Dynamic measurement of the surface tension of liquid helium with a two-dimensional electron probe

Electrons deposited above the free surface of liquid helium exhibit coupled electron-ripplon modes whose frequencies are simply related to the surface tension of helium. The hydrodynamic expression for the ripplon dispersion relation for pure⁴He is shown to be valid up to the wavevector range 10⁵ cm^–1<q<2×10⁶ cm^–1 of the coupled modes. For a small amount of³He (X₃10^–6–10^–8) added to pure⁴He, we measure the variation of the surface tension in the 60–600 mK temperature range. These experiments, which cover the frequency range v10–300 MHz, agree fairly well with previous static (capillary) or low-frequency (surface sound velocity) experiments.