Nuclear Shell Theory (eBook)

Igal Talmi, Amos de-Shalit (Autoren)

H. S. W. Massey (Herausgeber)

eBook Download: PDF

2013 | 1. Auflage
584 Seiten
Elsevier Science (Verlag)
978-1-4832-7579-6 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Nuclear Shell Theory 4
Copyright Page 5
Table of Contents 10
Dedication 6
PREFACE 8
INTRODUCTION 12
Part I: Single Particle Shell Model 22
Chapter 1. Wave Functions in a Central Field 23
Chapter 2. Total Angular Momentum of Spin-1/2 Particles 29
Chapter 3. Transformation Properties of Spherical Harmonics 36
Chapter 4. Radial Functions and Their Properties 42
Chapter 5. Central Potentials in Frequent Use 48
Chapter 6. Degeneracies in a Central Field 53
Chapter 7. Spin-Orbit Interaction and Order of Single Nucleón Levels 56
Chapter 8. Centrifugal and Coulomb Barriers 59
Chapter 9. Magnetic Moments and Beta Decay 63
Part II: Tensor Algebra. Two-Particle Systems 72
Chapter 10. Irreducible Tensors 74
Chapter 11. Tensor Fields 82
Chapter 12. Infinitesimal Rotations and Irreducible Tensors 91
Chapter 13. Vector Addition Coefficients 106
Chapter 14. Tensor Products. The Wigner-Eckart Theorem 123
Chapter 15. Racah Coefficients 139
Chapter 16. Multipole Expansion of the Electromagnetic Field 154
Chapter 17. Electromagnetic Transitions in Nuclei 169
Chapter 18. Two Interacting Particles in a Central Field 181
Chapter 19. Antisymmetric Wave Functions and Isospin 194
Chapter 20. The Two-Particle Interaction 203
Chapter 21. Tensor-Expansion of the Interaction 219
Chapter 22. Closed Shells. Particles and Holes 233
Chapter 23. Two Particles in the Harmonic Oscillator Potential 249
Part III: Three- or More-Particle Systems 254
Chapter 24. The m-Scheme 256
Chapter 25. The Transformation from the m-Scheme to the J-Scheme 272
Chapter 26. Coefficients of Fractional Parentage 279
Chapter 27. Pairs of Particles Coupled to / = 0 294
Chapter 28. C. f. p. and Matrix Elements in the Seniority Scheme 312
Chapter 29. Average Interaction Energies in the Seniority Scheme 343
Chapter 30. Applications to Nuclear and Coulomb Energies 353
Chapter 31. Antisymmetric States in LS-Coupling 369
Chapter 32. The Group Theoretical Classification of States 384
Chapter 33. Many-Nucleon Wave Functions with Definite Isospin 409
Chapter 34. The Seniority Scheme in the Nuclear jn Configuration 425
Chapter 35. Coefficients of Fractional Parentage in the Seniority Scheme 445
Chapter 36. Average Energies of States with Given T, v, and t 462
Chapter 37. Nonequivalent Particles Configuration Interaction
APPENDIX 520
Central Field Single Particle Hamiltonian and Wave Functions 520
Spherical Harmonics 521
Coulomb Potential 522
Associated Laguerre Polynomials Lmk(x) 522
Harmonic Oscillator 523
Single Nucleón States in the Nuclear Shell Model 523
Transformation Properties 523
Wave Functions of Particles with Spin 1/2 524
Lande Formula 524
Clebsch-Gordan Coefficients 525
Three-j Symbols 526
9j-Symbols 527
Racah Coefficients (6j-Symbols) 528
Change of Coupling Transformations 529
Some Special Clebsch-Gordan Coefficients and 3j-Symbols 530
Some Special Racah and 9j Coefficients 531
Irreducible Tensors 531
Vector Spherical Harmonics 534
Electromagnetic Transitions and Moments 534
Matrix Elements of Interactions 536
Coefficients of Fractional Parentage for Identical Particles 539
Seniority Operator and Seniority Scheme 540
Matrix Elements in the Seniority Scheme 542
Average Interaction Energies 543
Wave Functions with Isotopic Spin 544
The Seniority Scheme 545
Particles in Nonequivalent Orbits 548
Configuration Interaction 550
Coefficients of Fractional Percentage 551
Energies in Terms of Slater Integrals for Wigner Force in LS-Coupling 561
Energies in Terms of Slater Integrals for Wigner and Majorana Forces in jj-Coupling 562
Slater Integrals Fk and Gk in Terms of Harmonic Oscillator Integrals I, 574
INDEX 580

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 1-4832-7579-5 / 1483275795
• ISBN-13: 978-1-4832-7579-6 / 9781483275796