Abstract
A theory of electric-field-induced energy shifts and $g$ shifts in paramagnetic crystals is presented. This theory is based on the modern tensor-operator techniques. An "equivalent even interaction" is introduced which operates only among the states of the ground manifold. Using this method the $g$ shift of ${\mathrm{Yb}}^{3+}$ in CaW${\mathrm{O}}_{4}$ tungstate is treated in detail with good results. We also consider the effects of odd fields on the observed crystal-field parameters, optical shifts in external electric fields, and field-induced transition probabilities.
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