Pressure dependence of the low-momentum phonon dispersion relation in liquidHe4

Abstract

The pressure dependence of the low-momentum phonon dispersion relation in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been determined from an analysis of experiments on the interactions between sound waves and thermal phonons. Specifically, changes $\frac{\Delta C}{C}$ in sound velocity were studied in the frequency range 1-15 MHz for pressures $0\lesssim P\lesssim 20$ atm, at temperatures $0.1\le T\le 0.45$ K. The results were found to be in agreement with phonon dispersion, for small momenta, of the form $\epsilon =Cp(1+\gamma p^2\cdots )$, with $\gamma$ positive at low pressures. At saturated vapor pressure, the present study yields a value $\gamma =(16\mathrm{}\pm 1)\times {10}^{37}$ cgs; $\gamma$ decreases linearly with increasing density and reaches zero at a density corresponding to a pressure of ∼ 18 atm.