Charge distribution about an ionizing electron track in liquid helium

The dependence on an applied electric field of the ionization current produced by an energetic electron stopped in liquid helium can be used to determine the spatial distribution of secondary electrons with respect to their geminate partners. An analytic expression relating the current and distribution is derived. The distribution is found to be non-Gaussian with a long tail at larger distances.

Figure 1

Current from ${}^{63}$Ni source as a function of applied field. Symbols are data from measurements in two different cells and at different times with one of them. Representative error bars are shown for several points. The dashed and dotted lines are calculations of the escape probability using the Onsager theory of geminate recombination. The dashed line uses the distribution of charge separations shown in Fig. 2 while the dotted line is for a Gaussian distribution with $b=4\times {10}^{-6}$ cm and no tail.

Figure 2

Solid line: Distribution determined from field dependence of current using Eq. (10). Dotted line: Gaussian distribution $exp(-{(r/b)}^2)$ with $b=4\times {10}^{-6}$ cm. Dashed line: Distribution of electrons from track assuming all triplet excimers undergo Penning ionization. The vertical line at $r=4.3\times {10}^{-5}$ cm demarks the position given by $r={(e/4\pi {\epsilon }_0\mathcal{E})}^{1/2}$ corresponding to the high field separating regions where the current has been measured from that where it is extrapolated. The value r of $1.2\times {10}^{-4}$ cm marking the low field limit of current measurement is off scale in this plot.

Figure 3

The temperature dependence of the current at two different fields. Squares: 1000 V/cm. Circles: 500 V/cm.

Figure 4

Line: Empirical fit to the current at 2.5 K. Squares: current at 0.1 K in natural helium. Circles: Current at 0.1 K in helium with 6% ${}^3$He concentration.

Figure 5

Solid line: The analytic fit to the measurements of current versus field for $\beta$ particles as illustrated in Fig. 1. Dashed line: Measurements of Williams and Stacey [33] of the current produced by alpha particles stopped in liquid helium. The current for alphas is normalized such that the fraction of current is the same for $\beta$ particles at 10 V/cm.