A Macroscopic Approach to Determine Electron Mobilities in Low-Density Helium

Abstract

We have developed a macroscopic approach to predict electron mobilities and cavity sizes in liquid and supercritical helium using the free-volume concept. We demonstrate very good agreement with experimental electron mobility data and significant improvement with respect to the commonly used ‘bubble’ model, especially for low hydrostatic pressures. The reason for this advancement is the use of heuristically developed thermodynamic state laws that account for the variations with density, temperature, and the isothermal compressibility of dense helium. The state equation uses the scattering length as input and parameters that are adjusted to experimental data. The conventional ‘bubble’ method is based on the surface tension which is not defined for all accessible thermodynamic states. We investigate the limit of very low densities, with Knudsen numbers larger than 1.5. Here, the mobilities predicted by our method coincide well with experimental data until the mobility diverges abruptly. This behaviour is interpreted as a cross-over from Stokes-flow to gas kinetics behaviour.