Ratio of diffusion coefficient to mobility for electrons in liquid argon

Abstract

The ratio of the diffusion coefficient $D$ to the mobility $\ensuremath{\mu}$ for electrons has been measured in liquid argon by using a modified Townsend apparatus. The measured ratio $\frac{\mathrm{eD}}{\ensuremath{\mu}}$ monotonically increases from \ensuremath{\sim}0.1 to \ensuremath{\sim}0.4 eV with an increase in the electric field from \ensuremath{\sim}2 to \ensuremath{\sim}10 kV/cm. The ratio $\frac{\mathrm{eD}}{\ensuremath{\mu}}$ is smaller than that in gaseous argon at the same value of $\frac{E}{N}$, where $N$ is the atomic density. The mean momentum-transfer cross section $〈\ensuremath{\sigma}〉$ is estimated as a function of $〈\ensuremath{\epsilon}〉$ on the assumption $〈\ensuremath{\epsilon}〉=\frac{3eD}{2\ensuremath{\mu}}$, where $〈\ensuremath{\epsilon}〉$ is the mean electron agitation energy. Thus the $〈\ensuremath{\sigma}〉$ obtained is nearly constant (3\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$) for $〈\ensuremath{\epsilon}〉$ from 0.15 to 0.6 eV. This value of $〈\ensuremath{\sigma}〉$ is almost the same as that estimated from the low-field mobility of electrons in liquid argon. This result is consistent with both Derenzo's experiment and Lekner's theory. It is concluded that there is no Ramsauer minimum at about 0.4 eV of $〈\ensuremath{\epsilon}〉$, where the minimum exists in gaseous argon.