http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Angular Momentum Theory Applied to Interactions in Solids
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).
From the contents: Clebsch-Gordan Coefficients -- Wigner-Eckart Theorem -- Unit Spherical Tensors -- Racah Coefficients -- Racah Algebra -- Free-Ion Hamiltonian Unfilled Configuration nlN -- Crystal-Field Interactions -- Phenomenological Theory of Crystal Fields -- Matrix Elements of H3 in Total Angular Momentum State for the Electronic Configuration nlN -- Group Theoretical Considerations -- Numerical Example: 4FJ States of Nd3+ (4f3) -- Classical Point-Charge Model -- Point-Charge Model Developed at HDL -- Crystal-Field Effects not yet Fully Incorporated -- Miscellaneous Crystal-Field Effects.