Transition from the collective to the single-particle regimes in a quantum fluid

The evolution of the dynamic structure factor $S(q,\ensuremath{\omega})$ of liquid Ne with exchanged momentum q and frequency $\ensuremath{\omega}$ has been studied by inelastic x-ray scattering in the q range extending from 0.3 to $16{\mathrm{\AA{}}}^{\ensuremath{-}1},$ i.e., covering the whole transition region from the collective regime to the single-particle one. The values of the first three spectral moments are extracted from the experiment either by direct line shape integration of the spectra or as a result of line shape best fitting procedures. The q dependence of different ratios constructed using the measured spectral moments clearly shows the transition from a classical regime, characteristic of the low-q macroscopic limit, to a quantum one, reached in the high-q microscopic limit. Moreover, direct information on the values of physically relevant parameters such as the mean atomic kinetic energy and the kinetic structure function is derived.