From Current Literature

Diffraction of Single Electrons Flying One by One

In quantum mechanics, the notion of the wave properties inherent in individual particles (electrons, neutrons, etc.) plays an enormous role. These notions are based on experiments on the diffraction of particles by various objects. Up to now, however, all experiments have been performed with intense beams of particles, and only because the independence of the diffraction pattern from the beam intensity was shown over wide limits could one, by extrapolating this circumstance to single particles, ascribe wave properties to them—that is, assert that the diffraction pattern is not the result of some collective interactions of the particles in the beam with the diffracting object. Therefore, courses in quantum mechanics discuss a “thought experiment” on the diffraction of single electrons flying one by one. It is clear that the practical realization of such an experiment has very important significance in principle.

Recently such an experiment was carried out by L. Biberman, N. Sushkin, and V. Fabrikant at the Moscow Molotov Power Engineering Institute[^1]. To observe diffraction they used a magnetic electron microscope of the transmission type (EM-100)[^2], in which a number of design changes had been made: the pole pieces of the projection lens, together with their holder, were removed; the intermediate screen and two internal permalloy screens of the objective tube were taken out. In addition, an additional diaphragm was introduced above the diffracting object, a Faraday cylinder connected to a mirror galvanometer with a sensitivity of \(2.7 \cdot 10^{-11}\) ampere per division was installed, and a device was added that made it possible to move the photographic plate without breaking the vacuum, so that up to 28 exposures could be obtained on one and the same plate.

To measure the intensity of an extremely weak beam of electrons, lying far beyond the sensitivity limits of the galvanometer, the following method was used. First an electron beam was produced with an intensity sufficient for measurement by the galvanometer; the beam was captured by the Faraday cylinder, and its intensity was determined from the deflection of the galvanometer spot. After this the Faraday cylinder was moved aside, and the beam falling on the plate was, by means of the projection lens, spread out into a series of spots with gradually increasing diameters (up to 10 cm). A photometric check showed that the blackening density was the same within each spot; therefore, for each spot the electron density was determined as the quotient of the known beam intensity divided by the area of the spot. By the intensity of blackening

and electron density, a blackening curve was constructed for each photographic plate, making it possible to determine beam intensities at least five orders of magnitude below the sensitivity limit of the galvanometer. After this the beam intensity was sharply reduced, and, with the lenses switched off, the trace of the beam was recorded on the plate; from this the intensity of the weak electron beam was determined. Then a diffracting object was placed in the path of the beam—magnesium oxide crystals deposited on a collodion film—with the aid of which a diffraction pattern was obtained. To check the constancy of the intensity, the diffracting object was removed after the exposure, and the trace of the beam was again recorded on the plate. The diffraction patterns of strong beams were obtained in the usual way on photographic plates of considerably lower sensitivity.

Thus diffraction patterns were obtained from beams differing in intensity by almost seven orders of magnitude. They proved to be completely identical. Measurement of the intensity of the weak beam gave a value of \(4.2 \cdot 10^3\) electrons per second. Hence the average time between two passages of electrons through the apparatus was \(2.4 \cdot 10^{-4}\) sec. Since the electrons were accelerated to an energy of 72 keV, each of them traversed the entire path in the apparatus in \(8.5 \cdot 10^{-9}\) sec, i.e., the time of flight was \(3 \cdot 10^4\) times smaller than the interval between two electron impacts on the plate. In other words, the picture of the motion of electrons in the apparatus when obtaining the diffraction pattern from the weak beam was as follows: an electron traversed the apparatus in \(8.5 \cdot 10^{-9}\) sec, then during an interval 30,000 times (!) longer than the transit time through the apparatus, the apparatus remained empty, and only after this did a new electron pass through it. It is obvious that, with such an enormous time interval between successive passages, the probability of the simultaneous passage of even two electrons is completely negligible.

There is no doubt that this experiment will in the near future enter all courses of quantum mechanics.

V. L.

Cited Literature

1. L. Biberman, N. Sushkin, and V. Fabrikant, DAN SSSR, LXVI, 185 (1949).
2. N. Sushkin, The Electron Microscope, Gostekhizdat, 1949.