Angular Momentum Theory Applied to Interactions in Solids - Morrison, Clyde A.

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Résumé :
This book discusses those concepts of group theory that are applied to the spectra of impurity ion in crystals. Beginning with the simple hydrogen atom, spectroscopic notation and angular momentum operators are discussed. This is followed by a general discussion of angular momentum theory including Clebsch-Gordan coefficients, the Wigner-Eckart theorem, unit spherical tensors, and Racah coefficients. The extension of these techniques to the electronic configuration, nlN, for N equivalent electrons is discussed. The theory of point groups as applied to ions in solids is introduced, along with the use of the International Tables of Crystallography and character tables. The phenomenological theory of crystal fields is discussed in some detail along with the so-called free-ion parameters characterizing the Coulomb interaction, the spin-orbit interaction, and the interconfiguration interaction. The use of tables of 3-j and 6-j symbols used in the calculation of the matrix elements of the various interactions is presented, along with other tables and aids in the computation of the energy levels. The point ion model of crystal-field interaction is discussed with particular emphasis on recent work done on its development. The earlier work was applied to triply ionized rare-earth ions (4fN electronic configurations), and extensions of the point ion model are applied to the transition metal ions with the electronic configurations ndN (n=3, 4, and 5).

Sommaire:
1. Introduction and Review of Previous Literature.- 1.1 The Hydrogen Atom.- 1.2 Angular Momentum Algebra.- 1.3 Problems.- 1.4 Annotated Bibliography and References.- 2. Clebsch-Gordan Coefficients.- 2.1 Problems.- 2.2 Annotated Bibliography and References.- 3. Wigner-Eckart Theorem.- 3.1 A Single d Electron in a Crystal Field.- 3.2 Problems.- 3.3 Annotated Bibliography and References.- 4. Unit Spherical Tensors.- 4.1 Discussion.- 4.2 Bibliography and References.- 5. Racah Coefficients.- 5.1 Problems.- 5.2 Bibliography and References.- 6. Racah Algebra.- 6.1 Problems.- 6.2 Annotated Bibliography and References.- 7. Free-Ion Hamiltonian Unfilled Configuration n?N [N < 2(2? + 1)].- 7.1 Background for Free Ions.- 7.2 Significant Free-Ion Interactions.- 7.3 Summary.- 7.4 Problems.- 7.5 Annotated Bibliography and References.- 8. Crystal-Field Interactions-Phenomenological Theory of Crystal Fields.- 8.1 Discussion.- 8.2 Problems.- 8.3 Annotated Bibliography and References.- 9. Matrix Elements of H3 in Total Angular Momentum State for the Electronic Configuration n?N.- 9.1 Discussion.- 9.2 Bibliography and References.- 10. Group Theoretical Considerations.- 10.1 Discussion.- 10.2 Annotated Bibliography and References.- 11. Numerical Example: 4FJ States of Nd3+ (4f3).- 11.1 4F3/2.- 11.2 4F5/2.- 11.3 4F7/2.- 11.4 4F9/2.- 11.5 Calculations.- 11.6 References.- 12. Classical Point-Charge Model.- 12.1 Discussion.- 12.2 Bibliography and References.- 13. Point-Charge Model Developed AT HDL.- 13.1 Screening and Wave Function Spread.- 13.2 Effective Charge and Position.- 13.3 Annotated Bibliography and References.- 14. Crystal-Field Effects not yet Fully Incorporated.- 14.1 Self-Consistent Point Dipole and Point Multipole.- 14.2 Self-Consistent Results for Scheelite Structure.-14.3 Self-Induced Effects.- 14.4 Annotated Bibliography and References.- 15. Miscellaneous Crystal-Field Effects.- 15.1 Judd's Interaction for Two Electrons.- 15.2 Slater Integral Shifts.- 15.3 Problems.- 15.4 Annotated Bibliography and References.- Overall Bibliography.