Time-Dependent Displacement Correlations and Inelastic Scattering by Crystals

A function is defined which expresses quantum mechanically the correlation of the displacements of pairs of lattice points at different times due to the wave-like nature of crystal excitations. Methods are developed for summing implicitly the effects of multiple emission and absorption of lattice quanta occurring during a scattering process. The inelastic scattering cross sections found thereby are expressed entirely in terms of the time-dependent correlation function defined earlier. The resulting treatment thus emerges as a natural generalization of the static theory of x-ray scattering. The results are discussed in relation to a number of approximation methods.