Theory of Zeeman Effect for Rare-Earth Ions in Crystal Field with C3h Symmetry. IV

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Abstract
In earlier papers a quantum number ξ=±1 was assigned to states of the system (the ion in the crystal field and with magnetic field in the basal plane) according to their behavior under the antiunitary symmetry operation, time reversal combined with space reflection in the basal plane. The states were found to be of two types, Type A states for which the assignment of ξ number does not depend on choice of coordinate axes and Type B states for which it does. The types influence the dependence of absorption intensity on magnetic field direction: for A→ A and B→ B transitions it is qualitatively different than for A→ B and B→ A transitions. In this paper the type is shown to be related to the representations of C2h that the states make at the special magnetic field directions for which C2h is a symmetry of the system. It is shown also that the type of state may change when the energy levels, plotted as a function of magnetic field applied in one of those special directions, cross. This means that, wherever there is a crossing, there is a drastic change in the way the intensities of the lines vary with direction of the field. At high magnetic fields, past all crossings, all states are Type A. Application is made to some energy levels of erbium ethyl sulfate.