Vibronic structure observed in the emission and absorption spectra of alkali halides containing either Sm2+, Eu2+, or Yb2+ is reported, and shown to result from pseudolocalized vibrations occurring at the rare-earth defect. A model for the defect is defined, and an analysis of its vibrational frequencies is given for the sample case of a RbCl host lattice. A Green's function formalism is used in the analysis. The calculation, in which a number of approximations are made, yields the qualitative features of the experimental results. © 1965 The American Physical Society.