The localized-hole model of the V center in the alhdine earth oxides is represented as a positive hole trapped on one oxygen atom adjacent to a positive-ion vacancy (in the ground state and on the time scale of an ESR experiment). Upon trapping the hole, the oxygen atom is presumed to relax away from the vacancy, thus lowering the symmetry from octahedral to tetragonal. The vahdity of this model has recently been challenged on the basis that a proper description of the ground state is a molecular orbital representing a linear combination of states with the hole on either of the two oxygen atoms opposite one another about the vacancy. We present the analysis of some ESR spectra in which we observed the resolved hyperfine splitting dne to a single 'Mg + ion adjacent to the trapped hole and on the axis of the defect. From the natural abundance of the~Mg isotope one can calculate the expected hyperfine line intensities relative to that of the central line arising from V centers having only "Mg or ' Mg atoms in the axial positions, for the localized and for the delocalized models. The measured relative intensities agree with those calculated for the localized model. An analysis of the axial spectrum indicates the presence of an unusually intense forbidden line at X band. This becomes relatively more intense at the Xu band, as expected. Shifts of line position and intensity relative to the lines of an allowed hyperfine sextet agree with those predicted. The values of the hyperfine parameters are found to be A =+2.84 MHz and B = -0.86 MHz. The quadrupole parameter is found to be +0.18 MHz. The sign of A is anomalous in that a contact interaction is expected to give an isotropic parameter with the sign of the nuclear magnetic moment. This may result from exchange polarization. The magnitude o B is interpreted as indicating a compact unpaired charge distribution. The V centers studied here were generated by fast-neutron irradiation, and there is no confusion with impurity-associated hole centers; the former have a long-term stability in MgO, while the latter decay rapidly to negligible levels at room temperature. I

The energy level scheme for 4 f 13 in a cubic crystal field is relatively simple. The effect of a perturbation Hamiltonian containing electron and nuclear Zeeman terms and magnetic dipole and electric quadrupole hyperfine interactions can therefore be calculated easily, especially as the experimental results only justify calculation to second order. The second-order effects give several small unusual terms in the spin-Hamiltonian for the ground doublet Γ 7 . The high precision of endor experiments on 171 Yb and 173 Yb make it possible to measure these small terms and confirm that their magnitude is consistent with the second-order calculation. From the size of the second-order terms we also obtain a value for the energy of the Γ 8 state of the lowest J = 7/2 manifold (604 ± 10 cm -1 ), and a value for the electric quadrupole interaction in the free ion. We have also attempted to measure a hyperfine structure anomaly in order to estimate the contribution of core polarization to the hyperfine interaction, but such an anomaly is too small to be detectable with the precision of measurement we were able to achieve.

Endor experiments have been performed on 173 Yb at tetragonal sites in CaF 2 . The spin-Hamiltonian describing the frequencies of the endor lines contains many small terms, which arise in second order from matrix elements of Zeeman and hyperfine interactions that couple the ground doublet to excited states of the J = 7/2 manifold. From the experimental values of these small terms the energies of the excited states of this manifold are deduced. This information is used together with g values of the lowest doublet for both J = 7/2 and J = 5/2 manifolds, and the energy of the lowest doublet of the J = 5/2 manifold, to calculate the following crystal field parameters (all in cm -1 ): B 2 0 = + 8.4 ( 1.3 ) ; B 4 0 = + 0.19 ( 0.03 ) ; B 6 0 = + 0.054 ( 0.005 ) ; B 4 4 = + 2.8 ( 0.4 ) ; B 6 4 = − 0.735 ( 0.07 ) . . The measured value of the nuclear electric quadrupole interaction for 137 Yb( I = 5/2) is sepa­rated into a component due to the field gradient from the 4f electrons and one due to the field gradient from the surrounding lattice. Comparison of the latter component with the value of B 2 0 gives (1–γ∞)/(1–σ 2 ) = 75±18, considerably smaller than values of this ratio predicted theoretically or found in earlier experimental investigations. The most likely cause of this low value is the considerable contribution of covalent effects to B 2 0 .