Collective acoustic modes as renormalized damped oscillators: Unified description of neutron and x-ray scattering data from classical fluids

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.