Collective and single-particle excitations in liquid neon

The neutron inelastic scattering from orthobaric liquid neon at 26.9 °K has been measured with a triple-axis crystal spectrometer operating in its constant-$Q$ mode. The scattering was measured as a function of frequency $\nu$ for 34 values of $Q$ in the range 0.8-12.5 ${\mathrm{\AA }}^{-1\mathrm{}}$. Corrections for residual multiple scattering and instrumental resolution were applied to the theoretical cross sections before comparing with experiment. In the region of collective behavior, $Q\lesssim 4$ ${\mathrm{\AA }}^{-1\mathrm{}}$, the quasielastic peak that is observed is in qualitative agreement with the Kerr - Singwi theory and with the memory-function theory, which is applied to neon in the present work. The observed scattering at constant $Q(<\mathrm{}1.6\mathrm{}{\AA }^{-1\mathrm{}})$ shows a pronounced inelastic wing at values of $\nu$ where the memory-function theory predicts a small inelastic peak. No such wing is contained in the Kerr-Singwi theory. The latter theory evidently overestimates the damping of the collective motion while the former underestimates it. The observed scattering in the region $Q>\mathrm{}4\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ is characteristic of single-particle scattering. The peak position follows, but lies somewhat lower than, the recoil frequency $\frac{\hslash Q^2}{4\pi m}$, where $m$ is the mass of a neon atom, and the width of the scattering function increases approximately linearly with $Q$. Superimposed on this general behavior are well-defined oscillations characteristic of the coherent nature of the scattering. The single-particle scattering in liquid neon is very similar to that observed in liquid helium. The data in the single-particle region are in reasonable agreement with the Kerr-Singwi model and in even better agreement with a truncated Gram-Charlier expansion. The earlier data of Chen et al. are corrected for the nonlinearity inherent in a time-of-flight experiment and are found to agree with the present results in showing that there are no well-defined propagating excitations in liquid neon for $Q>~0.8$ ${\mathrm{\AA }}^{-1\mathrm{}}$.