Investigation of the phonon dispersion relation in liquidHe4by thermal-expansion measurements

Abstract

The thermal expansion of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ under the saturated vapor pressure has been measured in the temperature range 0.1-0.62 K. The expansion was found by filling a superconducting resonant cavity with the liquid and measuring the resonant frequency as a function of temperature. The density was related to the dielectric constant through the Clausius-Mossotti relation. Sensitivity to changes in fractional density of 4 × ${10}^{-9\mathrm{}}$ was achieved. The thermal-expansion data were used to obtain quantitative information about the dispersion relation for thermal phonons. In addition to the thermal-expansion measurements, tests of the validity of the Clausius-Mossotti relation were made.