adiabatic Approximation
  • Nonadiabatic Effects

The following sections are included:

• STATIONARY STATES OF PARTICLE MOTION IN SPHEROIDAL POTENTIAL
  • Symmetry and Shape of Nuclear Equilibrium Deformation
  • Deformed Potential
  • Structure of One-Particle Wave Functions

• ILLUSTRATIVE EXAMPLES TO SECTION 5-1

• CLASSIFICATION OF ODD-A SPECTRA

• MOMENTS AND TRANSITIONS
  • One-Particle Transfer
  • Single-Particle Moments and Transitions
  • Pair Transfer and α Decay
  • Coupling of Particles to Rotational Motion

• ILLUSTRATIVE EXAMPLES TO SECTION 5-3

• Appendix 5A Scattering by Nonspherical Systems
  • Treatment in Terms of Coupled Channels
  • Adiabatic Approximation

The following sections are included:

• INTRODUCTION

• QUANTAL THEORY OF HARMONIC VIBRATIONS
  • Creation Operators for Excitation Quanta
  • Vibrational Amplitudes
  • Collective Motion Generated by Vibrational One-Body Potential

• NORMAL MODES OF NUCLEAR VIBRATION
  • Shape Oscillations. Spherical Equilibrium
  • Vibrations about Spheroidal Equilibrium
  • Collective Motion in Fission Process
  • Isospin of Vibrations. Polarization and Charge Exchange Modes
  • Collective Modes Involving Spin Degree of Freedom
  • Two-Nucleon Transfer Modes. Pair Vibrations

• SUM RULES FOR MULTIPOLE OSCILLATOR STRENGTH
  • Classical Oscillator Sums
  • Vibrational Oscillator Strength in Sum Rule Units
  • Tensorial Sums
  • Charge Exchange Contributions to Eλ Oscillator Sum

• PARTICLE-VIBRATION COUPLING
  • Coupling Matrix Elements
  • Effective Moments
  • One-Particle Transfer Matrix Elements
  • Particle-Phonon Interaction Energy
  • Self-Energies
  • Polarization Contributions to Effective Two-Particle Interactions
  • Higher-Order Effects
  • Normal Modes Generated by Particle-Vibration Coupling

• ANHARMONICITY IN VIBRATIONAL MOTION. COUPLING OF DIFFERENT MODES
  • Anharmonic Effects in Low-Frequency Quadrupole Mode
  • Coupling between Quadrupole and Dipole Modes
  • Coupling between Vibration and Rotation

• ILLUSTRATIVE EXAMPLES TO CHAPTER 6
  • Response Function
  • Features of Dipole Modes (λπ = 1−)
  • Features of Quadrupole Modes in Spherical Nuclei
  • Features of Quadrupole Oscillations in Deformed Nuclei
  • Features of Octupole Modes
  • Structure of Shells in Single-Particle Spectra
  • Shell-Structure Effects in Nuclear Energy
  • Features of Fission Mode
  • Features of Spin Excitations
  • Features of Pair Correlations

• Appendix 6A Liquid-Drop Model of Vibrations and Rotations
  • Surface Vibrations about Spherically Symmetric Equilibrium
  • Large-Amplitude Deformations. Fission Mode
  • Compression Modes
  • Polarization Modes in Two-Fluid System
  • Rotational Motion of Irrotational Fluid

• Appendix 6B The Five-Dimensional Quadrupole Oscillator
  • Shape and Angle Coordinates. Vibrational and Rotational Degrees of Freedom
  • Oscillations about Spherical Equilibrium
  • Yrast Region for Harmonic Vibrations
  • Many-Phonon States

The following sections are included:

• BIBLIOGRAPHY

• INDEX