Analysis of the Spectrum of d3 Ions in Trigonal Crystal Fields

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Abstract
The effect of a trigonal crystal field on the energy levels of d3 ions is evaluated within the framework of the crystal‐field model. Matrices of the trigonal‐field potential for the d3 configuration are presented and used to discuss details of the ruby spectrum. Perturbation expressions for the effect of parameter changes on the energy levels are given. These enable some refinement of electrostatic and crystal‐field parameters to be carried out. In particular the effect of the second trigonal parameter is found to be appreciable. Finally, the effect of the spin—orbit interaction is included and the eigenvalues of the total Hamiltonian are found to be in good agreement with the observed energy spectrum of ruby.