Resonance Absorption of Gammas by Impurity Nuclei in Crystals

Abstract

The aspects of the dynamics of a simple cubic crystal model with a dilute impurity which are relevant to the M\"ossbauer effect are considered. Harmonic nearest-neighbor forces are used, and the mass and force constant of the active nucleus differ from those of the host lattice. The calculations are carried out using a Green's function approach with the aid of an IBM 7090 computer. The recoilless fraction, temperature shift, frequencies and amplitudes of localized mode, and absorption spectra are calculated as functions of temperature, impurity mass, and coupling constant. One interesting feature of the results is that the recoilless fraction is independent of the properties of the host lattice over a fairly wide range of variation of mass and force constant. Others are that, in general, the absorption spectrum is not simple related to the phonon spectrum, and that there sometimes exists an approximate low-frequency localized mode.