Electronic Structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi></mml:math>Centers: 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 ${|\ensuremath{\Psi}(\mathrm{K})|}^{2}=0.70\ifmmode\times\else\texttimes\fi{}{10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and ${|\ensuremath{\Psi}(\mathrm{Cl})|}^{2}=0.12\ifmmode\times\else\texttimes\fi{}{10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$.