ON THE NATURE OF COSMIC RADIATION

F. Halperin, Moscow

1. Ever since the discovery of cosmic rays in 1911 by Hess and Kolhörster, the conception of these rays as wave radiation became established in physics. Historically, the first argument in favor of such a nature of cosmic rays was the circumstance that their penetrating power at that time did not differ very greatly from the penetrating power of $\gamma$-rays. But this argument cannot be considered weighty, since it is known that rapidly moving electrons also possess great penetrating power. Among a number of other arguments in favor of the wave nature of cosmic rays, an extraordinarily strong argument was that the absorption coefficients calculated from Dirac’s formula for waves emitted in the formation, in a single act, of helium, oxygen, silicon, and iron atoms from hydrogen atoms—these coefficients, within the limits of accuracy of the experimental measurements, coincided with the absorption coefficients of the corresponding curves into which Millikan and Cameron decomposed the experimental curve showing the dependence of atmospheric ionization on altitude. On the basis of the almost exact coincidence of these coefficients, Millikan and Cameron asserted that cosmic rays are quantum radiation accompanying the formation of the above-mentioned complex atoms from hydrogen atoms in a single act, and not gradually.* The question of the nature of cosmic rays could be regarded as almost definitively settled in favor of their wave character,

* Cf. Millikan and Cameron.

but it was again raised by the latest works of Bothe and Kolhörster. In their experiments with Geiger–Müller counters they counted the number of coincidences in electrometers connected with these counters, i.e. the number of simultaneous passages of a cosmic ray through both counters, and this number proved to be very large. This result, in the authors’ opinion, proves that in these experiments they were dealing with corpuscular radiation. Having obtained an absorption coefficient of the latter almost equal to the absorption coefficient of cosmic rays, Bothe and Kolhörster finally confirmed themselves in the conclusion that cosmic rays possess a corpuscular structure and represent a stream of rapidly moving cosmic electrons. It is important to note that such an electronic nature of cosmic radiation excludes those assumptions which Millikan built concerning the origin of cosmic rays, for according to Einstein’s well-known equation \(mc^2 = E\), in atomic formations due to the mass defect, wave radiation is emitted. Cosmic electrons cannot be emitted in such processes, and if Bothe and Kolhörster’s views on the nature of cosmic rays were correct, then it is clear that they would automatically entail the rejection of Millikan’s constructions concerning the origin of these rays. The experimental and theoretical works reviewed in this article are devoted to new proofs of the wave nature of cosmic rays.

1. The basic idea of Millikan’s latest experiments (1929–1930) is as follows: if cosmic rays are indeed a stream of cosmic electrons moving with high velocities (which follows from the assumptions of Bothe and Kolhörster), then these electrons must be noticeably deflected in the earth’s magnetic field, and moreover not equally in its different places: more strongly in places close to the poles, more weakly in those more distant from the poles. Therefore, at different geographical latitudes, under such an interpretation of the nature of cosmic rays, the intensity of the latter must be different. Having at his disposal

...or an electroscope more perfect and twice as sensitive as the electroscope with which experiments were carried out in 1928, Millikan continuously, day and night from 26/VII to 3/VIII 1930 in Pasadena, at latitude 34°, and from 25/VII to 1/IX 1930 in Churchill, at latitude 59°, measured the intensity of cosmic rays. The results of these measurements, published in The Physical Review, December 1930, show an almost identical mean intensity—in Pasadena 26.30 ions per cm³ per second, in Churchill 28.31 ions per cm³ per second. Millikan estimates the error in these measurements at no more than 1%. From these data Millikan concludes, first, that cosmic rays penetrate the earth’s atmosphere as electromagnetic radiation, and not as electrons, and, second, since the region of the sky from which the rays pass through to Churchill is entirely different from that from which the rays reach Pasadena, that cosmic rays arrive at the earth uniformly from all regions of the sky. Further, Millikan proved experimentally that the intensity of cosmic rays is independent of the position in the sky of the Milky Way. In the course of two weeks, measuring the intensity of these rays in Pasadena, Millikan noticed that it passes through its maximum after noon (Table I).

TABLE I

Intensity of cosmic rays

(only mean values are given in the table)

1. The Milky Way overhead during the entire time. 2. The Milky Way overhead for the greater part of this time. 3. The Milky Way not visible at all. 4. The Milky Way partly overhead. 5. The Milky Way overhead for the greater part of this time. 6. The Milky Way not visible at all. 7. The Milky Way partly overhead. 8. The Milky Way overhead during the entire time.

The intensities are expressed in ions per cubic centimeter per second. In the table no account is taken of the correction for ionization in the electroscope produced by rays of local radioactive origin passing through the lead shield of the electroscope. Millikan at first assumed that this maximum of intensity was connected with the position of the Milky Way in the sky, but soon established himself that this is not so; Table I shows this. In the data from 19/VII—27/VII 1930 the intensity passes through its maximum after noon (afternoon), when the Milky Way is not visible at all in the sky. The position of the Milky Way in the sky is the same in the morning (see the measurements from 6/X to 12/X 1929), and yet the maximum intensity of the cosmic rays again occurs after noon. Millikan’s conclusion from this is that the Milky Way has no influence whatever on the intensity of the cosmic rays and that therefore the latter must originate in the “depths of space outside the Milky Way.” The real explanation of this behavior of the cosmic rays lies in changes occurring in the atmosphere. When the sun rises and begins to heat the earth, the air begins to expand and rise upward. Something like a hole is formed in the atmosphere, through which the cosmic rays after noon (by that time the earth is most heated) pass with the greatest intensity.

1. Likewise devoted to proving the incompatibility of the electronic nature of cosmic rays with experimental observations above us is a mathematical paper by P. Epstein, printed in the “Proceedings of the National Academy of Sciences of the USA” for October 1930. Epstein takes the energy of the cosmic electrons to be \(10^8\) V, a value adopted by him from Rossi, a follower of Bothe and Kolhörster. By means of a whole series of mathematical calculations, which we do not reproduce here because of their cumbersomeness, Epstein proves that cosmic electrons possessing such energy can arrive at the earth only in two quite limited zones around the earth’s magnetic poles.

Practically all places on Earth where cosmic rays are observed lie outside these zones. This leads, in the opinion of the author of these arguments, to the following three possibilities: 1) cosmic rays are electromagnetic waves, 2) they are corpuscular rays, but in order for them to reach those places on Earth where cosmic rays have actually been observed, they must possess considerably greater energy than \(10^9\) V (at least \(6 \cdot 10^{10}\) V), 3) they are of terrestrial, non-cosmic origin.

1. The curve representing the dependence of the ionization of the atmosphere on depth, obtained by Millikan and Cameron in 1928, suffered from two defects: first, it gave ionization for depths below the “top” of the atmosphere, in absorption equivalent to a column of water not more than 67 m high; at greater depths the apparatus of these investigators proved insensitive to the detection of radiation of such great penetrating power, while already in 1928 experiments by Regener had been carried out at considerably greater depths; secondly, the upper part of the above-mentioned curve corresponded to radiation with an absorption coefficient of 0.35 per meter of water, whereas at levels corresponding to the upper part of this curve, in Millikan’s opinion, radiation should be observed which accompanies the formation of helium from hydrogen atoms in a single act, and for this radiation the absorption coefficient calculated by Dirac’s formula is equal to 0.30 per meter of water. These two circumstances prompted new experiments by Millikan and Cameron with the aim of improving the curve of the dependence of ionization on depth, both in its lower part (for great depths below the top of the atmosphere) and in its upper part (for great heights above sea level). To detect weak effects at great depths under water and to increase sensitivity, a new spherical electroscope was constructed. Its internal volume is \(1\,622\ \text{cm}^3\), its internal pressure about 30 atm. The thickness of its steel walls is 3 mm. The capacitance of the electroscope is 0.979 electrostatic units. The pressure in it was maintained for two years without any sign of decrease. The insulating quartz sup-

the setting was so good that the potential over four hours decreased only by 0.5 volts, from 226.5 to 226.0 volts.

For observations over land the electroscope was surrounded by a lead shield 7.64 cm thick. The sensitivity of the electroscope was thus doubled in comparison with the sensitivity of this instrument in 1928. This electroscope is shown in Fig. 1.

The electroscope, during the summer months of 1928–1929, was lowered into two lakes: Arrowhead, at an elevation of 5,100 ft above sea level, and Gem, at an elevation of 9,120 ft. The greatest depth under water to which the electroscope was lowered was 72.6 m. Taking into account the atmospheric column above the surface of the lake, this amounts to 80 m of water below the “top” of the atmosphere. At this depth ionization in the instrument was still observed, averaging 2 ions per cubic centimeter per second. Data relating to depths of immersion of the electroscope less than 0.85 m were not taken into account, and thus the participation in the ionization of radioactive rays coming from the rocks and soil surrounding the lake was excluded. Taking into account the absorption of the atmospheric column above the surface of the lake, this highest level of immersion of the electroscope was 8.25 m of water below the “top” of the atmosphere. At this level the observed ionization was 64.1 ions per cubic centimeter per second.

Fig. 1.

On the other hand, with this same electroscope, during the summer months of 1928–1929 and 1930, observations were made on the summit of Pikes Peak (14 thousand ft above sea level). Ionization was observed in the instrument once when it was surrounded by a lead shield, and another time without a shield. Knowing from preliminary experiments that through lead pass—

...will constitute 2.4% of the rays of local radioactive origin. It was easy to determine the ionization produced only by cosmic rays. The number of rays of local origin can be found by subtracting from the ionization at a given level, obtained when the electroscope is surrounded by an ionization shield, the ionization for the same level taken from the data for measurements under water. The greatest height of ascent of the electroscope is 6.195 m of water below the upper boundary of the atmosphere, whereas in 1928 it was about 8 m of water.

Millikan and Cameron attach very great importance, for the question of the origin and nature of cosmic rays, to the fact that this time it was possible so to extend the curve of the dependence of ionization on depth in its upper part. It is precisely at great heights that the greatest discrepancy between theory and experimental data has hitherto been found.

Fig. 2.

Analysis of the curve constructed from the results of underwater and above-water measurements shows, first, that even a layer of water 80 m thick does not absorb all cosmic rays. At the point of the curve corresponding to a depth of 80 m, the curve continues to descend. Millikan and Cameron point out that, in order to determine the zero of the electroscope, i.e. the ionization (when all external rays have been absorbed), and the absorption coefficient of these hard rays, they analyzed this curve with the aid of Gold’s tables and found that, if the zero of the electroscope is 1.2 ions per cm³ per second and the absorption coefficient is 0.028 per meter of water, then the obtained experimental curve is well reproduced in the interval from 40 to 80 m of water. From the existence of such an absorption coefficient it follows that even at a depth of 180 m of water an ionization of 0.03 can still be detected by very sensitive instruments.

ions per cubic centimeter per second. The penetrating power of the rays producing ionization at such a depth is twice as great as that which until now had been directly observed by Millikan and Cameron. This result agrees well with Regener’s measurements, made by him when the apparatus was actually lowered to such a depth.

Secondly, the absorption coefficient corresponding to the upper end of the curve obtained from the data for underwater measurements is equal to 0.27 per meter of water, whereas for the 1928 curve this coefficient, obtained from direct observations, is equal to 0.22 per meter of water, i.e. it is greater, not smaller.

And thirdly, the new curve, like the 1928 curve, reveals a banded structure. At the request of Millikan and Cameron, Bowen constructed a curve from four components, which represented the same dependence of the ionization of the atmosphere on depth as the experimental curve. Table II gives a comparison of the ionizations given by Bowen’s synthetic curve and by the experimental curve of Millikan and Cameron.

TABLE II

Comparison of the observed curve with the curve constructed synthetically

Four absorption coefficients from which the synthetic curve is constructed are the following: 0.03, 0.10, 0.20, and 0.80.

Next, Millikan and Cameron compare these coefficients with coefficients computed from the Klein–Nishina formula, the equation \(mc^2=E\), and Aston’s curve for the cases of the formation of helium, oxygen, silicon, and iron atoms from hydrogen atoms in a single act. The Klein–Nishina formula, which makes it possible to compute the absorption coefficient for very hard rays, has the form:

\[ \mu=\frac{2\pi Ne^4}{m^2c^4} \left\{ \frac{1+\alpha}{\alpha^2} \left[ \frac{2(1+\alpha)}{1+2\alpha} -\frac{1}{\alpha}\log(1+2\alpha) \right] + \frac{1}{2\alpha}\log(1+2\alpha) -\frac{1+3\alpha}{(1+2\alpha)^2} \right\}, \]

where \(\alpha=\frac{h\nu_1}{mc^2}\), \(N\) is the number of electrons. The values of \(\alpha\) found with the aid of Aston’s data are as follows:

\[ \begin{array}{lr} \mathrm{H}\longrightarrow \mathrm{He} & 52.9\\ \mathrm{H}\longrightarrow \mathrm{O} & 227\\ \mathrm{H}\longrightarrow \mathrm{Si} & 423\\ \mathrm{H}\longrightarrow \mathrm{Fe} & 876 \end{array} \]

Table III gives a comparison of the empirical coefficients with those found theoretically in this way:

TABLE III

(in meters of depth)

Millikan and Cameron call the observed coefficients the coefficients of Bothe’s synthetic curve. Millikan and Cameron consider it extremely important for confirming their theory of the origin of cosmic rays that, for helium radiation, the most characteristic of these rays and possessing about 90% of all their energy, the computed and observed absorption coefficients—

tions almost completely coincide. As for the ever greater divergence between these coefficients as one passes to more penetrating radiation (these coefficients differ most of all for the radiation corresponding to the formation \(H \to Fe\)), Millikan and Cameron also do not regard this as a difficulty for their theory, and explain this divergence in the following way.

When a beam of photon quanta of energy enters the atmosphere, then, owing to Compton encounters of these photons with the electrons of air molecules, secondary, tertiary, etc., components of the primary cosmic ray are formed. After a certain amount of matter has been traversed, equilibrium of the ray with its secondary components sets in. This state of equilibrium will be reached when, in the ray, at the expense of absorption of the primary components, as many secondary components are formed per second as secondary components are absorbed during this time. The absorption coefficient of the ray after the attainment of this equilibrium will be of the same magnitude as the absorption coefficient of the ray when it first reaches the atmosphere, since in an equilibrium ray the percentage content of secondaries does not change throughout the motion of the ray; only the number of primaries changes, but this is precisely the state in which the rays are when they first reach matter. Before equilibrium is attained the absorption coefficient of the ray must be less than the absorption coefficient of the primary ray; the fact that for helium radiation the calculated and observed absorption coefficients almost coincide permits one to suppose that, at those levels at which cosmic radiation corresponding to the formation of helium from hydrogen is observed, this radiation is in an equilibrium state. Millikan and Cameron suppose that in measuring the ionization produced by the more penetrating rays they were dealing with radiations farther from equilibrium, which explains why the observed absorption coefficient is smaller than the calculated one. For our part, we believe that these are only qualitative considerations, which in no way explain

such a serious quantitative discrepancy as is observed for the formation \( \mathrm{H}\to\mathrm{Fe} \).

From these considerations it follows that the absorption coefficient passes through its maximum somewhere below the surface of the atmosphere. This is in good agreement with the measurements of the intensity of cosmic rays at an altitude of \(15.5\) km by Millikan and Cameron in 1922, on the one hand, and by Hess and Kolhörster at an altitude of \(9\) km, on the other. It is known that the first investigators obtained an absorption coefficient four times smaller than that obtained by Hess and Kolhörster. These data for a long time seemed contradictory, but now, in connection with the considerations developed above, this is understandable and is explained by the fact that the absorption coefficient has its maximum value somewhere between \(9\) and \(15.5\) km and, as one approaches the latter level, decreases, taking the value obtained for it by Millikan and Cameron in 1922. Such behavior of the absorption coefficient, as also of the magnitude of the ionization by cosmic rays, whose maximum is not located at the surface of the atmosphere but below it, once again proves that cosmic rays enter the atmosphere as electromagnetic, and not as corpuscular, radiation.

Millikan and Cameron note, incidentally, that the Klein–Nishina formula should be considered only an approximate formula for determining the absorption coefficient of cosmic rays. According to this formula, the absorption of cosmic rays is proportional to the number of extranuclear electrons. However, the curve of the dependence of ionization on depth clearly proves that nuclei also take part in the absorption of cosmic rays. If the law of mass absorption is valid, i.e. the law of dependence of ionization on density, then the water equivalent of the lead surrounding the electroscope is equal to \(0.85\) m. It is obtained by multiplying the thickness of the lead by the density of the latter. The actual water equivalent of this lead shield for weakly penetrating cosmic rays is obtained from the distance along the \(x\)-axis between the upper parts of both curves (Fig. 1)

and it is equal to 122 cm. For more penetrating rays this distance between the curves increases, and at a height of 10 m above sea level the water equivalent of lead is equal to 170 cm. This confirms the influence of nuclei on the absorption of cosmic rays. Chao, having recently elucidated a similar behavior of γ-rays, thus once again confirmed the identity of the nature of cosmic and γ-rays.

Regener’s new experiments, carried out by him in the winter of 1929/30 and in the summer of 1930, the results of which were published in Nature, No. 3198, 1931, show above all that the decrease of ionization at great depths under water (236.5 m) is not explained by a decrease in the radioactivity of the water as one approaches the bottom of the lake. For this purpose the ionization chamber was surrounded by a tank 2.5 m in diameter, which was filled with water from the surface of the lake. When the apparatus was lowered to great depths, the ionization chamber was thus surrounded by a constant layer of water 1 m thick. This layer protected the chamber from the radioactivity of the surrounding water. The results obtained this time were in complete agreement with the 1928 curve, which had been obtained by Regener without this protective tank. Fig. 2 depicts the curve of the dependence of ionization on depth, obtained in 1930 for depths greater than 75 m under water. The data obtained without the protective tank are marked by circles, and those with the tank by black dots.

In the summer of 1930 these results were checked once again with the aid of Müller–Geiger counters, which were lowered to various depths and operated an electric clock, the dial of which was automatically photographed at known moments of time. The absorption curve of cosmic rays obtained by this method and the curve obtained by the ionization method are in good agreement for depths under water of 7 m and more. For depths closer to the surface of the lake, they—the curves—diverge; the number of pulses counted by the counters is smaller than it should be for complete agreement of the curves at these depths, and this is probably explained by the mechanical and electrical lag of the recording instruments. The curve was

was analyzed by Regener’s collaborator Kramer and decomposed into four components. The relative intensities of penetration through the atmosphere of the three hardest of these components are \(0.81 : 6.4 : 16.35\). The hardest radiation has the last of these intensities. The absorption coefficients are \(0.020\), \(0.073\), and \(0.21\) per meter of water. The fourth component, with the greatest wavelength, could not be distinguished.

Regener calculates from the Klein–Nishina formula the wavelength of the hardest radiation and finds that it is \(0.63 \times 10^{-13}\) cm. He assumes that this radiation arises in the complete conversion of a proton and an electron into radiation, whose wavelength is \(1.313 \times 10^{-13}\) cm; the fact that the hardest cosmic radiation can be explained by the conversion of a proton and an electron into radiation also serves as confirmation, rather than refutation, of the wave nature of cosmic rays.