Debye-Waller Factor and Second-Order Doppler Shift ofI129in Alkali Iodides

Abstract

We have computed the Debye-Waller factor (or recoilless fraction) and the second order Doppler shift of ${\mathrm{I}}^{129}$ in alkali iodides of NaCl structure as a function of temperature corresponding to a transition of 26.8 keV in ${\mathrm{I}}^{129}$. In each case, the lattice-vibration eigenfrequencies and eigenvectors required in these calculations are calculated for 8000 points in the first Brillouin zone using the deformation-dipole model for the lattice. In this model we take into account the short-range forces, long-range Coulomb forces, polarization and deformation of the ions. Our results for the recoiless fraction are in agreement with those of the M\"ossbauer experiments, whereas calculations based on nearest-neighbor short-range interactions show very poor agreement with the experimental results. Thus, the nearest-neighbor-interaction model is very inadequate for calculations in alkali halides and a more realistic model like the deformation-dipole model should be employed in order to compare the theory with the experiment. The results for the second-order Doppler shift approach the same value in the high-temperature limit while at very low temperature the maximum variation is about 5% in all the cases. Thus, to indicate the behavior of this quantity as a function of temperature, we give the results for one of these compounds only.