Measurement of anomalous dispersion and the excitation spectrum of HeII

A detailed account of the propagation of superthermal phonons ($\hslash \omega \gg \mathrm{kT}$) in HeII is presented as a function of pressure up to the solidification point and at low temperatures. Superconducting A1 fluorescers and tunnel junctions are used for this study. The measurements show that a well-defined cutoff energy $E_c$ exists, below which the spontaneous decay of a high-frequency phonon via the three-phonon process occurs in He. From measurements of $E_c$ and the group velocity ${\nu }_g$ at $E_c$, we obtain numerical estimates for the magnitude of the anomalous dispersion as a function of pressure. The results show that simple polynomial expansions do not quantitatively describe all the available data and that current models involving two branches in the excitation spectrum describe the situation somewhat better.