In the Q range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor S(Q, omega) generalize in different ways the results obtained from linearized-hydrodynamics theory in the Q-->0 limit. Here we show that the models most commonly fitted to experimental S(Q, omega) spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation Q range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the Q dependence of the mode frequencies. The emerging picture describes the acoustic modes as Q-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.

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A review of the available tools for the calculation of the neutron double-differential cross-section of fundamental molecules, such as hydrogen and methane, is reported here. The most common cases occurring in neutron data analysis are treated in detail with the aim of providing the reader with intelligible and efficient procedures. The utility nowadays of these kinds of computation are widely described, and applications discussed, with examples based on the comparison with experimental data. New advances and refinement/corrections of earlier work are given throughout the paper, as well as suggestions for practical implementation. Please note, a correction was made to this review (definition after equation (13)) on 10 November 2003

A detailed inelastic neutron scattering investigation of the THz dynamics of liquid zinc is presented. The observed Q dependence clearly reveals the existence of a complex dynamics made up of two distinct excitations. The highest energy mode is the prolongation of the longitudinal acoustic density fluctuations whereas the comparison with the phonon dynamics of crystalline hcp zinc suggests a transverse acousticlike nature for the second one. This mode seems related to peculiar anisotropic interactions, possibly connected to the behavior of the crystalline phase.

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.