Calorimetric Evidence for Positive Phonon Dispersion in Liquid Helium-4

Abstract

The constant-volume heat capacity of liquid ${\mathrm{He}}^4$ has been measured from 0.3 K to above the $\lambda$ point. Below 0.9 K the phonon heat capacity corresponds to a dispersion relation $\epsilon =cp(1-\gamma p^2)$ with $\gamma$ varying from -4.1 × ${10}^{37}$ ${\mathrm{g}}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^2$ at the saturated vapor pressure to 19.6 × ${10}^{37}$ ${\mathrm{g}}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^2$ near the freezing pressure.