EXPERIMENTAL VERIFICATION OF THE PHOTON THEORY OF SCATTERING

E. V. Shpolsky, Moscow

It is known that the photon theory of scattering, based on the application to the collision of a photon and an electron of the laws of conservation of energy and momentum, gave a very simple and quantitatively exact explanation of the change in frequency in the scattering of X-rays and γ-rays discovered by A. Compton. However, the Compton phenomenon also received an explanation in another theory, associated with an entirely different conception—namely, in the theory of Bohr, Kramers, and Slater¹, formulated at about the same time. According to this distinctive theory, photons do not exist at all, and the phenomenon is interpreted from a purely wave point of view. Specifically, according to the theory of Bohr, Kramers, and Slater, the picture of scattering is as follows: if the scattering electron is in the field of the incident wave, then it creates the field of a scattered wave, which propagates according to the classical laws and, moreover, as though it were emitted by a “virtual electron” moving with velocity

\[ \beta=\frac{\alpha}{1+\alpha}, \tag{1} \]

where \(\alpha\) is equal to the ratio of the “Compton wavelength” \(\Lambda=\frac{h}{mc}\) to the wavelength of the primary radiation \(\lambda_0\). The appearance of recoil electrons, according to this conception, occurs at the expense of the classical radiation pressure. But since this pressure is distributed uniformly over all electrons, while in reality only an insignificant fraction of them receives acceleration, it is assumed that the laws of conservation of energy and momentum are inapplicable to an individual act of scattering: the appearance of a recoil electron is a random event, causally unconnected with the act of scattering. At the same time, however, statistically, i.e., on the average for a large number of recoil electrons, the conservation laws are fulfilled. Thus, in the theory of Bohr, Kramers, and Slater, the domain of application of statistics is shifted: instead of the statistics of collisions, with which the photon theory deals, there appears on the scene a statistics of the correlation between the appearance of a recoil electron and the scattering of a radiation wave.

A choice between the one theory and the other can be made only on the basis of experiment. Indeed, if the photon theory is correct—

of scattering, based on the application of the conservation laws, then the following phenomena, required by these laws, must occur: 1) the recoil electron must appear simultaneously with the scattered quantum; 2) between the angles of the recoil electron and of the scattered quantum with the initial direction of flight of the quantum there must hold a simple relation following from the theory of impact; 3) the momentum vectors of the incident quantum, the scattered quantum, and the recoil electron must be coplanar. By contrast, the theory of Bohr, Kramers, and Slater requires no correspondence whatever between the recoil electron and the scattered wave, except a correspondence due to chance.

The corresponding experiments were performed soon after the appearance of these theories by Bothe and Geiger², on the one hand, and by Compton and Simon³, on the other. Let us recall the schemes and results of these experiments. In the experiments of Bothe and Geiger, a narrow beam of hard X-rays underwent scattering in the space between two counters placed close to one another opposite each other (Fig. 1), which were placed in an atmosphere of hydrogen, which thus served as the scattering substance. The recoil electrons were registered by the right (open) counter, and the scattered radiation by the left counter, filled with air and closed in front with platinum foil. Since photons themselves do not ionize air, the action of the left counter was due to photoelectrons torn from the inner surface of the foil (see the drawing). Of course, far from every scattered quantum caused the appearance of a photoelectron, and therefore the “\(h\nu\) counter” reacted only to a very small fraction of the scattered photons. But the “\(e\) counter” also reacted not to every recoil electron, but only to 1 out of 10. The deflections of the electrometers connected to the counters were recorded on a moving photographic film. According to what was said above, one could not expect every deflection of the “\(e\) counter” to correspond to a deflection of the “\(h\nu\) counter,” but one could expect, conversely, that every deflection of the “\(h\nu\) counter” should correspond to a deflection of the “\(e\) counter,” provided, of course, that the photon theory of scattering is correct. In fact it turned out that every 11th deflection of the photon counter was accompanied by a simultaneous deflection of the electron counter. The resolving power of the apparatus was \(10^{-3}\) sec., so that a coincidence could be established with an uncertainty within this time interval. In reality the situation was still less favorable, since the photon counter gave a delay of the order of \(10^{-2}\) sec. The experimenters attributed the reason for this delay to the mechanism of operation of the counter itself and tried to reduce it to a minimum by means of special attachments, shown in our schematic drawing. However, completely elim—

Fig. 1.

...it was not possible to find the lag in this way. Nevertheless, after subjecting their results to statistical analysis, Bothe and Geiger came to the conclusion that the odds could be put at 400,000 to 1 in favor of the assertion that the coincidence of the discharges of the two counters observed by them was not accidental.

Another experiment to confirm the photon theory was carried out by A. Compton and Simon. In this experiment an attempt was made, with the aid of a Wilson chamber, to record directly the elementary act of scattering and, by measuring the angles made by the recoil electron and the scattered quantum with the direction of the primary quantum, to verify that these angles satisfy the relation following from the conservation laws. To this end a narrow beam of hard X-rays was passed into a Wilson chamber (Fig. 2). The place where the scattering occurs can be established from the appearance at that place of a recoil electron (short track); if, in addition, the scattered quantum is accidentally absorbed inside the chamber, then the direction of its flight after scattering can be established from the position of the beginning of the photoelectron’s flight (long track).

Fig. 2.

If only one recoil electron and one photoelectron appeared in the photograph, then with the aid of such a photograph one could check to what extent the relation between the angles required by the photon theory was satisfied. In all, 850 stereoscopic photographs were obtained; of these only 38 proved suitable for measurements. Among these 38 photographs, in 18 the direction of flight of the scattered photon agreed with the theoretically calculated one within 20°; in the remaining 20 photographs the angles were randomly scattered, without any clearly expressed concentration about any particular value. The results obtained were also subjected to statistical treatment in the following way. First, the angle of flight of the recoil electron was measured from the photograph. From this angle the angle of flight of the scattered photon was calculated, and the difference \(\Delta\) between the observed and the theoretical value was found (cf. Fig. 2). Next, weights were assigned to the observations as follows: if one electron was found recorded on the plate, then in this case \(\Delta\) was assigned weight 1; if two recoil electrons appeared, then \(\Delta\) was determined for each of them, and each such value was assigned weight \(1/2\), etc. The results of this treatment are represented graphically in Fig. 3, from which it is seen that the actually observed deviations \(\Delta\) are noticeably concentrated around the angles \(0\)—\(20^\circ\).

At approximately the same time as Bothe and Geiger, a similar experiment was carried out by Bennett\(^4\) in Chicago. Two counters, one of which was intended for counting quanta and the other for counting ele-

of recoil electrons, were located on the shoulders of the spectrometer. The whole apparatus was placed in a vacuum. The primary radiation was supplied by an X-ray tube operating at 180 kV; the radiation was filtered through 7 mm of brass. The scattering body was oiled paper, mica; in some experiments—air at atmospheric pressure. Owing to the above-mentioned “lag” in the operation of the coincidence counters, the results proved inaccurate, and therefore this experiment did not give an unambiguous answer to the question.

Bardeen carried out a similar experiment in Chicago (unpublished). In these experiments the recoil-electron counter was first placed in position \(R_a\), where, according to photon theory, coincidences should have been observed; then it was moved to position \(R_b\), where coincidences should not have been observed. The photon counter remained in both cases in one and the same position \(P\). The result obtained was as follows: “in position \(R_a\), 71 counts were observed in \(P\) and 31000 in \(R\), of which only 8 coincided; in position \(R_b\), 112 counts were observed in \(P\), and in \(R\)—42000 with 9 coincidences. Thus coincidences are observed in the same quantity both in the correct position required by the theory and in the incorrect one.”

Fig. 3.

Finally, quite recently, P. Shankland\(^5\), in A. Compton’s laboratory, performed experiments that likewise contradict the photon theory of scattering. In contrast to the experiments described above, which were carried out with X-rays, Shankland’s experiments were set up with the \(\gamma\)-rays of radium C, which give recoil electrons of considerably higher energy. In addition, improvements were made in the construction of the photon and \(\gamma\)-quantum counters. The arrangement of Shankland’s experiment is shown in Fig. 4. The scattering body was placed at \(S\); the source of the \(\gamma\)-quanta was a tube with radon, placed at \(\gamma\). A narrow beam of rays was directed through channel \(C\) (diameter 0.80 cm); by means of special lead screens and lead shot the scattering body and the counters were protected from accidentally scattered rays. At \(P\) there was a row of five photon counters. Since the absorption of \(\gamma\)-rays in the volume of gas inside the counter is negligible, it is necessary, in order to register the scattered photons, to ensure their absorption by the walls of the counters. For this purpose the walls of the counters were made of gold (lead is unsuitable because it is slightly radioactive). The counters were connected in such a way that if a photon was absorbed in any one of them, this was sufficient for its registration. Special experiments carried out to estimate the efficiency of the arrangement showed that it registers 1 out of 125 photons, so that the prob-

the probability of absorption of a photon was \(8 \cdot 10^{-3}\). The counters were filled with air at a pressure of \(10.5\ \mathrm{cm}\) and operated at \(1400\ \mathrm{V}\).

The recoil-electron counters were placed at \(R\) at such an angle to the direction of the primary beam that it corresponded to the photon scattering angle, if these angles were calculated by applying the conservation laws to the collision of a photon with an electron. The construction of these counters was different. In accordance with the fact that they were intended for counting electrons, it was necessary to ensure that the walls were permeable to electrons. Two cylinders \(A\) and \(B\) (Fig. 5) were made of thin aluminum foil (thickness \(7 \cdot 10^{-4}\ \mathrm{cm}\)); the electrons entered the counter after passing through a thin cellophane window \(C\) (thickness \(1.7 \cdot 10^{-3}\ \mathrm{cm}\)). This counter was used in two ways: 1) coincidences were recorded when the scattered quantum caused a discharge in one of the counters \(P\), while the recoil electron discharged only one counter \(A\); these coincidences are called “double” in the table given below; 2) coincidences were recorded when the scattered quantum discharged one of the counters \(P\), while the recoil electron caused a discharge in both counters \(A\) and \(B\) at once. These coincidences are called “triple” below. The advantage of the latter arrangement was that it registered a significantly smaller number of accidental coincidences than the former. The author estimates the time resolving power of the apparatus as \(4.4 \cdot 10^{-6}\ \mathrm{min} = 2.64 \cdot 10^{-4}\ \mathrm{sec}\), i.e., one order of magnitude higher than the resolving power of the Bothe and Geiger apparatus. The expected number of accidental coincidences for each case was estimated using special statistical formulas. To check the operation of the double electron counter, preliminary experiments were carried out consisting in the following: first, a source of \(\beta\)-rays \(Y\) was placed before the counter, and then a source of \(\gamma\)-rays. In the first case, a large number of coincident pulses was obtained, indicating that the electrons do indeed pass through both counters. In the second case, the number of coincident pulses was considerably smaller than the number of discharges of each counter separately; the number of simultaneous pulses agreed satisfactorily with the calculated number of accidental coincidences. The operation of the entire

installations was carried out by placing all counters \(P\), \(A\), and \(B\) in a vertical plane and counting triple coincidences caused by cosmic-ray particles. The results obtained, according to the author (the figures are not given), agree well with results obtained by other investigators in observations of cosmic particles.

TABLE 1

Experiments with triple coincidences

TABLE 2

Experiments with double coincidences

After it had thus been established that the apparatus was working properly, experiments were carried out in order to test the photon theory of scattering. The counters of photons and recoil electrons were placed at angles calculated with the aid of the conservation laws, and the number of coincidences in the discharges of the various counters was measured. The results of these experiments are compared in two small tables, which we reproduce in full (see p. 463).

In these tables $\theta$ denotes the angle between the direction of the primary beam and the position of the electron counters. If this angle is given without any sign, this means that the counters were placed at the angle required by the photon theory; the minus sign means that the electron counters were placed on the same side, relative to the direction of the incident beam, as the photon counters; finally, the symbol $j$ before the value of the angle means that the photon counters were turned through $90^\circ$ and placed perpendicular to the plane passing through the primary beam and the centers of the photon counters. In this position, according to the photon theory, no coincidences (apart from accidental ones) are to be expected, since the conservation laws require the coplanarity of all three momentum vectors: those of the incident and scattered quanta and of the recoil electrons. The last column gives the number of coincidences expected on the basis of the photon theory, taking into account the strength of the source, the geometry of the arrangement, and the efficiency of the counters. The author himself summarizes the results obtained as follows: “A study of the tables makes it possible to establish the following facts: the number of coincidences is always smaller than that calculated according to the photon theory and in reality agrees very well with the expected number of accidental coincidences. Further, when the electron counter is placed at the angle $-\theta$ or $j\theta$, the observed number of coincidences is just as large as in the correct position $\theta$. This confirms the view that all the observed coincidences were only accidental and that the predictions of the photon theory are not confirmed by our experiment. Thus the present series of experiments, together with the experiments of Bennett and Bärden, gives results that contradict the results of Bothe and Geiger and of Compton and Simon. It is difficult to understand why the experiments described could not have detected coincidences if the latter were real; but all the experiments performed by the author, without exception, gave negative results.”

Thus the final conclusion at which Shankland arrives is that the photon theory of scattering, based on the laws of conservation of energy and momentum, is incorrect. One must treat both Shankland’s experiments themselves and, of course, his final conclusion with great caution. The paper is published with unusual brevity in such cases. The details of the experimental apparatus are not given; there are no samples whatever of protocols, etc. All this makes it difficult to judge the reliability of the results. The strongest argument in the author’s favor is that his work вы

performed under the direction of A. Compton, who, thus, together with the author bears responsibility for its results. However, this argument, of course, is insufficient for regarding the question as finally settled. A careful verification of Shankland’s work is one of the most urgent immediate problems of physics*.

It is necessary, moreover, to bear the following in mind. The photon theory of scattering, which Shankland subjected to verification, is based entirely on classical mechanics. A quantum-mechanical theory should lead to somewhat less stringent requirements concerning coincidences. Wentzel’s theory⁶, based on the application of wave mechanics, does, it is true, lead to results practically coinciding with the classical theory; however, this theory is suitable only for cases in which \(h\nu \ll mc^2\), whereas for the case of the \(\gamma\)-rays used by Shankland, \(h\nu\) is in any case of the same order of magnitude as \(mc^2\). A more precise quantum-mechanical theory, suitable also for high frequencies, may lead to less stringent conditions for angular relations, and in that case coincidences should be considerably less probable.

The applicability of the conservation laws to elementary processes in which heavy particles participate, according to the latest results of nuclear physics, is beyond any doubt. It is enough to recall Wilson photographs relating to the artificial transformation of lithium and boron by protons, with their tracks directed relative to one another at an angle of \(180^\circ\) or, respectively, \(120^\circ\), or the most precisely established relation between the mass defect and the kinetic energy of the decay products, or the emission of high-frequency quanta—strictly corresponding to the kinetic energy of the possible decay products in those cases when decay does not occur and the excess energy is returned in the form of a light quantum. In the same way, the well-known experiments of Klemperer, recently repeated by Alikhanov, Alikhanian, and Artsimovich⁷ with considerably greater care and precision, testify to the applicability of the law of conservation of momentum even to such a process as the formation of two \(\gamma\)-quanta in the annihilation of a proton-electron pair. All this compels us to treat Shankland’s results with particular caution, although, of course, the process studied by him is not identical with those just indicated. Only repeated and careful verification of these results can show whether we are dealing here with an experimental error or, indeed, with a new fact of very great significance. But even in this latter case the philosophical premise of the indestructibility of motion, of course, remains in force. If it turned out that invariants found for macroscopic motions and found to be faultlessly applicable also to elementary microscopic processes with heavy—

* According to the information available to us, such a verification has already been undertaken at the Leningrad Physico-Technical Institute by A. I. Alikhanov.

particles, are inapplicable to the case of the interaction of a photon and an electron, then this should have served only as an incentive to seek new, more general invariants.

References

1. N. Bohr, H. Kramers and J. Slater, Phil. Mag. 47, 785, 1924.
2. W. Bothe and H. Geiger, Z. Physik, 32, 639, 1925.
3. A. Compton and A. Simon, Phys. Rev., 25, 309, 1925; 26, 289, 1925.
4. R. Bennet, Proc. Nat. Acad. Sci.
5. R. Shankland, Phys. Rev. 49, 8, 1936.
6. G. Wentzel, Z. Physik, 43, 1, 1927.
7. A. I. Alikhanyan, A. I. Alikhanov, L. A. Artsimovich, DAN 1 (10), No. 7, 1936.