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

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Abstract
Rare‐earth ions in ethyl sulfate crystals give rise to sharp‐line optical absorption spectra. In this paper a part of the theory of the Zeeman effect for these lines is developed. The case when the crystal‐field and Zeeman splittings are comparable is treated; this is a frequent experimental situation. Only magnetic fields in the basal plane are considered. There is then an antiunitary symmetry operation which leads to simplifications in the energy‐level calculations and to the assignment of a quantum number ξ=±1 to the states. A selection rule for electric‐dipole transitions is found that shows that the matrix element is real or pure imaginary, depending on the initial and final ξ numbers. Furthermore, the states are found to be of two kinds: Type A, in which the assignment of ξ number to the state does not depend on the choice of coordinate axes, and Type B, in which it does. The possibility of an effective D3h symmetry applying in the optical absorption problem is analyzed. Then the dependence of absorption intensity on magnetic‐field direction for transitions between different types of states is found to be qualitatively different from that for transitions between the same types of states.