Neutron Scattering by Rotons in Liquid Helium

The elementary excitations in superfluid helium have been studied in the wave-vector range $1.5<Q<\mathrm{}2.3\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ by inelastic neutron scattering. The single-excitation scattering function ${\mathcal{S}}_1 (Q, \hslash \omega )$ was measured for pressures between 1 atm and the solidification pressure and for temperatures from 1.3°K to above the transition temperature $T_{\lambda }$. The dispersion curves were fitted to parabolas and the appropriate Landau parameters tabulated vs temperature and pressure. By accounting for the effect of the instrumental resolution it was possible to observe a line broadening at low temperatures which sets in when the slope of the dispersion curve equals the sound velocity. There are strong indications that this is due to the roton-phonon interaction proposed by Pitaevskii. The line broadening observed when the temperature approaches $T_{\lambda }$ is well accounted for by the roton-roton interaction as calculated by Landau and Khalatnikov. The results have been related through thermodynamics to other properties of the liquid and the spectral form of the excitations compared to those observed in magnetic systems close to the critical temperature.