Invariants in the paramagnetic resonance spectra of impurity-doped crystals

We show that in cubic crystals with anisotropic impurity centers the sum of squares magnetic resonance [electron paramagnetic (EPR)] frequencies is invariant respect to field direction. The connection between such an and $g$-tensor components derived for different types centers. established regularity confirmed experimentally spin-noise spectra a $\mathrm{Ca}{\mathrm{F}}_{2}\ensuremath{-}{\mathrm{Nd}}^{3+}$ crystal. how this property EPR can be efficiently used assignment crystals.