Long-Wavelength Phonons in Liquid Helium

Abstract

High-resolution neutron-scattering measurements have been made of long-wavelength-phonon energies $\hslash \omega$ in liquid helium at 1.1 °K as a function of wave vector $Q$. The results are approximately described by $\omega =cQ(1-\gamma {\hslash }^2{Q}^2-\delta {\hslash }^4{Q}^4)$, with $\gamma$ very small (<2×${10}^{36}$ ${\mathrm{g}}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^2$) and $\delta =(2.4\mathrm{}\pm 0.2)\times {10}^{75}$ ${\mathrm{g}}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-4\mathrm{}}$ ${\sec }^4$.