GENERALIZED SUM-RULES FOR THE MOMENTS OF A ONE-PHONON SPECTRAL-FUNCTION

The low-order moments of the one-phonon spectral function of a Crystal are shown to be related directly to the self-energy of the phonon. Th ese relationships are generalizations of the Placzek sum rule and of a well-known high-temperature extension. The rules can be used to simpl ify a lattice-dynamical calculation of the moments, or, if the moments have been calculated by some other method, such as a Monte Carlo simu lation, the rules can be applied in the other direction to yield infor mation about the self-energy of the mode. This information can, in rum , be used to test the quality of a lattice-dynamical approximation. As an illustration, the rules are applied to transverse and longitudinal zone-boundary phonons in argon at 81 K.