Pressure Dependence of Charge Carrier Mobilities in Superfluid Helium

Accurate measurements were made of the mobility of positive and negative charge carriers in ${\mathrm{He}}^4$, at pressures up to the melting pressure and temperatures in the range 0.27 <T <1.0 °K. The data are analyzed in terms of the scattering of phonons and rotons by the charge carriers. The phonon-dominated mobility of the negatives agrees well with existing theories, and analysis of these results provides a new determination of the electron-bubble radius as a function of pressure. The phonon-scattering term for positives is calculated from the electrostriction model, and is in good agreement with the experimental results. Roton-limited mobilities are obtained by subtracting the known phonon contributions. One may express the results in the form ${\left(\frac{e}{\mu }\right)}_{\pm }=f_{\pm }\mathrm{}(P,T)\mathrm{}{e}^{ \frac{-\Delta \mathrm{}(P,T)\mathrm{}}{\mathrm{kT}}}$, where $\Delta \mathrm{}(P,T)\mathrm{}$ is the pressure- and temperature-dependent energy gap derived from neutron-scattering experiments. The measured pressure and temperature dependences of the prefactors $f_{\pm }\mathrm{}(P,T)\mathrm{}$ are discussed in light of recent theories for the scattering of rotons by the charge carriers.