Isotope Effects Induced by Local Modes in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>Band

Abstract

The experimental investigation in the temperature range from 4 to 400\ifmmode^\circ\else\textdegree\fi{}K of the ultraviolet $U$ band in KCl, KBr, and RbCl crystals containing ${\mathrm{H}}^{\ensuremath{-}}$ and ${\mathrm{D}}^{\ensuremath{-}}$ ions has revealed the following isotope effects: (a) The half-width of the ${U}_{\mathrm{H}}$ band is from 4 to 8% larger than that of the ${U}_{\mathrm{D}}$ band. (b) The ${U}_{\mathrm{H}}$ band occurs at energies \ensuremath{\sim}0.02 eV smaller than those of the ${U}_{\mathrm{D}}$ band. In order to describe these results the method of moments, in the harmonic and Condon approximations, has been applied. From the symmetry of the defect it is shown that only the vibrational modes which transform according to the ${{\ensuremath{\Gamma}}_{15}}^{\ensuremath{-}}$ representation of the full cubic point group can be responsible for the isotope effects; these modes are just those active in the infrared. It is found that during optical transitions, allowed in dipole approximation, the ${{\ensuremath{\Gamma}}_{15}}^{\ensuremath{-}}$ modes suffer, via the electron-phonon interaction, only a frequency shift, and that only the local mode has to be taken into account in order to predict the observed isotope effects, since the contribution coming from the ${{\ensuremath{\Gamma}}_{15}}^{\ensuremath{-}}$ continuum is negligible. Finally, the local-mode frequency of the excited $U$ center has been estimated.