Gand Hyperfine Components ofVKCenters

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Experimental values of the $g$ and hyperfine components of ${{X}_{2}}^{\ensuremath{-}}\ensuremath{-}{V}_{K}$ centers and ${{Y}_{2}}^{\ensuremath{-}}\ensuremath{-}{V}_{K}$-type centers ($X, Y=\mathrm{F},\phantom{\rule{0ex}{0ex}}\mathrm{C}\mathrm{l},\phantom{\rule{0ex}{0ex}}\mathrm{B}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{I}$) in a large number of pure ($\mathrm{AX}$) and doped ($AX:{Y}^{\ensuremath{-}}$) alkali halides have been determined through a careful analysis of their electron-paramagnetic-resonance (EPR) spectra. Expressions for the $g$ components have been derived. For an accurate quantitative analysis, it is necessary to take into account the overlap terms in the calculation of $\ensuremath{\delta}$, the matrix element of the orbital angular momentum $\stackrel{\ensuremath{\rightarrow}}{1}$ between the $^{2}\ensuremath{\Sigma}_{u}^{+}$ ground state and the $^{2}\ensuremath{\Pi}_{u}$ state. A calculation for ${\mathrm{Cl}}_{2}^{\ensuremath{-}}$ yields $\ensuremath{\delta}=0.78$. Representative experimental values for ${\mathrm{Cl}}_{2}^{\ensuremath{-}}$ and ${\mathrm{Br}}_{2}^{\ensuremath{-}}$ are $\ensuremath{\delta}=0.73 \mathrm{and} 0.70$, respectively. The $^{2}\ensuremath{\Sigma}_{u}^{+}\ensuremath{-}^{2}\ensuremath{\Pi}_{u}$ energy differences thus determined decrease going from the Rb salt to the Li salt. This behavior, in general, parallels that of the $^{2}\ensuremath{\Sigma}_{u}^{+}\ensuremath{-}^{2}\ensuremath{\Sigma}_{g}^{+}$ and $^{2}\ensuremath{\Sigma}_{u}^{+}\ensuremath{-}^{2}\ensuremath{\Pi}_{g}$ energy differences which are known from the optical-absorption measurements. The crystal field splitting of the $^{2}\ensuremath{\Pi}_{u}$ state is determined from the orthorhombic character of the $g$ tensor. Expressions for the hyperfine components have been derived which include the first- and second-order correction terms originating from the combined effect of the spin-orbit and hyperfine operators. From the analysis of the combined behavior of the orthorhombic character of the $g$ and hyperfine (hf) components, it can be concluded that ${A}_{\ensuremath{\parallel}}>0$ and ${A}_{\ensuremath{\perp}}>0$ for ${\mathrm{Cl}}_{2}^{\ensuremath{-}}$, ${\mathrm{Br}}_{2}^{\ensuremath{-}}$, and ${\mathrm{I}}_{2}^{\ensuremath{-}}$, and ${A}_{\ensuremath{\parallel}}>0$ and ${A}_{\ensuremath{\perp}}<0$ for ${\mathrm{F}}_{2}^{\ensuremath{-}}$. The analysis of the hf components then shows that the isotropic part of the hf interaction decreases monotonically going from the Rb to the Li salt, while the anisotropic part remains approximately constant. EPR results for ${V}_{\mathrm{KA}}$, ${V}_{\mathrm{KAA}}$, and ${V}_{F}$ centers are also given and they are compared with the ${V}_{K}$-center data.