Theory of anomalous dispersion in liquidHe4

The zero-temperature dispersion curve in liquid ${\mathrm{He}}^4$ is calculated assuming anomalous dispersion, $\omega \mathrm{}\left(k\right)=c k(1+\gamma {\hslash }^2{k}^2)$, in zeroth order and including three-phonon interactions within the continuum model. It is shown that the damped-phonon mode changes to a collective-type excitation at higher momenta. Estimates of $\gamma$ at saturated vapor pressure and 10 atm are obtained from experimental data on the onset of the long-lived excitation in liquid ${\mathrm{He}}^4$.