Crystal field matrix reduction and polarisation interference calculations

• Main Author: Lee, Michael James
• Language: en
• Published: University of Canterbury. Physics and Astronomy 2013
• Online Access: http://hdl.handle.net/10092/8169

The theory of one-electron crystal field parametrisation for optical spectra of rare-earth doped crystalline lattices dates back over forty years. The effect of the crystal host material is to split the free-ion degeneracy of the rare-earth multiplets. Some of these multiplets have structure which defies explanation in terms of crystal field theory and new developments have emerged within the last five years to address the problem. One of these methods takes the set of crystal field operators and appends two-electron correlation operators. Another adjusts the crystal field operators to include excited state configuration effects. A direct comparison of fitted parameters is meaningless, the corresponding operators being defined on different spaces. Here the techniques of matrix reduction, as developed in effective operator theory, are applied to larger configuration Hamiltonians to model their effects in correlation space. Correlation operators are then fitted to the reduced configuration matrices to establish a connection between the two approaches. Transition intensity parametrisation has a similar lengthy history and formulation. Geometric effects first brought to light fifteen years ago suggest the possibility of polarisation dependent interference between the transition moments of different Cartesian axes. This would manifest itself in the directional dependence of fluorescence intensity for low symmetry crystal hosted rare-earth centres. To date there have been no experimental tests of these predictions and here a case is made for certain transitions of hydrogenated praseodymium doped fluorite. There are certain practical difficulties which must be overcome and these are also addressed.