Nuclear Shell Theory

Nuclear Shell Theory

1st Edition - January 1, 1963

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  • Authors: Amos de-Shalit, Igal Talmi
  • eBook ISBN: 9781483275796

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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

  • 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


Product details

  • No. of pages: 584
  • Language: English
  • Copyright: © Academic Press 1963
  • Published: January 1, 1963
  • Imprint: Academic Press
  • eBook ISBN: 9781483275796

About the Authors

Amos de-Shalit

Igal Talmi

About the Editor

H. S. W. Massey

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