Nuclear Shell Theory - 1st Edition - ISBN: 9781483230627, 9781483275796

Nuclear Shell Theory

1st Edition

Authors: Amos de-Shalit Igal Talmi
Editors: H. S. W. Massey
eBook ISBN: 9781483275796
Imprint: Academic Press
Published Date: 1st January 1963
Page Count: 584
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Nuclear Shell Theory is a comprehensive textbook dealing with modern methods of the nuclear shell model. This book deals with the mathematical theory of a system of Fermions in a central field. It is divided into three parts. Part I discusses the single particle shell model. The second part focuses on the tensor algebra, two-particle systems. The last part covers three or more particle systems. Chapters on wave functions in a central field, tensor fields, and the m-Scheme are also presented. Physicists, graduate students, and teachers of nuclear physics will find the book invaluable.

Table of Contents




Part I. Single Particle Shell Model

1. Wave Functions in a Central Field

2. Total Angular Momentum of Spin-½ Particles

3. Transformation Properties of Spherical Harmonics

4. Radial Functions and Their Properties

5. Central Potentials in Frequent Use

6. Degeneracies in a Central Field

7. Spin-Orbit Interaction and Order of Single Nucleon Levels

8. Centrifugal and Coulomb Barriers

9. Magnetic Moments and Beta Decay

Part II. Tensor Algebra. Two-Particle Systems

10. Irreducible Tensors

11. Tensor Fields

12. Infinitesimal Rotations and Irreducible Tensors

13. Vector Addition Coefficients

14. Tensor Products. The Wigner-Eckart Theorem

15. Racah Coefficients

16. Multipole Expansion of the Electromagnetic Field

17. Electromagnetic Transitions in Nuclei

18. Two Interacting Particles in a Central Field

19. Antisymmetric Wave Functions and Isospin

20. The Two-Particle Interaction

21. Tensor-Expansion of the Interaction

22. Closed Shells. Particles and Holes

23. Two Particles in the Harmonic Oscillator Potential

Part III. Three- or More-Particle Systems

24. The m-Scheme

25. The Transformation from the m-Scheme to the J-Scheme

26. Coefficients of Fractional Parentage

27. Pairs of Particles Coupled to J = 0

28. C. f. p. and Matrix Elements in the Seniority Scheme

29. Average Interaction Energies in the Seniority Scheme

30. Applications to Nuclear and Coulomb Energies

31. Antisymmetric States in LS-Coupling

32. The Group Theoretical Classification of States

33. Many-Nucleon Wave Functions with Definite Isospin

34. The Seniority Scheme in the Nuclear j" Configuration

35. Coefficients of Fractional Parentage in the Seniority Scheme

36. Average Energies of States with Given T, v, and t

37. Nonequivalent Particles; Configuration Interaction


Central Field Single Particle Hamiltonian and Wave Functions

Spherical Harmonics

Coulomb Potential

Associated Laguerre Polynomials k" (x)

Harmonic Oscillator

Single Nucleon States in the Nuclear Shell Model

Transformation Properties

Wave Functions of Particles with Spin ½

Landé Formula

Clebsch-Gordan Coefficients

Three-j Symbols


Racah Coefficients (6j-Symbols)

Change of Coupling Transformations

Some Special Clebsch-Gordan Coefficients and 3j-Symbols

Some Special Racah and 9j Coefficients

Irreducible Tensors

Vector Spherical Harmonics

Electromagnetic Transitions and Moments

Matrix Elements of Interactions

Coefficients of Fractional Parentage for Identical Particles

Seniority Operator and Seniority Scheme

Matrix Elements in the Seniority Scheme

Average Interaction Energies

Wave Functions with Isotopic Spin

The Seniority Scheme

Particles in Nonequivalent Orbits

Configuration Interaction

Coefficients of Fractional Percentage

Energies in Terms of Slater Integrals for Wigner Force in LS-Coupling

Energies in Terms of Slater Integrals for Wigner and Majorana

Forces in jj-Coupling

Slater Integrals Fᴷ and Gᴷ in Terms of Harmonic Oscillator Integrals 1



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© Academic Press 1963
Academic Press
eBook ISBN:

About the Author

Amos de-Shalit

Igal Talmi

About the Editor

H. S. W. Massey

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