Self-energy of phonons in an anharmonic crystal of order ${\lambda }^4$. III. Approximate numerical results for ionic crystals

The results of numerical calculations of all anharmonic contributions of $O\left({\lambda }^4\right)$ to the temperature dependence of width and position of the fundamental lattice-vibration absorption peak in sodium chloride and lithium fluoride crystals are presented. Expressions for the Fourier-transformed anharmonic force constants are obtained for ionic crystals of sodium-chloride structure in the Peierls approximation. Using these and a simple approximation for a few expressions, it has been possible to estimate all anharmonic contributions of $O\left({\lambda }^4\right)$ to the phonon self-energy at high temperatures. It is found that there is an overall improvement over earlier theoretical results. For sodium-chloride crystal the $T^2$ dependence of the width of the absorption peak shows better agreement with experiment than earlier theoretical results. The results for the frequency dependence of the imaginary part of dielectric constant also show improvement and are in good agreement with experiment especially in the high-frequency region of the absorption peak. The results for the lithium-fluoride crystal are of the same quality as those obtained by Ipatova et al., which are already in good agreement with experiment.