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Angular Momentum Theory Applied to Interactions in Solids

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This report discusses those concepts of group theory that are applied to the spectra of impurity ions 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 Gordon coefficients, the Wigner Eckart theorem, unit spherical tensors, and Racah coefficients. The extension of these techniques to the electronic configuration, l to the Nth power, 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 inter configuration 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 the work done at the Harry Diamond Laboratories HDL on its development. The earlier work at HDL was applied to triply ionized rare earth ions l to the Nth power electronic configuration, and the preliminary extensions presently being undertaken at HDL are applied to the transition metal ions with the electronic configurations d to the Nth power n3,4, and 5. Keywords Angular momentum theory group theory crystal field interactions spectroscopy of solids, rare earth ions transition metalions.

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  • Solid State Physics

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