Electron Drift Velocities in Liquefied Argon and Krypton at Low Electric Field Strengths

In this paper we report measurements of the drift velocity of electrons in liquid Ar and Kr as a function of temperature, pressure, and electric field strength. The experimental findings are as follows: (a) At low temperatures (115°K) in liquid Ar and at all temperatures in liquid Kr the electron drift velocity (4-20×${10}^4$ cm/sec) at electric field strengths from -50 to -150 V/cm increases with increasing temperature. There may be a maximum in the electron drift velocity-temperature profile of liquid Kr. In this region the drift velocity is not linear in the electric field strength. It is demonstrated that an elementary scattering theory (with several variants for the scattering cross section) provides a reasonable zeroth-order description of the electron mobility in liquid Ar in the low-field, low-temperature (<115°K) region. The theory incorporates the effects of coherence in the electron scattering from nearby atoms into the cross section of a modified Boltzmann equation. The magnitude of the mobility and the pressure and temperature dependence (85-115°K in liquid Ar) of the mobility are all reproduced to better than a factor of 2. It is found that the electron velocity distribution is not thermal and that the mean electron energy may be as large as 0.5 eV, even when the electric-field strength is as low as 100 V/cm. By numerical calculation based on the elementary scattering theory, we find the onset of nonlinearity in the electric-field dependence of the electron drift velocity at $E\approx 1$ V ${\mathrm{cm}}^{-1\mathrm{}}$ in disagreement with the experimental findings described in (a). The anomalous rise of the drift velocity per unit field in liquid Ar above 115°K, and at all temperatures in liquid Kr, intuitively suggests that there may be a Ramsauer minimum in the effective electron-atom scattering cross section in the liquid. Within the framework of the elementary theories considered, we have, at present, no explanation for the anomalous temperature dependence of the electron drift velocity in liquefied Ar and Kr.