Mean-square displacement of an atom in an anharmonic crystal toO(λ4)

Abstract

General expressions for all anharmonic contributions of $O({\ensuremath{\lambda}}^{4})$ to the mean-square displacement of an atom in a crystal have been obtained. Numerical estimates have been made for a nearest-neighbor central-force model of a fcc lattice in the high-temperature limit and in the leading-term approximation. Our estimates for Lennard-Jones systems show that anharmonic contributions of $O({\ensuremath{\lambda}}^{4})$ cannot be ignored. Estimated recoilless fraction of 9.4-keV transition of $^{83}\mathrm{Kr}$ in solid krypton is found to be quite close to experimental values.