Theory of Electric Shifts of the Optical and Magnetic Resonance Properties of Paramagnetic Ions in Crystals

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.