Applications of group theory in solid state physics
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Recent progress in the theory of generalized 6j symbols and 3jm factors has led to a building up method of calculation which uses only character theory results. This thesis both extends the method and uses 3jm factors in several solid state applications. We compute tables of transformation coefficients between the standard angular momentum basis and various point group bases. These coefficients are used to show that some of the phase freedoms in the 3jm factors affect the orientation of the point group axes. Tables of 6j symbols for SU₆ and SU₃ and 3jm factors for SU₆ ⊃ SU₂ x SU₃, SU₃ ⊃ U₁ x SU₂ and SU₃ ⊃ SO₃ have also been computed for use in multiquark hadron calculations and in strong crystal field calculations, The example of Reᶾ⁺ ions in tetragonal (C₄ᵥ) CaF₂ sites is used to illustrate the advantages of point group 3jms. The use of a point group basis results in more natural parameters, and basis states which are not greatly mixed by the Hamiltonian. For some ions the data are sparse or contradictory but for others the crystal field parameters follow a smooth trend. The superposition model is used to calculate co-ordination angles for these ions and the results are consistent with endor experiments. Intensity calculations for Erᶾ⁺are in reasonable agreement with experiment. Pair interactions are studied in point group bases. A general prescription is given for constructing pair states from single-ion states and general results are derived for pairs of identical Kramers ions.