Selection rules for effective intra-atomic and optical transition operators in partly-filled shell ions
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The important role played by the operator of time reversal in physics is further extended in this thesis. The time reversal selection rules of Abragam and Bleaney (1970) and Stedman and Butler (1980) have been further extended to higher group levels in a Racah group chain. In the spin-orbit product group SU S/2 x SO L/3 new selection rules are obtained, which restrict the spin-orbital ranks of many-body operators strictly according to an operator's HT (hermitian conjugation and time reversal) signature. At the symplectic group level, time reversal selection rules restrict the HT -even and HT -odd many-body operators to transform as certain irreps of the symplectic group Sp4l+2. This time reversal symmetry classification combined with the power of group theory methods is very useful for the calculation of many-body interactions. These new results also correct and generalise the previous rules based on hermiticity alone. Such new time reversal selection rules are also applied in perturbation theory. Relativistic corrections arising from Dirac-Foldy-Wouthuysen analysis for electron have been reinvestigated. A new spin-dependent E1 matter-field interaction H’s = eÅ . S x p2m²c² has been revealed, and also some new M1 operators. The possible significance of this new operator H’s has been discussed qualitatively for both intra-configurational and inter-configurational spin-forbidden transitions in the light of time reversal selection rules. The Goldstone diagrammatic perturbation method is used to discuss optical transition processes. The Goldstone diagrams suitable for intra-configurational transitions of the lanthanide ions in crystal and in solutions are discussed. The relationships between Goldstone diagrams, angular momentum diagrams, many-particle coupling, and effective tensor operators are discussed. Other selection rules including the quasi-spin classification of half-filled shells are briefly reviewed, and a quantitative calculation for the crystal field splitting for a half-filled rhenium atom has been carried out with its aid.