PHOTON SCATTERING AND THE LAWS OF CONSERVATION OF ENERGY AND MOMENTUM¹

K. Vulfson, Moscow

Shankland’s experiments² aroused the liveliest interest and drew the attention of physicists to the question of the applicability of the laws of conservation of energy and momentum to elementary processes of interaction between radiation and matter. Following Shankland’s publication, a number of papers³, ⁴, ⁵ appeared discussing the consequences following from these experiments. The cardinal importance of one or another solution of this fundamental question did not allow one to confine oneself to Shankland’s experiments alone. It was necessary to increase the amount of experimental material, applying various methods of studying this phenomenon, before introducing changes into our ideas about the conservation laws. A whole series of the largest laboratories undertook to verify the results of Shankland’s experiments; and he himself continued his work and, after modifying the apparatus, came to a different conclusion. All the work carried out at the present time may be divided into three groups according to the research methods used in them: Group I, represented by the largest number of works, in which the Compton phenomenon is studied with the aid of counters; this includes the works of Bothe and Maier-Leibnitz⁶, Jacobsen⁷, and Shankland⁸. The use of counters makes it possible to record very accurately the simultaneity of emission of the scattered quantum and the recoil electron and at the same time to determine, with small accuracy, the angles of scattering and recoil. Group II, in which the phenomenon is studied with the aid of a Wilson chamber. Finally, in Group III an entirely new method, proposed by Piccard* and Stahel⁹, is used, making it possible to test the simultaneity of emission of the electron and the quantum with exceptional accuracy—down to one ten-millionth of a second. At the same time, this method leaves completely open the question of the directions of scattering and recoil.

Anticipating somewhat, let us say that all the experiments described permit one to draw the unequivocal conclusion that Shankland’s first work was erroneous and lead to the conclusion that the conservation laws are applicable to elementary acts of photon scattering.

* The well-known stratosphere researcher.

Particularly convincing in this respect is the work of Bothe and Maier-Leibnitz. In their apparatus these authors took all measures to eliminate possible sources of error not excluded by Shankland in his first work; at the same time they tried to reproduce the conditions of his work as accurately as possible. Whereas Bothe and Geiger used soft X-ray waves, Shankland employed hard γ-rays, and therefore in the new experiments of Bothe and Maier-Leibnitz γ-rays even harder than in Shankland’s experiments were used. However, unlike Shankland, Bothe and Maier-Leibnitz took measures to ensure the possible monochromaticity of the γ-rays, regarding violation of this condition as one of the most important sources of error.

Fig. 1.

The apparatus of Bothe and Maier-Leibnitz, shown schematically in Fig. 1, consisted of a massive piece of lead, in which a narrow channel 7 mm in diameter was carefully drilled; this limited the primary beam of γ-rays with quantum energy 2.65 MeV (the amount of preparation was equal to 20 mg radium equivalent). By using a filter (1 cm of lead) the possible homogeneity (monochromaticity) of the beam was ensured. The scatterer was a thin cellophane film weighing 0.028 g per 1 cm². Geiger–Müller counters served to detect recoil electrons and scattered quanta. The chief difficulty associated with the use of counters for detecting γ-quanta is the low efficiency of the counter (of the order of \(1/1000\)). This means that approximately only one out of 1,000 quanta is counted. Such a small efficiency is a consequence of the large difference between the absorption coefficients of electrons in the walls of the counter and of the γ-quanta that produce them. Some improvement can be achieved by arranging several counters in succession, but at the same time this measure leads to an increase in the number of accidental coincidences, complicates the apparatus, and makes the experiment less transparent. For this reason, more than two counters arranged in succession were not used (whereas in Shankland’s first work their number reached five). The counters, 12 mm in diameter and 15–20 mm long, were made of aluminum foil 0.8 mm thick. The γ-quantum counters also had removable,

lead housings. In the first series of experiments the distance from the scatterer to the counters was 45 cm, and the scattering angle of the electrons and photons was chosen to be the same and, according to classical theory, was equal to \(30^\circ\). Coincidences of pulses from the \(\beta\)- and \(\gamma\)-counters were recorded according to the circuit proposed by Rossi \(^{10}\). The circuit operated quite stably even at a resolving power of \(3\cdot 10^{-5}\) sec. Such a high resolving power is necessary because of the rarity of systematic coincidences. To exclude possible accidental coincidences, most of which are caused by cosmic rays, radioactivity of surrounding objects, etc., coincidences were counted in the absence of a scattering substance (the zero effect). In order that the absolute number of pulses given by the \(\beta\)-counter should not decrease in this case, it was subjected to additional \(\beta\)-irradiation by a weak radioactive preparation (compensation). Owing to this procedure, exact knowledge of the resolving power of the circuit is not necessary. The use of compensation greatly increases the reliability and accuracy of the measurements. The sequence of measurements was as follows: first the “zero effect” was determined; then, over the course of 14.5 hours, coincidences were counted. From time to time the operation of the recording circuit was checked by producing artificial coincidences. The results of all four series of experiments are compared in Table 1.

The first experiment was carried out with one \(\gamma\)-counter; in the remaining parts the apparatus corresponds to Fig. 1. The scattering angle indicated in the second column denotes the angle between the primary direction and the line connecting the middle of the layer with the middle of the counter.

Fig. 2.

Fig. 3.

From the table it is seen that insertion of the layer increases the number of coincidences many times over. This increase can be explained only by coincidences caused by the simultaneous appearance of \(\gamma\)-quanta and recoil electrons. In the last column is given the number of systematic coincidences, referred to the number of additional \(\beta\)-pulses caused by the recoil electrons.

TABLE 1

* without compensation
* rejections compensated
** one γ-counter.

To increase the absolute frequency of systematic coincidences, in the subsequent experiments two γ-counters were used, placed one after the other in succession and connected in parallel (Fig. 2). In addition, the counters were filled with argon instead of air, which also increased the probability of their triggering. In all other respects the second experiment exactly repeated the first. The table shows that in this way the number of coincidences increased appreciably. The third experiment corresponded to a position of the counters in which the primary ray and the scattering directions were non-coplanar. For this purpose the β- and γ-counters were turned upward about the primary direction by 45° (Fig. 3). In this case only the lower edges of the counters fell אין

from the plane of scattering. In such a position, coincidences could be caused only by particles flying almost exactly horizontally. Turning only one counter through \(90^\circ\) increased the “zero effect” more than twofold. This shows especially convincingly how important it is to determine the “zero effect” with the geometrical arrangement of the apparatus unchanged. As can be seen from the table, the coincidences during the third experiment, insofar as they occur at all,

Fig. 4.

constitute only a small fraction in comparison with the number of coincidences in the second experiment.

The fourth experiment was intended to confirm that scattering occurs predominantly in the directions indicated by the photon theory. Unlike Shankland, who moved the counters during an individual experiment, a different method of changing the angle was chosen, one that guaranteed the constancy of the number of coincidences caused by cosmic rays. For this purpose the counters were moved somewhat away from the opening of the channel, so that the “correct” position of the scattering layer was \(1.8\ \mathrm{cm}\) from the edge of the channel. Measurements were made for three positions of the layer: \(0\), \(1.8\), and \(3.6\ \mathrm{cm}\) from the edge of the channel. Figure 4 shows the relative arrangement of the counters and the layer, and also indicates the directions of photon scattering and the conjugate directions of recoil, determined by the position of the \(\beta\)-counter. The results of the measurements and the mean errors are presented in the diagram of Fig. 5. The predominance of the number of coincidences in the direction required by the theory is quite clearly visible.

A natural question arises: cannot the simultaneous appearance of a quantum and an electron be explained by other processes? Indeed, simultaneous β- and γ-rays can arise in pair formation and the subsequent annihilation of the positron. However, in view of the negligible probability of these processes, they cannot explain the number of coincidences observed. In this connection it is of interest to compare the number of observed coincidences with that which would be expected on the basis of the efficiency of operation of the counter itself.

Fig. 5.

Bayer \(^{11}\) determined that, for a counter similar in construction to that used in this work, the probability of response for γ-rays of 3 MeV is approximately \(6\cdot 10^{-3}\). Introducing corrections for the difference in the dimensions and material of the counter, and also for the energy of the γ-ray quantum and the voltage applied to the counter, Bothe and Maier-Leibnitz determine the probability of response of one γ-counter as \(4.2\cdot 10^{-3}\), and of two as \(7.6\cdot 10^{-3}\). Comparing with this the observed number of coincidences per electron, \(1.6\cdot 10^{-3}\) (the mean of the second and fourth experiments, see Table 1), we see that it is 4.8 times smaller than would follow for an ideal arrangement, in which every γ-quantum correlated with the recoil electron necessarily entered the γ-counter. In practice, however, this cannot be fully realized. Owing to the finite size of the β-counter, not all γ-directions correlated with the admissible β-directions fall into the γ-counter. Moreover, the recoil electrons undergo scattering in the cellophane layer, which disturbs the strict coordination of directions and thus also reduces the number of correlated quanta entering the γ-counter. The circumstances indicated, although they cannot be accounted for very accurately, lead to a coefficient of 3 by which the number of observed coincidences must be multiplied. Thus there remains only the factor \(\frac{4.8}{3}=1.6\). It can be fully explained by the not absolute monochromatization of the primary beam and by other small imperfections of the apparatus.

It is also possible to estimate the absolute number of coincidences. Using the data of Shenstone and Schlundt \(^{12}\), who studied the radiation of ThC,

it can be determined that 1 g radium equivalent of RaTh emits in 1 sec. \(1.57 \cdot 10^{10}\) \(\gamma\)-quanta. Hence, using the Klein–Nishina formula, it can be calculated that each minute, in the “correct” position, 25 quanta should enter the \(\gamma\)-counter. From the second and fourth experiments 58 coincidences are obtained, which amounts to only \(1/370\) of all the quanta that entered. It was shown above that in an ideal setup only \(1/33\) of all the quanta that entered would be recorded. The discrepancy by a factor of 2.8, with excess (coefficient 3), is covered by the imprecise geometrical correspondence of the directions of scattering and recoil, and also by scattering of the electrons in the layer itself. With such a method of calculation there naturally drops out the influence of the inhomogeneity of the radiation and of the interfering radiation scattered by the walls of the lead channel. Thus the experiments described show that the simultaneity, required by the theory, of the emission of scattered quanta and recoil electrons in the directions indicated by it exists, and is absent for any deviation from these directions.

The number of coincidences, within the accuracy of the experiment, agrees with that calculated on the basis of theoretical considerations and the data of the apparatus.

By the same method as that used by Bothe and Meier-Leibnitz, Jacobsen carried out his experiments. In his apparatus the source of the primary \(\gamma\)-rays was also a RaTh preparation (10 g radium equivalent), the radiation of which was filtered in a layer of lead 5 mm thick. The scattering layer was a layer of paraffin 0.05 cm thick. The angles of scattering and recoil were equal to \(30^\circ\). The counters (single-operation) were 20 mm in diameter.

To determine the number of random coincidences, Jacobsen, unlike the work described above, does not remove the scattering layer, but shields the \(\beta\)-counter with a lead plate. The constancy of the number of operations of the \(\beta\)-counter is maintained by additional irradiation with a RaD preparation. The results of the experiments, carried out only in the “correct” position, are summarized in Table 2.

TABLE 2

* The increase in the number of random coincidences in the second series of observations is explained by irradiation of the counter with a weak RaD preparation;

The predominance of systematic coincidences over measurement errors is quite obvious. A rough estimate of the efficiency of the apparatus gives eight coincidences per hour, which agrees quite well with the number found experimentally. The last column of Table 2 gives the number of coincidences referred to one recoil electron*. It is somewhat higher than in the experiments of Bothe and

Fig. 6a and b

Meyer-Leibniz \((0.58 \cdot 10^{-3})\). This is probably explained by some difference in the dimensions of the apparatus—the larger diameter of the counters and the smaller distance to the scattering layer. Thus, Jakobsen’s experiments, although not as comprehensive as the above-described experiments of Bothe and Meyer-Leibniz, confirm the correctness of the usual theory of the Compton effect.

The last in this group of investigations should be named the second work of Shankland. The arrangement of the apparatus used by him is shown in Figs. 6a and 6b. This figure shows the mutual arrangement of the counters and the scattering layer of paraffin (dimensions \(4 \times 1 \times 0.05\ \text{cm}\)). The \(\gamma\)-counter was made of copper, the thickness of which was sufficient to stop electrons. The positions of the counters in which the largest number of coincidences was observed did not stand out sharply because of the insufficient homogeneity of the \(\gamma\)-radiation \((84\ \text{millicurie RaC})\).

* These numbers were obtained by us from a comparison of the data given by Jakobsen.

Observations were carried out in a vacuum in order to exclude electrons scattered by air. The results of the experiments are presented in Table 3.

TABLE 3

It is clear from the table that, when the counters are in the mismatched position (experiments $C$ and $D$), the number of coincidences does not depend on the presence of the scatterer. In the correct position, however, the number of coincidences increases sharply. On the basis of these experiments, Shankland himself, without mentioning his first experiments, draws the conclusion that the scattered quantum and the recoil electron appear simultaneously.

Williams and Pickup[^13], in order to test Shankland’s experiments, used a Wilson chamber. They passed a narrow beam of X-rays ($h\nu = 20\,000\ \mathrm{V}$) into a Wilson chamber filled with argon. Photoelectrons torn from the $K$-level are, in most cases, accompanied by electrons arising as a result of the Auger effect. Such processes give double tracks in photographs, designated in Fig. 7 by the letter $P$. In those cases where

Fig. 7.

the scattered quantum is absorbed in another atom, it in turn produces in it a photoelectron, recorded in the photographs as a short separate track. This process is represented in Fig. 7 by the combination of two tracks $F$ and $Q$. The dashed line represents the path of the light quantum.

A total of 350 photographs were obtained (approximately 10 tracks on each, with an effective chamber length of 14 cm); the photographs were measured and the distances $x$ along the primary beam between the $F$- and $Q$-tracks were determined. In Fig. 8 the solid line represents the found-

...distribution of distances obtained from experiments. The hatched line shows the distribution computed from the conservation laws, and, finally, the dotted line shows the distribution corresponding to the statistical theory. From Fig. 8 it is evident that the experimental data agree much better with the curve calculated from the laws of conservation of energy and momentum.

The new method of investigating the simultaneity of absorption and emission proposed by Piccard and Stahel \(^{9}\) is based on the use of a moving (rotating) scatterer.

Fig. 8.

Fig. 9.

If the electron and the quantum are emitted with some time delay relative to one another, then their emission cannot coincide with the primary process of absorption of the incident quantum. In other words, a body irradiated with \(\gamma\)-rays continues, owing to the Compton effect, to emit recoil electrons and scattered quanta even if the source of irradiation is removed.

The apparatus used by these authors is shown schematically in Fig. 9. \(C_1\) and \(C_2\) are small ionization chambers, charged approximately to \(+500\) and \(-500\ \mathrm{V}\). The electrometer, connected to the central electrodes, thus measures the difference of the ionization currents. At a distance of several millimeters from the chambers there is a disk \(D\), 35 cm in diameter, capable of rotating in both directions at a speed of 30 rev/sec. Radium, in an amount of 600 \(m\) [[unclear: unit]], was placed either between the disk and the chambers (position \(B\)) or behind the disk (position \(A\)). Part of the measured ionization was caused by electrons and photons formed in the disk owing to Compton—

effect. If their emission occurred with some delay, then the current in chamber \(C_2\) would increase upon rotation in the direction indicated in Fig. 9. Changing the direction of rotation would give an effect of the opposite sign. The situation would be as though the radium were being carried along by the rotation.

To calibrate the apparatus it was possible to displace the radium preparation micrometrically. The rate of fall of the electrometer fiber (it determines the ionization current) is a function of the position of the preparation. To each change in the rate there corresponds a definite displacement of the radium (Fig. 10).

Fig. 10.

In studying the emission of recoil electrons, disks of aluminum, iron, and iron coated with lead were used. The radium was placed behind the disk in position \(A\). In order that the electrons could penetrate into the ionization chambers, the entrance apertures were made of aluminum foil \(0.008\) mm thick. About \(30\%\) of the ionization was caused by recoil electrons arising in the disk.

Table 4 gives the results of one series of measurements. The sign \(+\) indicates that the change corresponds to entrainment of the radium in the direction of rotation of the disk. (It should be noted that such a change of current corresponds on average to \(1/200000\) of the total ionization current.) The calibration described above shows that a displacement of the radium preparation to the side by \(0.01\) mm produces a change in the rate of fall of the electrometer fiber by \(0.96\) div/sec. Hence the observed effect will be equivalent to a virtual displacement of the radium equal to \(0.065 : 0.96 = 0.00068\) mm. The linear velocity of the disk in the part passing by the chambers is approximately \(2800\) cm/sec. A displacement of \(0.00068\) mm would correspond to a delay of \(0.000068\) cm \((2800\ \text{cm/sec} = +\,2.2 \cdot 10^{-8}\ \text{sec})\), if all the ionization were caused by recoil electrons. Taking into account that only \(30\%\) of the ionization is caused by them, we find the delay time in this series of meas—

TABLE 4

Rate of decrease of the electrometer readings

TABLE 5

measurements equal to \(+7\cdot10^{-8}\) sec. A summary of the results of all series of measurements concerning recoil electrons is given in Table 5.

The table shows that there is no systematic delay in the emission of recoil electrons. It may be asserted that recoil electrons are emitted with a delay unquestionably less than \(10^{-7}\) sec.

Similar measurements were also carried out for scattered \(\gamma\)-rays. The disk was of iron, 5 mm thick. The radium was placed between the disk and the ionization chambers (position \(B\)) so as to permit the study of \(\gamma\)-rays scattered at large angles. Under these conditions only \(4\%\) of the ionization was caused by scattered \(\gamma\)-radiation. In addition, it must be borne in mind that, owing to the greater distance of the disk, a virtual displacement of the disk is less effective than an actual displacement of the radium. Certain measurements made in this direction showed that the correction coefficient is \(1:4\). Ultimately the “entrainment” of scattered \(\gamma\)-rays would be 100 times less effective than the real shift of the radium. The experiment showed that a change in the rotation of the disk causes a change in the ionization current corresponding to a displacement of the radium by \(+0,0001\) mm; in another series of measurements it was \(0,00007\) mm. On the average the change is less than \(0,0001\) mm. Taking into account the factor 100 indicated above, we find that this displacement corresponds to a delay of less than \(2\cdot10^{-7}\) sec. From these experiments it may be concluded that, within the accuracy attained and within \(10^{-7}\) sec, the absorption of the primary quantum and the emission of secondary rays occur simultaneously.

All the work described confirms the strict applicability of the laws of conservation of energy and momentum to elementary acts of interaction between radiation and matter.

To this same assertion also comes, in his letter published in Nature[^14], Niels Bohr, who in his time, together with Kramers and Slater, proposed the hypothesis[^15] of the statistical character of the conservation laws in atomic processes. Objecting to Dirac, he points out that the situation in physics, from the time his theory appeared up to the present, has changed greatly. The development of quantum mechanics has confirmed these laws to an even greater degree, and there are now no grounds whatever for doubting their validity.

References

1. For a review of the preceding works on this question, see E. V. Shpolsky, Uspekhi fizich. nauk, 16, 458, 1936.
2. Shankland, Phys. Rev., 48, 8, 1936.
3. P. Dirac, Nature, 137, 298, 1936.
4. Williams, Nature, 138, 614, 1936.
5. Peierls, Nature, 137, 904, 1936.
6. W. Bothe and Meyer-Leibnitz, Z. Physik, 102, 143, 1936.
7. C. Jacobsen, Nature, 138, 25, 1936.
8. Schankland, Phys. Rev., 50, 571, 1930.
9. A. Pikard & Stahel, Journ. Phys. et Radium, 7, 326, 1936.
10. Rossi, Nature, 125, 636, 1930.
11. H. Bayer, Z. Physik, 95, 417, 1935.
12. Schenston and Schlundt, Phyl. Mag., 43, 1038, 1922.
13. E. Williams and E. Pickup, Nature, 138, 46, 1936.
14. N. Bohr, Nature, 138, 25, 1936.
15. N. Bohr, H. Kramers and J. Slater, Z. Physik, 24, 69, 1924.