Nuclear Structure Theory

Nuclear Structure Theory provides a guide to nuclear structure theory. The book is comprised of 23 chapters that are organized into four parts; each part covers an aspect of nuclear structure theory. In the first part, the text discusses the experimentally observed phenomena, which nuclear structure theories need to look into and detail the information that supports those theories. The second part of the book deals with the phenomenological nucleon-nucleon potentials derived from phase shift analysis of nucleon-nucleon scattering. Part III talks about the phenomenological parameters used to describe their various nuclear models. The last part of the book deals with the technology of nuclear structure theory. The book will be of great use to nuclear physicists who wish to gain a better understanding of the nuclear structure theory.

Preface

Introduction

Part I. Nuclear Phenomenology

Chapter 1. Elementary Particles

1.1 Leptons

1.2 Baryons

1.3 Bosons

Chapter 2. The Two-nucleon System

2.1 Scattering States

2.2 Bound States

2.3 The Nucleon-Nucleon Interaction

Chapter 3. Nuclear Masses and Charges

3.1 Mass Numbers and Charge Numbers

3.2 Binding Energies and Separation Energies

Chapter 4. Nuclear Shapes and Sizes

4.1 The Radius and Density of Spherical Nuclei

4.2 The Electrostatic Moments of Non-spherical Nuclei

4.3 Nuclear Spins and Magnetic Moments

Chapter 5. Nuclear Spectroscopy

5.1 Energy Level Diagrams

5.2 Nuclear Systematics

Par II. The Nuclear Many-Body Problem

Chapter 6. Perturbation Formalism

6.1 Introduction

6.2 Brueckner Ladder Sum

6.3 Goldstone Linked Cluster Expansion

6.4 The Energy-shell and Hole-Bubble Insertions

6.5 The Occupied-state Potential

6.6 Rearrangement and Convergence of the Perturbation Expansion

6.7 Three-body Clusters and the Unoccupied-state Potential

Chapter 7. Nuclear Matter and Approximate Reaction Matrices

7.1 Nuclear Matter

7.2 The Reference Spectrum Approximation

7.3 Approximate Reaction Matrices

Chapter 8. Ground States of Spherical Nuclei (Closed Shells)

8.1 Introduction

8.2 The Brueckner-Hartree-Fock Equations

8.3 Reaction Matrix Elements

8.4 The Shell-model Potential

Chapter 9. Open-shell Nuclei

9.1 Introduction

9.2 Nearly Closed Shells

9.3 Deformed Configurations

Chapter 10. Thomas-Fermi Theory

10.1 Introduction

10.2 Kinetic Energy

10.3 The Reaction Matrix

10.4 Variational Calculation

Chapter 11. Landau-Migdal Theory

11.1 Quasiparticles

11.2 The Quasiparticle Interaction

11.3 Quasiparticles in an External Field

11.4 Conclusion

Part III. Nuclear Models

Chapter 12. The Liquid-drop Model

12.1 Semi-empirical Mass Formula

12.2 Vibrational States

12.3 Rotational States

12.4 Nuclear Fission

Chapter 13. The Shell Model

13.1 Introduction

13.2 Configuration Mixing

13.3 Spurious Center-of-mass Motion

13.4 Double Closed-shell Nuclei

13.5 Nuclei with Two Valence Particles or Holes

13.6 The 0p- and 0f-shell Nuclei

13.7 More Complex Configurations

Chapter 14. Transitions and Moments

14.1 Electromagnetic Transition Probabilities

14.2 Electromagnetic Moments

14.3 Beta-decay

14.4 Alpha-decay

Chapter 15. Nuclear Correlations

15.1 Quasiparticles Revisited

15.2 The Particle-Hole RPA

15.3 Pairing Correlations

Chapter 16. Deformed Nuclei

16.1 Introduction

16.2 Moments of Inertia

16.3 TheNilsson Model

16.4 Generalized Deformed Schemes

Chapter 17. The Unified Model

17.1 Introduction

17.2 Configuration Mixing

17.3 Conclusion

Part IV. The Technology of Nuclear Structure Theory

Chapter 18. Occupation Number Representation and Graphology

18.1 Occupation Number Representation

18.2 Quasiparticles

18.3 Propagators and the Goldstone Graphs

18.4 Rajaraman Graphs

Chapter 19. Single Particle Wave Equations

19.1 Schrodinger Equation

19.2 Radial Eigenfunctions

19.3 Special Radial Functions

19.4 Relativistic Wave Equations

19.5 Two-component Neutrino Theory

Chapter 20. Angular Momentum

20.1 Single Particle Angular Momentum

20.2 Addition of Two Angular Momenta

20.3 Coupling of Three Angular Momenta

20.4 Coupling of Four Angular Momenta

20.5 Coefficients of Fractional Parentage (CFP)

20.6 Angular Momentum and the Occupation Number Representation

20.7 Angular Momentum Projection Operators

Chapter 21. Two-body Matrix Elements

21.1 Introduction

21.2 Slater Integrals

21.3 Talmi Integrals

Chapter 22. Applications of Group Theory to Nuclear Structure

22.1 Formalism and Definitions

22.2 Angular Momentum and the Rotation Groups

22.3 Spin and Isospin; the Groups SU2 and SU4

22.4 Elliott Model, Quarks, and SU3

22.5 ln and jn Configurations: The Symplectic and Permutation Groups

22.6 Pairing Interactions and Quasispins

Chapter 23. Scattering Theory

23.1 Introduction

23.2 Partial Wave Expansion

23.3 Low Energy Limits

23.4 PWBA and DWBA

Physical Constants and Conversion Factors

Further Reading

Name Index

Subject Index