Experiments with single electrons in liquid helium

We describe experiments we have performed in which we are able to image the motion of individual electrons moving in liquid helium 4. Electrons in helium form bubbles of radius ~19 Å. We use the negative pressure produced by a sound wave to expand these bubbles to a radius of about $10\mu \text{m}$. The bubbles are then illuminated with light from a flash lamp and their position recorded. We report on several interesting phenomena that have been observed in these experiments. It appears that the majority of the electrons that we detect result from cosmic rays passing through the experimental cell. We discuss this mechanism for electron production.

Figure 1

Energy of an electron bubble as a function of radius. The curves are labeled by the pressure in bars.

Figure 2

Calculated radius of a bubble as a function of time based on Eq. (5). The different curves are labeled by the amplitude of the sound wave in bars.

Figure 3

Cross-sectional view of the lithium niobate ultrasonic transducer.

Figure 4

Two images of an electron moving down the cell. The temperature is 1.5 K.

Figure 5

Amplitude of the sound wave needed to explode an electron bubble as a function of temperature. The solid curve is the data of Classen et al. (Ref. 2) and the crosses are the present data.

Figure 6

Images in which an electron bubble is first seen at a point in the interior of the cell rather than near to the surface of the transducer. The temperature is 1.8 K.

Figure 7

Images in which more than one electron are seen. The temperature is 1.8 K.

Figure 8

Images of an electron moving under the combined influence of the upward convective flow of the liquid and an applied electric field. The electrode is at the bright spot at the top of the window. Voltage on the electrode is (a) 50, (b) 150, and (c) 500 V. The temperature is 2.4 K.

Figure 9

Images of an electron following a snakelike track which may relate to the electron being trapped on and sliding along a vortex line. The temperature is 1.5 K.

Figure 10

Image taken when the cell contained a 5 mCi ${}^{63}\text{N}\text{i}$ beta source in the liquid. The transducer is at the bottom of the cell. Only those electron bubbles that are in the sound field of the transducer explode.

Figure 11

Results of a computer simulation of the escape probability $f_{\text{gold}}$ from the gold film on the transducer as a function of the mean range of the photoejected electrons. The different curves are labeled by the velocity of the normal fluid in $\text{cm}{\text{s}}^{-1}$. The simulations are for a temperature of 1.8 K.

Figure 12

Calculated escape probability $f_{\text{ion}}$ of an electron bubble from a positive ion as a function of the mean range of the electron. The calculation is for a temperature of 1.8 K.