HEAVY NUCLEI IN THE COMPOSITION OF PRIMARY COSMIC RADIATION

At present it is generally recognized that primary cosmic radiation, arriving from world space at the boundary of the atmosphere, consists of protons. The first information on the nature of primary cosmic radiation, obtained on the basis of the study of geomagnetic effects, showed that it consists of positively charged particles. Direct study of the composition of cosmic radiation in the stratosphere, carried out with the aid of apparatus—telescopic systems of Geiger–Müller counters or ionization chambers—raised on pilot balloons, showed that at altitudes of about 25 km

high-energy electrons \((10^9—10^{11}\ \mathrm{eV})\), producing cascade showers in lead, are practically absent. This result, together with the results obtained on the basis of the study of geomagnetic effects, gave great credibility to the hypothesis of the proton nature of the primary cosmic radiation. The presence of a considerable number of high-energy protons in cosmic radiation, even at moderate altitudes, was first directly shown in experiments on the magnetic analysis of cosmic radiation carried out by A. I. Alikhanian, A. I. Alikhanov and their collaborators on Mount Alagez (3250 m) in 1946 and 1947 [1, 2]. These experiments showed that at an altitude of 3250 m the number of fast protons amounts to about 5% of the total intensity of cosmic radiation.

In 1947 Adams, Andersen, and others\(^3\), using a Wilson chamber placed between the poles of a powerful electromagnet, found that at altitudes of about 10 km there were several times more fast protons than at the altitude of Alagez. It may be thought that the observed fast protons are remnants of the primary proton cosmic radiation that have reached moderate altitudes.

The authors of the papers under review\(^3\) succeeded in showing that in the primary cosmic radiation observed in the stratosphere, in addition to protons there are \(\alpha\)-particles and nuclei whose atomic numbers lie in the range from \(Z=6\) (carbon) to \(Z=41\) (niobium). The kinetic energy of these particles is proportional to the charge of the nucleus and is approximately equal to \(1—2\ \mathrm{BeV}\) per nuclear particle. This result sheds some light on the question of the origin of cosmic rays, which until recently had almost no experimental basis. Indeed, if the kinetic energy of primary particles is proportional to their charge \(Z\), it follows that these particles, freed from their electron shell, before entering the earth’s atmosphere were accelerated in one and the same electric field. Such proportionality between \(Z\) and \(E\) could not be expected if cosmic radiation were born as a result of such “catastrophic” processes as nuclear explosions or the annihilation of nuclei.

The papers under review were carried out with the aid of photographic plates and an automatically operating Wilson chamber, raised into the stratosphere on balloons.

The apparatus was placed inside a hermetically sealed aluminum sphere 75 cm in diameter, within which a constant temperature was maintained during the flight.

Two stacks of photographic plates, 12 plates in each stack, were placed below and above the Wilson chamber. The emulsion was arranged in a vertical plane. Four lead plates, each 8 mm thick, were placed in the Wilson chamber.

Before setting forth the results obtained, let us consider how the charge \(Z\) and the energy \(E\) of particles whose tracks are observed in the photoemulsion can be determined.

Let \(E\), \(Z\), \(K\), and \(R\) be, respectively, the kinetic energy, charge, specific energy loss, and range of a particle whose track is found in a layer of photoemulsion. It is easy to show that, knowing any two of these quantities, one can determine the remaining two, in particular, knowledge of \(K\) and \(R\) makes it possible to determine \(E\) and \(Z\). For light and medium nuclei one may put \(M=2Z\), where \(M\) is the mass of the nucleus. Therefore the quantity

\[ \frac{E}{M}=\frac{E}{2Z}=\frac{v^2}{2} \tag{1} \]

directly determines the velocity of the particle.

Further, it is well known that, in the first approximation, up to semirelativistic values of the energy, the magnitude of the specific energy loss depends only on the velocity \(v\) and the charge \(Z\) of the particle:

\[ -\frac{dE}{dx}=K=a\frac{Z^2}{v^2}, \tag{2} \]

where \(a\) depends neither on \(Z\) nor on \(v\).

It follows from this that the quantity

\[ \frac{K}{Z^2}=\frac{a}{v^2} \tag{3} \]

is completely determined by the velocity of the particle.

From (2) it follows that the quantity \(RZ\), equal to

\[ RZ=Z\int_0^R dx=-Z\int_E^0 \frac{dE}{K} =Z\int_0^E \frac{v^2\,dE}{aZ^2} =\frac{v^4}{2a}, \tag{4} \]

also depends only on the velocity of the particle.

Thus, the three quantities \(\dfrac{E}{2Z}\), \(\dfrac{K}{Z^2}\), and \(RZ\) depend only on the velocity of the particle. Eliminating \(v\) from (1), (3), and (4), we obtain two equations relating the quantities \(E\), \(K\), \(Z\), and \(R\). Hence it is clear that, knowing \(R\) and \(K\), one can determine \(E\) and \(Z\). To determine the quantity \(K\), it is necessary to have, as calibration photomulsions, photomulsions irradiated by particles whose mass, charge, and energy are known. By comparing the density of grains in the track of the investigated multiply charged particle with the density of grains in the track of a particle of known energy, mass, and charge, one can determine \(K\). Such particles, used for the “calibration” of the photomulsions employed, were \(\alpha\)-particles, deuterons, and protons accelerated in the large Berkeley synchrocyclotron. The maximum value of the energy loss that could be determined at the end of the range in the photomulsions used was \(0.9\ \mathrm{MeV}\) per \(m/\mathrm{cm}^2\).

Another method for determining the charge, used by the authors, is the determination of \(Z\) from the range \(R\) and the number \(n\) of \(\delta\)-electrons produced by the particle per unit length of its track.

In the case of heavy particles this method makes it possible to determine \(F\) with an accuracy considerably exceeding that attainable by the preceding method. The number of \(\delta\)-electrons whose energy lies between \(w_1\) and \(w_2\), produced by the particle per unit length of its path, is determined by the formula

\[ n=A\left[\frac{m_e c^3}{w_1}-\frac{m_e c^3}{w_2}\right]\frac{Z^2}{\beta^2} =b\frac{Z^2}{\beta^2}, \tag{5} \]

where \(A\) is a constant, and \(m_e\) is the electron mass.

The value of the minimum energy \(w_1\) of the electrons to be counted is determined by the background in the plates. The value of the maximum energy \(w_2\) is determined by the sensitivity of the plates to electrons. For example, with Ilford NTB plates it is possible to detect electrons whose energy lies between \(10\) and \(30\ \mathrm{KeV}\). In order that formula (5) could give directly the value of \(Z^2/\beta^2\), it was necessary to determine the value of the proportionality coefficient \(b\).

FROM CURRENT LITERATURE

For this purpose, various types of plates that had been used were irradiated with α-particles accelerated in a synchrocyclotron, whose energy was known. By counting the number of δ-electrons along the trajectories of these α-particles, it was possible to determine the value of \(b\). The value of \(b\) was determined for particles of different energies and in doing so remained practically unchanged. In the work of Bredt and Peters it is indicated that for an emulsion of the Eastman NTB type,

\[ b = 0.03 \]

δ-electrons per \(100\,\mu\) of trajectory.

Fig. 1.

In order, from (5), knowing \(b\), to determine \(Z\), it is necessary to know the velocity of the particle. We have seen above that the quantity \(RZ\) determines the velocity of the particle. Thus, knowing the range \(R\) and the number of δ-particles per unit path length, we can determine \(Z\). As an example of applying both methods of determining \(Z\) and \(E\), let us consider the trajectory of a particle shown in Fig. 1. The particle passed almost vertically through a layer of emulsion and, at the end of its range, produced the formation of a large star consisting of 22 particles. The length of the observed range is equal to \(1700\,\mu\) (\(1.7\) cm). The grain density, which shows no appreciable change along the entire trajectory, as indicated by the authors, is the same as the density of grains produced by an α-particle with a residual range of \(800\)—\(1000\,\mu\). Such a grain density corresponds to specific energy losses lying within the limits

\[ 0.11 < K < 0.125 \text{ MeV per } m_e/c^2 . \]

On the basis of (2) we can write:

\[ \frac{Z^{3}}{\beta^{2}}=\frac{4}{\beta_{\alpha}^{2}}, \]

where \(Z\) and \(\beta\) are the charge and velocity of the observed particle, and \(\beta_{\alpha}\) is the velocity of an \(\alpha\)-particle with a residual range of \(800\text{--}1000\,\mu\). Further, on the basis of the formula (4) derived earlier for the range of the particle, we obtain:

\[ \frac{\beta^{2}}{\beta_{\alpha}^{2}}=\sqrt{\frac{Z^{2}R}{2R_{\alpha}}}, \]

whence, for \(R_{\alpha}=1000\,\mu\) and \(R=17\,000\,\mu\), we obtain \(Z=6\).

The value obtained for \(Z\) is, obviously, a lower limit, since the actual range of the particle was greater than \(17\,000\,\mu\). To obtain an upper limit for \(Z\), we note that the observed constancy of the energy losses along the track indicates that the particle is at the minimum of its ionization-loss curve. For the emulsion the minimum energy losses are equal to \(0.00166\) MeV per \(m^{2}/\mathrm{cm}^{3}\). Therefore we obtain

\[ Z^{2}\cdot 0.00166<0.125, \]

whence

\[ Z<9. \]

Table I

Thus, the charge of the particle whose track is visible in Fig. 1 is equal either to 6 (carbon), or to 7 (nitrogen), or to 8 (oxygen).

Table I gives the assumed values of \(Z\) and the magnitude of the particle energy at the beginning of its range and at the end of its range near the star formed by it.

Let us now consider the determination of \(Z\) from the density of \(\delta\)-particles \(n\). For the plates used in this case the coefficient \(b\) in formula (5) is equal to 0.03.

\[ n=\frac{0.03Z^{2}}{\beta^{2}}. \tag{6} \]

Measurements show that \(n\) varies only slightly along the track, and the mean value of \(n\) is equal to

\[ n=(2.8\pm0.5)\ \delta\text{-particles}/100\,\mu . \]

The constancy of the density \(n\) of \(\delta\)-electrons along the track is an additional confirmation that the particle is at the minimum of its ionization curve. The minimum of the ionization curve corresponds to \(\beta=0.96\). Substituting in (6) \(n=2.8/100\,\mu\) and \(\beta=0.96\), we obtain \(Z=9\), which is in agreement with the preceding determination of \(Z\) from the range and the specific energy losses.

The photograph considered by us (Fig. 1) is of special interest because of the star consisting of 22 charged particles observed at the end of the track of a multiply charged particle. This star, apparently, was caused by the penetration of a particle into a nucleus. To each particle forming the star one can assign, knowing its range and the density of grains in the track or the thickness of the track, its charge. The total charge carried away by all

particles, is equal to 37. It must be borne in mind that very fast protons may possibly escape registration. Thus one may suppose that the star in Fig. 1 owes its origin to the explosion of a silver nucleus \((Z = 47)\). The total energy carried away by all the particles of the star proves to be equal to 3–4 BeV, which is in agreement with the energy of the primary particle. The authors point out that, apparently, nuclear processes caused by collisions of multiply charged particles with nuclei are very rare. The total length of all the tracks ending in the emulsion was 29 cm. At the same time only 2 stars were found, one of which is shown in Fig. 1. The cross section for the formation of a star, determined from these data, proves to be somewhat smaller than the geometrical cross section of the nucleus.

Finally, the third method by which the authors of the papers under review determined the charge of \(Z\)-particles is the measurement of the “length of thinning.” If a multiply charged particle is slowed down in matter, then, when its velocity becomes comparable with the velocity of motion of an electron in its \(K\)-shell, it will capture an electron and will move further with an effective charge \(Z - 1\). As its velocity decreases, it will fill its remaining shells with electrons, and its charge will continually decrease. A decrease in charge will cause a decrease in ionization. Thus the density of grains in the track of a multiply charged particle in a photoemulsion at first, as the velocity of the particle decreases, increases (according to the law \(1/v^2\)); then, after the grain density becomes greatest, the particle begins to lose charge, its ionization weakens, and the grain density in the particle track gradually decreases. The described effect of “thinning” of the track was observed by the authors for the first time. They note that this effect is not observed in registration by the photoemulsion of multiply charged fragments obtained in the fission of thorium, because the ranges of these fragments are very small. Proceeding from the Bohr model of the atom and from the assumption that capture of an electron into the corresponding shell occurs when the velocity of the particle becomes equal to the velocity of the electron in this shell, the authors obtained the dependence of the “length of thinning” on \(Z\). In Fig. 2 a characteristic track of a multiply charged particle is shown, on which the thinning occurring over a length of about 200 microns is clearly visible. The charge of this particle, determined from the range and the density of \(\delta\)-electrons, is equal to 15. The thinning occurs over a length of 200 microns, which, according to the dependence obtained by the authors of \(Z\) on the length of thinning, corresponds to the value \(Z = 17\). Thus, both determinations are in good agreement.

After these examples let us consider the results obtained by the authors.

1. Spectrum of atomic numbers and angular distribution. In the papers\(^3\) 48 determinations were made of the charge of particles found in photoemulsions. In Fig. 3 the spectrum of atomic numbers from \(Z > 10\), constructed from these 48 tracks, is given. We see that the spectrum falls toward large \(Z\) and extends to \(Z = 41\) (niobium). In Fig. 4 the angular distribution of multiply charged particles, obtained at an altitude of 31 km (residual pressure 15 g/cm\(^2\)), is shown. From Fig. 4 it is seen that the angular distribution exhibits a sharp anisotropy: the intensity rapidly falls on passing to large angles. The anisotropy of the angular distribution is an additional indication that multiply charged particles are not formed in the atmosphere, but come from outer space: particles arriving at large angles to the vertical pass through great thicknesses of matter and are more strongly absorbed. If it is assumed that the probability of fixing particles that fall into the photographic plates is equal to unity, and that all particles reaching the boundary of the atmosphere in a direction close to the vertical reach the plates, then from

Beginning of the track

End of the track

10 μ

Fig. 2.

From Fig. 4 one can determine the intensity of the primary radiation \(I\) for \(Z>10\). Using the data for angles \(0\text{--}20^\circ\), the authors obtain for \(I\) the value \(I=3.2\cdot10^{-4}\) particles per \(\mathrm{cm}^2\) per second per unit solid angle. The total flux of primary particles is equal to \(12\cdot10^{-2}\) particles per \(\mathrm{cm}^2\) per second per unit solid angle. Thus, the intensity of the flux of multiply charged particles amounts to about \(1/400\) of the total intensity of the flux of primary particles. The ordinate for hydrogen and helium in Fig. 3 is plotted in accordance with this ratio of the two intensities. The hydrogen/helium intensity ratio was measured in the Wilson chamber.

Fig. 3.

2. The ratio of the hydrogen/helium intensities. Using the Wilson chamber, the authors obtained a considerable number of photographs of trajectories of multiply charged particles, four of which are given in the papers under review. These photographs are independent confirmation of the existence of multiply charged particles detected in the photoemulsion. Since photographic plates do not register fast protons, the determination of the hydrogen/helium ratio was carried out from data obtained in the Wilson chamber. In all, 74 photographs were obtained: 44 at an altitude of 29 km (residual atmospheric pressure \(17\ \mathrm{g}/\mathrm{cm}^2\)) and 30 at altitudes of 25–26 km (residual atmospheric pressure \(25\ \mathrm{g}/\mathrm{cm}^2\)). In doing this, particles were considered which had passed through no fewer than 3 plates of lead and were scattered by no more than \(2\%\) (the limit determined by eddy currents in the chamber). This circumstance, as well as the great altitude of observation, ensured the exclusion of mesons from consideration. The photographs obtained were divided into two groups, corresponding to minimum ionization (protons) and fourfold ionization (\(\alpha\)-particles). In the first group there are 19 trajectories, in the second 5, whence for the hydrogen/helium intensity ratio a value equal to 4 is obtained. The value obtained is in qualitative agreement with astrophysical determinations. Indeed, the magnitude of this ratio, determined

with the aid of astrophysical methods, is equal to 4 for the Sun and 10 for planetary nebulae.

The authors point out that photographic plates have proved to be an exceptionally convenient means for recording nuclei present in primary cosmic radiation. The fact that the kinetic energy of these nuclei turns out to be proportional to their charge \(Z\) and equal to approximately \(1\ \mathrm{BeV}\) per nucleon makes it possible to suppose that primary cosmic radiation owes its origin to acceleration in strong electric fields arising in certain places in the universe. One of the possible sources of such electric fields was indicated by Terletskii\(^4\), who showed that, when the magnetic and geographic poles of a rotating cosmic body do not coincide (such a noncoincidence, as is known, occurs for the Earth and the Sun, and there is no reason to think that it is absent in other bodies), streams of charged particles may be induced whose energy is great enough to explain the origin of cosmic rays.

Fig. 4.

The intensity with which the various \(Z\)’s are represented in the spectrum of Fig. 3 coincides with the relative abundance of the elements in the universe, obtained from astrophysical data.

Let us note that Li, B, Be, whose low abundance is known to astrophysicists, are likewise not represented in the spectrum of Fig. 3.

A. V.

References Cited

1. A. I. Alikhanian, A. I. Alikhanov, V. M. Morozov, A. V. Khrimian, DAN 61, 35 (1948).
2. C. D. Anderson, R. V. Adams, et al., Rev. of Modern Phys. 20, No. 1, (1948).
3. P. Freier, E. Lofgren, E. Ney, F. Oppenheimer, Phys. Rev. 74, No. 12, 1818 (1948).
4. H. Bradt and B. Peters, Phys. Rev. 74, No. 12, 1828 (1948).
5. Ya. Terletskii, ZhETF, vol. 16, 1948, issue 5, p. 403.