The interactions between ${\mathrm{Pr}}^{3+}$ ions in a tetragonal site of 0.01-at.% ${\mathrm{Pr}}^{3+}$:Ca${\mathrm{F}}_{2}$ and the surrounding nuclei are investigated, primarily by means of optically detected NMR (ODNMR). This technique is based on the fact that hole burning in the 5941-\AA{} $^{3}H_{4}\ensuremath{\leftrightarrow}^{1}D_{2}$ transition takes place due to coupling between the rare-earth ion and neighboring $^{19}\mathrm{F}$ nuclear spins. ODNMR lines are identified which are due to nearest-neighbor (NN), next-nearest-neighbor (NNN), and interstitial ($i$) fluorines. The distorted positions of the NNN fluorines are determined from the ODNMR data, but this is impossible for the other near neighbors due to strong covalent-bonding effects. Physical models for the hole-burning and refilling processes are proposed which agree qualitatively with the hole shapes and ODNMR line intensities, and with the observation of rf-assisted optical hole burning when a strong magnetic field ${H}_{0}$ is applied parallel to ${C}_{4}$.
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