Higher symmetries in Jahn-Teller systems.
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis provides primarily a full and frank review of the many roles the SO(3) algebra of quasispin has to play in nuclear, atomic and ligand-field theory. It is shown that the intriguing conclusion drawn by Ceulemans in 1984, i.e. that first order Jahn-Teller activity is forbidden in half-filled shell states, is directly related to the particularly simple expressions for the quasispin character of the half-filled shells, and also of the single-particle irreducible-tensor operators responsible for such activity. The process of making transparent the relationships between the disparate formalisms used to derive selection rules for half-filled shell states involves the definition of a new antiunitary particle-hole conjugation operator with well defined properties and effects with respect to second quantized operators. It is also shown that this new operator is equivalent to the one used by Ceulemans in 1984. Other "higher" symmetries in Jahn-Teller systems are the subject of discussion in Chapter 5, where a first attempt is made at merging the formalisms of supersymmetry and of para-bose statistics in E x e Jahn-Teller Hamiltonians.