Evidence for Upward Phonon Dispersion in LiquidHe4from the Angular Spreading of Phonon Beams

Measurements have been made of the angular spreading of initially well-defined beams of phonons of energies $\frac{\hslash \omega }{k_B}\lesssim 12$ K in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at $T\sim 0.1$ K and at pressures between saturated vapor pressure and 24 bars. The spreading is consistent with three-phonon decay processes and the results strongly suggest that in the dispersion relation $\omega =cq(1-\gamma {\hslash }^2{q}^2)$ the constant $\gamma$ is negative at $p\lesssim 17$ bars and positive at higher pressures.