Asymptotic Descriptions of Defect Excitations

Abstract

Within the wide variety of elementary excitations of defect solids those referred to as “resonances” or “localized” modes are particularly interesting and occur frequently. Theoretical methods have been developed for handling the defect excitation problem generally; the Green’s function approach is particularly useful and has been applied to defect vibrations, localized moments, and localized electronic excitations. The input to these theoretical analyses range from parameterized models to actual experimental lattice dispersion or band data. But frequently certain asymptotic features appear independently of the model details. For example, in the defect vibration case both localized and resonance modes seem to have many of the features of a simple Einstein oscillator. It is the purpose of the present remarks to indicate how this arises. The method has developed from previous work, particularly in collaboration with M. Wagner and with J. A. D. Matthew, ⁽¹⁾ it is similar to that of Okazaki et. al. ⁽²⁾ The results are not only pedagogical but also may be used for numerical estimates. For simplicity only defect lattice vibrations in the harmonic approximation are discussed here. The extension to other systems is apparent. ⁽²⁾

Supported in part by the U. S. Atomic Energy Commission under contract AT (30–1)-3699, Technical Report #NYO-3699-15.