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The dynamic structure factor is the quantity, which can be measured by meansof Brillouin light-scattering as well as by means of inelastic scattering ofneutrons and X-rays. The spectral (or frequency) moments of the dynamicstructure factor define directly the sum rules of the scattering law. Thetheoretical scheme formulated in this study allows one to describe the dynamicsof local density fluctuations in simple liquids and to obtain the expression ofthe dynamic structure factor in terms of the spectral moments. The theorysatisfies all the sum rules, and the obtained expression for the dynamicstructure factor yields correct extrapolations into the hydrodynamic limit aswell as into the free-particle dynamics limit. We discuss correspondence ofthis theory with the generalized hydrodynamics and with the viscoelasticmodels, which are commonly used to analyze the data of inelastic neutron andX-ray scattering in liquids. In particular, we reveal that the postulatedcondition of the viscoelastic model for the memory function can be directlyobtained within the presented theory. The dynamic structure factor of liquidlithium is computed on the basis of the presented theory, and various featuresof the scattering spectra are evaluated. It is found that the theoreticalresults are in agreement with inelastic X-ray scattering data.

Self-Consistent Description of Local Density Dynamics in Simple Liquids. The Case of Molten Lithium