A crucial element in the development of physical theories of nuclear and atomic structure, the theory of angular momentum can be applied with great effect to the formulation and solution of problems associated with the static magnetic and electric nuclear moments which are coupled to the electric and magnetic fields arising from surrounding charges. The theory relates to a variety of physical problems including those associated with low-temperature studies and microwave spectroscopy.
This high-level treatment, based on a series of lectures the author gave at Oak Ridge National Laboratory, offers clear discussions of the general theory and its applications. Beginning with basic principles, the development is carried through the introduction of coupling coefficients for vector addition, the transformation properties of the angular momentum wave functions under rotations of the coordinate axes, irreducible tensors and Racah coefficients. Applications include static moments of systems composed schemes in nuclear reactions and more. In this volume, the author has attempted to achieve simplification by concerning himself only with the properties of rotations because of their intimate connection with the concept of angular momentum. In addition, the reasoning is inductive, and, as the theory initially develops, it makes a "smooth-join" with those aspects of quantum mechanics that are, comparatively speaking, common knowledge. A graduate-level knowledge of quantum mechanics is helpful for gaining maximum benefit from this highly regarded study.
ISBN-13: 9780486684802
Media Type: Paperback
Publisher: Dover Publications
Publication Date: 11-02-2011
Pages: 272
Product Dimensions: 5.50(w) x 8.50(h) x (d)
Series: Dover Books on Physics
Table of Contents
Part A. GENERAL THEORY
I. REVIEW OF BASIC PRINCIPLES
1. HERMITIAN OPERATORS
2. UNITARY TRANSFORMATIONS
3. DIAGONALIZATION OF OPERATORS
4. EXPONENTIAL FORM OF THE UNITARY OPERATORS
II. THE ANGULAR MOMENTUM OPERATORS
5. DEFINITION OF ANGULAR MOMENTUM OPERATORS
6. ORBITAL ANGULAR MOMENTUM
7. COMMUTATION RULES FOR ANGULAR MOMENTUM OPERATORS
8. EIGENVALUES OF THE ANGULAR MOMENTUM OPERATORS
9. PHYSICAL INTERPRETATION OF ANGULAR MOMENTUM
III. COUPLING OF TWO ANGULAR MOMENTA
10. DEFINITION OF THE CLEBSCH-GORDAN COEFFICIENTS
11. SYMMETRY RELATIONS OF THE CLEBSCH-GORDAN COEFFICIENTS
12. EVALUATION OF CLEBSCH-GORDAN COEFFICIENTS
IV. TRANSFORMATION PROPERTIES UNDER ROTATIONS
13. MATRIX REPRESENTATIONS OF THE ROTATION OPERATORS
14. THE CLEBSCH-GORDAN SERIES
15. DETERMINATION OF THE ROTATION MATRICES
16. ORTHOGONALITY AND NORMALIZATION OF THE ROTATION MATRICES
V. IRREDUCIBLE TENSORS
17. DEFINITION OF IRREDUCIBLE TENSOR OPERATORS
18. RACAH'S DEFINITION OF IRREDUCIBLE TENSOR OPERATORS
19. THE WIGNER-ECKART THEOREM
20. THE PROJECTION THEOREM FOR FIRST-RANK TENSORS
21. ANGULAR MOMENTUM OF A VECTOR FIELD
VI. RACAH COEFFICIENTS
22. COUPLING OF THREE ANGULAR MOMENTA
23. PROPERTIES OF THE RACAH COEFFICIENTS
24. BASIC APPLICATIONS
25. THE GRADIENT FORMULA
Part B. APPLICATIONS
VII. THE ELECTROMAGNETIC FIELD
26. THE MAXWELL EQUATIONS
27. THE MULTIPOLE FIELDS
VIII. STATIC INTERACTIONS
28. MULTIPOLE MOMENTS OF AN ELECTROSTATIC CHARGE DISTRIBUTION
29. SPIN INTERACTIONS
IX. PARTICLES OF SPIN 1/2
30. NON-RELATIVISTIC DESCRIPTION
31. RELATIVISTIC DESCRIPTION
X. ORIENTED NUCLEI AND ANGULAR CORRELATIONS
32. CAPTURE OF POLARIZED NEUTRONS BY POLARIZED NUCLEI
33. ANGULAR CORRELATION
34. EMISSION OF ALPHA PARTICLES BY AN ORIENTED NUCLEUS
XI. ANGULAR DISTRIBUTIONS IN NUCLEAR REACTIONS
35. j-j AND L-S COUPLING
36. ANGULAR MOMENTUM COUPLING IN NUCLEAR REACTIONS
XII. IDENTICAL PARTICLES
37. IDENTICAL PARTICLES IN j-j COUPLING
38. IDENTICAL PARTICLES IN L-S COUPLING
39. THE ISOTOPIC SPIN
APPENDIX I. CLEBSCH-GORDAN AND RACAH COEFFICIENTS
APPENDIX II. THE ROTATION MATRICES
APPENDIX III. THE SPHERICAL HARMONICS
AUTHOR INDEX
SUBJECT INDEX
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