A vibrational model of F centres in alkali halides

A model of F-centres in alkali halides, which relates absorption energies in F-bands to the dynamic parameters of host lattices, is proposed. According to this model, the electrons trapped in F-centres are treated as classical particles with a proper mass \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m^{*}=m\varepsilon_{loc}^{4}/\varepsilon_{\infty }^{2}$\end{document} , m standing for the actual electron mass, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varepsilon_{loc}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varepsilon_{\infty }$\end{document} for local high frequency and optical dielectric constants, respectively. Hence, by considering the trapped electrons as substitutional impurities of small mass, the dynamics of the lattice is investigated by means of the theory of local modes with the assumption of isotopicity. A simple equation allowing calculation of the local mode frequencies is obtained. Knowledge of the Debye frequency and of transverse and longitudinal mode frequencies at the long wavelength limit is required. With this model, F-band absorption energy is reasonably well accounted for.