Transferred hyperfine interactions for trapped-hole centers in tetragonal GeO2

$\gamma$-ray, x-ray, or uv irradiation at 77 K of single crystals of tetragonal Ge${\mathrm{O}}_2$ containing substitutional ${\mathrm{Ga}}^{3+}$ impurity cations generates holelike centers analogous to the ${\mathrm{}\left[\mathrm{Al}\right]\mathrm{}}^0$ centers reported previously in Aldoped crystals. The measured ${\mathrm{}\left[\mathrm{Ga}\right]\mathrm{}}^0$-center spin-Hamiltonian parameters are: $g_{x^{\prime }}=2.0249\mathrm{}\pm 0.0003$, $g_{y^{\prime }}=2.0132\mathrm{}\pm 0.0003$, $g_{z^{\prime }}=2.0039\mathrm{}\pm 0.0003$; $\left|{}_{}{}^{69}{}_{}{}^{}A_{x^{\prime \prime }}^{}{}_{}{}^{}\right|=9.13\mathrm{}\pm 0.05$, $\left|{}_{}{}^{69}{}_{}{}^{}A_{y^{\prime \prime }}^{}{}_{}{}^{}\right|=10.27\mathrm{}\pm 0.05$, and $\left|{}_{}{}^{69}{}_{}{}^{}A_{z^{\prime \prime }}^{}{}_{}{}^{}\right|=9.62\mathrm{}\pm 0.05$. These $\overleftrightarrow{\mathrm{A}}$ components, in units of ${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, are given for the ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ isotope; hyperfine components for ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ are larger by the ratio of the nuclear moments. From symmetry, the only contribution to the isotropic part of the hyperfine interaction for both ${\mathrm{}\left[\mathrm{Al}\right]\mathrm{}}^0$ and ${\mathrm{}\left[\mathrm{Ga}\right]\mathrm{}}^0$ centers arises from exchange core polarization. Detailed analysis, which includes calculation of the anisotropic part of the hyperfine interaction using free-ion wave functions for ${\mathrm{Al}}^{3+}$, ${\mathrm{Ga}}^{3+}$, and ${\mathrm{O}}^{-}$, yields the signs of the hyperfine components, the internuclear distance between the impurity cation and the ${\mathrm{O}}^{-}$ ion, and verifies the ionic nature of the centers. A two-step mechanism is proposed for the positive exchange core polarization occurring in the ${\mathrm{}\left[\mathrm{Ga}\right]\mathrm{}}^0$ center.