Collective and single-particle excitations in liquid neon

Abstract

The neutron inelastic scattering from orthobaric liquid neon at 26.9 \ifmmode^\circ\else\textdegree\fi{}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 $\ensuremath{\nu}$ for 34 values of $Q$ in the range 0.8-12.5 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. 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, $Q\ensuremath{\lesssim}4$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, 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 $Q(<1.6{\AA{}}^{\ensuremath{-}1})$ shows a pronounced inelastic wing at values of $\ensuremath{\nu}$ 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 $Q>4$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ is characteristic of single-particle scattering. The peak position follows, but lies somewhat lower than, the recoil frequency $\frac{\ensuremath{\hbar}{Q}^{2}}{4\ensuremath{\pi}m}$, 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 $Q>~0.8$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$.