Theory of Electron-Phonon Interaction and Defect-Center Optical Spectra

An electron-lattice interaction potential is derived and applied to the calculation of defect-center optical-spectra line shapes. Results have been limited to a model in which the electron-lattice interaction involves band-mode phonons; local modes and eigenvector-in-band resonance effects have been neglected. Spectral line shapes are analyzed in terms of a per-mode Huang-Rhys factor $S_j$. $S_j$ is given by the defect-center wave functions and the electron-lattice interaction potential. Calculations are presented for the two extreme cases: broad-band spectra, in which many phonons are excited, and spectra with detailed attendant phonon structure, in which only a few phonons are excited. The former computations are the half-width and effective lattice frequency of the NaCl and KCl $F$-center absorption and luminescence spectra, which agree resonably well with experiments. The latter calculations are a measure of one-phonon contributions to line shapes of centers in NaCl, KCl, and LiF. For this, only part of $S_j$, the per-mode lattice factor $L_j$, was evaluated. Comparison of frequency distributions formed from $L_j$ to attendant phonon spectra of various $F$-aggregate centers showed agreement as to position of major features in the spectra.