Electronic Structure ofFCenters: Hyperfine Interactions in Electron Spin Resonance

It is shown that the observed width of the microwave electron spin resonance absorption lines associated with $F$ centers in KCl, NaCl, and KBr crystals can be attributed to hyperfine interactions between the $F$-center electron and the nuclear magnetic moments of the ions adjacent to the $F$ center. The width arises from the distribution of nuclear moment components. Theoretical calculations of the width are in good agreement with observation provided that the $F$-center wave function is treated as a linear combination of atomic orbitals; wave functions calculated on continuum models are shown to be unsatisfactory. The theory is confirmed by a comparison of observations on $F$ centers in crystals of ${\mathrm{K}}^{39}$Cl and ${\mathrm{K}}^{41}$Cl. If the width is attributed to interactions with the nearest sets of K and Cl ions, the experiments lead directly to quantitative values of the electronic charge density at the K and Cl nuclei: one finds ${\left|\Psi \right(\mathrm{K}\left)\right|}^2=0.70\mathrm{}\times {10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and ${\left|\Psi \right(\mathrm{Cl}\left)\right|}^2=0.12\mathrm{}\times {10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$.