Full Text
Primary Component of Cosmic Radiation
M. I. Fradkin
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
I. General properties of primary cosmic radiation . . . . . . . . . . . . . . . . . 306
II. Protons in the composition of primary cosmic radiation . . . . . . . . . . . . . 314
III. Electrons and photons in the composition of the primary component of cosmic radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
1. Electrons and photons of high energies . . . . . . . . . . . . . . . . . . . . . 323
2. Electrons and photons of low energies . . . . . . . . . . . . . . . . . . . . . 327
3. Significance of the absence of primary electrons and photons for theories of the origin of cosmic rays . . . . . . . . . . . . . . . . . . . . . 330
IV. Complex nuclei in primary cosmic radiation . . . . . . . . . . . . . . . . . . . 331
1. Methods for determining the charge and energy of nuclei by means of photoemulsions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
2. Other methods for studying the nuclear component of primary cosmic radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
4. Evolution of nuclei in interstellar space . . . . . . . . . . . . . . . . . . . . 365
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
Introduction
Several decades have passed since the discovery of cosmic rays, but the question of the composition of the primary flux of cosmic radiation (the flux arriving from interplanetary space at the boundary of the Earth’s atmosphere) had not been resolved until recently. Numerous investigations of cosmic radiation, as a rule, were carried out at the surface of the Earth, where what is actually observed is not the radiation arriving from “space,” but the secondary and tertiary particles produced by this radiation.
The development and improvement in recent years of the technique of raising instruments to great altitudes by means of balloon sondes and rockets has made it possible to carry out direct investigations on a broad scale.
experiments on the study of the primary component of cosmic rays, and at the present time most questions connected with the composition and properties of the primary component have been clarified. The experiments carried out have proved the non-electronic character of primary radiation, the predominance in it of positively charged particles, elucidated the character of the interaction of primary protons with matter, and solved a number of other questions. A major contribution to the study of the primary component was made by the group of Soviet physicists working under the direction of S. N. Vernov.
Knowledge of the composition of primary radiation is important both for understanding the processes caused by cosmic rays in the Earth’s atmosphere and, to an even greater extent, for solving the question of the origin of cosmic rays—a question to which an exhaustive answer has not yet been found, and whose solution only in recent years, thanks to progress in physics and astrophysics, has begun to rest on a firm foundation of experimental data rather than on purely hypothetical constructions*).
The present article contains a review of contemporary experimental data on the primary flux of cosmic rays (with a brief description of new research methods) and a number of considerations on the significance of these data for theories of the origin of cosmic rays.
I. GENERAL PROPERTIES OF PRIMARY COSMIC RADIATION
The discovery of the existence of penetrating radiation of a new type² and the proof of its extraterrestrial origin³ attracted the attention of a large number of physicists to the study of this “cosmic” radiation. There is no possibility here of dwelling in any detail on the interesting history of the study of cosmic rays, which is highly characteristic of modern science. Those interested in this question may obtain the necessary information in the books by D. V. Skobeltsyn⁴ and Jánossy⁵.
Immediately after it had been established that the newly discovered radiation arises beyond the limits of the Earth, the question of its origin arose. Many works were devoted to attempts to localize the source of cosmic radiation. For this purpose, observations were made of changes in intensity as a function of the time of day, the time of year, sidereal or solar time, and so on. The observations showed that, at a given place, the intensity of cosmic radiation does not depend on the position of the Earth in space, i.e. cosmic radiation is distributed isotropically in space. The observed fluctuations of intensity in the great—
*) A review of contemporary theories of the origin of cosmic rays is contained in the article by V. L. Ginzburg¹.
part were caused by factors of a terrestrial nature and were very small*).
It should be noted, however, that the existence of isotropy has been proved only for that part of cosmic radiation which is formed by particles of comparatively not very high energies. For cosmic rays with energies greater than \(10^{13}—10^{14}\) ev, which are studied, as a rule, by investigating the extensive showers they produce or by registering particles with great penetrating power, there are no sufficiently reliable data on the existence or absence of isotropy. The results of works that have appeared in recent years \(^{95—99}\), in which temporal variations in the intensity of high-energy particles were studied, contradict one another.
In the experimental detection of sources of particles of superhigh energies, it may be useful to study the spatial distribution of light pulses correlated with extensive showers \(^{100}\). These light pulses are, in all probability, the result of Cherenkov radiation from particles of an extensive shower, and therefore the direction from which these pulses arrive makes a small angle with the direction of motion of the primary particle that produced the shower.
For a long time cosmic radiation was considered to be a kind of “ultra-\(\gamma\)-radiation,” i.e., it was assumed to be electrically neutral (and therefore, in accordance with the views existing at that time, to possess great penetrating power). The first indications that cosmic rays consist of charged particles were obtained \(^{9}\) in studying the absorption of particles passing through two counters arranged parallel to one another at some distance from each other (a telescope made of counters). However, more direct indications of the presence of charged particles in the primary flux of cosmic rays were obtained by Clay \(^{10}\), who established that the intensity of cosmic radiation at sea level is different at different latitudes**). The change in the intensity of cosmic rays with latitude could be explained only on the assumption that the radiation arriving at the Earth consists of charged particles of various energies. Indeed, the Earth, as is known, possesses a magnetic field which is rather well approximated by the field of a dipole with moment \(M = 8.1 \cdot 10^{25}\) gauss·cm\(^3\) and with an axis,
*) Variations of cosmic radiation have not yet been sufficiently studied either experimentally or, chiefly, as regards the interpretation of the results obtained. The question of temporal variations is considered in more detail in the book by L. V. Skobel’tsyn \(^{4}\) (Chapter 1), in the review by Elliot \(^{6}\), and in the reports by E. S. Glokova \(^{7}\) and S. N. Vernov, N. L. Grigorov, and E. S. Glokova \(^{8}\). See also the recently published works \(^{53, 68, 174}\).
**) Subsequently it was shown \(^{18}\) that the latitude effect measured by Clay at great altitudes is 10 times greater than the corresponding actual effect.
inclined to the axis of rotation of the Earth by \(10^\circ 30'\). In this magnetic field charged particles will be deflected, and at a given latitude only those particles will be able to reach the boundary of the Earth’s atmosphere whose quantity of motion is sufficiently large to overcome the deflecting action of the magnetic field. The theory of the motion of charged particles in a magnetic field of the dipole type was developed by S. A. Boguslavskii \(^{11a}\), Störmer \(^{11}\). The application of this theory to cosmic-ray particles \(^{12,13}\) led to the explanation of a number of effects, primarily such as the latitude effect and the effect of east-west asymmetry*).
Latitude effect. According to the theory developed by Lemaître and Vallarta \(^{12,13,15}\), a charged particle of a given energy (more precisely, with a given momentum) can arrive at a definite point on the surface of the Earth only along certain “allowed” directions. Therefore, for each latitude one can indicate such a limiting value of the momentum that a particle with a smaller momentum cannot arrive at this latitude from any direction. The theory of geomagnetic effects \(^{13}\) (see \(^{4,5}\)) makes it possible to determine, for each latitude, the expected intensity of cosmic rays arriving from one direction or another. In solving this problem the theory of geomagnetic effects is based on Liouville’s theorem, known from statistical physics, which, when applied to the case of the motion of particles in a constant magnetic field, leads to the conclusion that the motion of a group of particles with a certain momentum occurs in such a way that the intensity of the flux of these particles at any segment of the trajectory is constant and equal to the intensity of the flux of these particles “at infinity.” If the distribution of particles “at infinity” is isotropic, then the intensity of particles with momentum \(p\) at any point of space accessible to these particles will be one and the same, i.e. the same as in the absence of a magnetic field. Hence it follows that if for particles with a given momentum \(p\) some direction is allowed, then the intensity of particles registered in this direction on the Earth will be equal to the intensity of such particles at all other points of interstellar space**). In the case that the direction under consideration is “forbidden,” the arrival of particles with the given momentum in this direction is completely excluded and the intensity of this kind of particles is zero. If the cosmic rays include charged particles with different momenta, then the intensity of the cosmic rays
*) The question of geomagnetic effects is treated in greater detail in \(^{4}\) and \(^{5}\). The foundations of the Lemaître and Vallarta theory are also set forth there (see also reviews \(^{13}\) and \(^{14}\)).
**) It follows from this that measuring the intensity of cosmic rays on the Earth gives us information about the intensity of cosmic rays in interstellar space.
at different latitudes will be different. (This will be the so-called latitude effect.)
The latitude effect observed on the surface of the Earth was studied in detail by Compton et al.^16, who measured the ionization produced by cosmic rays. Measurements of the latitude effect at high altitude using ionization chambers^17 and measurements by S. N. Vernov in the stratosphere using a telescope of counters^18 not only confirmed the existence of the latitude effect, but also showed that at high altitudes the latitude effect is even more sharply expressed than at the level of the Earth: if at sea level the latitude effect from 0 to 49–50° is \(\sim 15\text{–}20\%\)^16, then at high altitude (\(\sim 18\ km\)) for approximately the same latitudes it is \(300\%\)^18,32. These measurements made it possible to determine the energy distribution of the primary particles (see Section II) and showed that a large fraction \(\left(\sim \dfrac{1}{2}\right)\) of the energy carried by cosmic rays arrives in the form of charged particles with momenta less than \(14 \cdot 10^{9}\ \mathrm{eV}/c\). Thus, the question of the nature of the primary radiation was to some extent resolved: the greater part of the primary flux consists of charged particles. However, measurements of the latitude effect cannot provide information about the sign of the particle charge. Such information can be provided by the study of another geomagnetic effect—the east-west asymmetry.
East-west asymmetry. In the magnetic field of a dipole, particles of different signs having the same momentum will be deflected differently. Therefore the “allowed” directions will be determined not only by the momentum of the particle, but also by the sign of its charge. Thus, for positively charged (positive) particles arriving from the west, the threshold momentum is smaller than for the same particles arriving from the east (at the same angle to the horizon). This effect is called the east-west asymmetry.
It was indicated above that the intensity of cosmic rays in an “allowed” direction will be the same as in the case of the absence of a magnetic field, while in a “forbidden” direction the intensity of particles with the corresponding momentum will be equal to zero. On the basis of this assertion one can say that the intensity, for example, of positive particles arriving at a certain angle to the vertical from the west at the equator \([p > p_1(0^\circ,\alpha)]\), is equal to the intensity of positive particles arriving vertically at some latitude \(\lambda\), where the threshold value of the momentum for particles arriving vertically is exactly \(p_1\) (independently of the sign of the charge). From symmetry considerations it is clear that the threshold momentum for negative particles arriving at the equator from the east at the same angle to the vertical will also be \(p_1\). If the fluxes of positive particles are denoted by \(N^{+}(p>p_1)\) and \(N^{-}(p>p_1)\)
and, respectively, negative particles with momentum greater than \(p_1\), then for the results of measurements at latitudes corresponding to the threshold momenta \(p_1\) and \(p_2\) for the vertical direction, and of measurements in the eastern and western directions corresponding to the same threshold momenta, at some latitude \(\lambda\) one can write a number of relations.
The intensity measured in the western direction will be
\(I_{\text{W}}=N^{+}(p>p_1)+N^{-}(p>p_2)\). The intensity in the eastern direction will be
\(I_{\text{E}}=N^{+}(p>p_2)+N^{-}(p>p_1)\). The intensity at the latitude corresponding to the threshold momentum \(p_1\) for the vertical direction is:
\(I_1=N^{+}(p>p_1)+N^{-}(p>p_1)\). The intensity at the latitude corresponding to the threshold momentum \(p_2\) for the vertical direction is:
\(I_2=N^{+}(p>p_2)+N^{-}(p>p_2)\). Using these notations, we can write
\[ A_{\text{W-E}}=2\frac{I_{\text{W}}-I_{\text{E}}}{I_{\text{W}}+I_{\text{E}}}= \]
\[ =2\frac{[N^{+}(p>p_1)-N^{+}(p>p_2)]-[N^{-}(p>p_1)-N^{-}(p>p_2)]} {[N^{+}(p>p_1)+N^{+}(p>p_2)]+[N^{-}(p>p_1)+N^{-}(p>p_2)]}, \tag{1} \]
\[ A_{\text{lat}}=2\frac{I_1-I_2}{I_1+I_2}= \]
\[ =2\frac{[N^{+}(p>p_1)-N^{+}(p>p_2)]+[N^{-}(p>p_1)-N^{-}(p>p_2)]} {[N^{+}(p>p_1)+N^{+}(p>p_2)]+[N^{-}(p>p_1)+N^{-}(p>p_2)]}. \tag{2} \]
If we assume that the spectra of positive and negative particles are identical, i.e.
\[ \frac{N^{+}(p>p_2)}{N^{+}(p>p_1)} = \frac{N^{-}(p>p_2)}{N^{-}(p>p_1)} =\alpha, \tag{3} \]
then the relations written above can be rewritten in the form
\[ A_{\text{W-E}}=2\frac{(1-k)(1-\alpha)}{(1+k)(1+\alpha)} =\frac{1-k}{1+k}\cdot A^{+}_{\text{W-E}}, \tag{4} \]
\[ A_{\text{lat}}=2\frac{1-\alpha}{1+\alpha}=A^{+}_{\text{W-E}}, \tag{5} \]
where \(k=\dfrac{N^{-}(p>p_1)}{N^{+}(p>p_1)}\) is the ratio of the number of negative particles to the number of positive ones, and \(A^{+}_{\text{W-E}}\) is the asymmetry in the case of only positive primary particles. Hence we find:
\[ \frac{A_{\text{W-E}}}{A_{\text{lat}}} = \frac{I_{\text{W}}-I_{\text{E}}}{I_{\text{W}}+I_{\text{E}}} : \frac{I_1-I_2}{I_1+I_2} = \frac{1-k}{1+k}. \tag{6} \]
From this relation we see that measurements of \(I_3\), \(I_{\mathrm{B}}\), \(I_1\), \(I_2\) are sufficient to determine the ratio between the numbers of positive and negative particles (provided that the form of the spectrum is independent of the sign of the charge). Instead of measuring \(I_1\) and \(I_2\), one may compute \(\alpha\) from the known energy spectrum of the particles and, from formula (4), determine the ratio between the numbers of positive and negative particles.
Relations (4) and (5) are usually used in interpreting the results of experiments measuring the east–west asymmetry.
Measurements of the east–west asymmetry at the surface of the Earth were carried out as early as the 1930s[^19][^20], and the results of these measurements showed that the primary radiation producing the penetrating component consists mainly of positive particles. For a review of these experiments see the monographs[^4][^5]. Measurements of the east–west asymmetry at low altitudes carried out in recent years[^29][^94][^166][^169] have confirmed the earlier results.
For a long time it was believed that at great altitudes the east–west asymmetry is negligibly small. This conclusion was based on the results of the sole experiment of Johnson and Barry[^21], who found that in the stratosphere at latitude \(20^\circ\) N the east–west asymmetry is only \(7\%\), instead of \(60\%\), as was expected for the case of positive primary particles*). This result, if it were correct, would mean the presence in the primary flux of negative particles in an amount of \(\sim 44\%\). The work[^21] gave rise to all sorts of speculation concerning the nature of cosmic rays. Suggestions were made[^5] that the hard and soft components are produced by different primary particles: the former is produced by positive particles (protons), and the latter by particles of both signs (electrons and positrons). Another attempt to explain the results of Johnson and Barry consisted in reconciling these results with the assumption of a positive sign of the charge of the primary particles, regarding scattering of secondary particles as the cause of the smoothing of the east–west asymmetry effect. However, both theoretical considerations[^5][^22] and direct experiments carried out by S. N. Vernov and A. M. Kulikov[^23] showed that the scattering is too small for
*) According to Yanossy’s calculations[^5], the expected asymmetry should have been \(40\%\), which corresponds to the presence in the primary flux of \(\sim 41\%\) negative particles. The smallness of the expected value of the asymmetry (compared with that calculated from formula (5)) is explained by the fact that, in the Johnson and Barry experiment, the apparatus rotated continuously, and the measured intensity referred to a very wide interval of angles: the interval \(\left(+\dfrac{1}{2}\pi,\ -\dfrac{1}{2}\pi\right)\) from the direction strictly west or strictly east.
in order to explain the absence of east–west asymmetry *). On the other hand, the results of investigations of the interaction of primary particles with matter, carried out by S. N. Vernov \(^{24}\) and others \(^{25,176}\), showed that the soft component is formed in the same processes as the hard component, i.e., the hypothesis of two components in the primary flux was refuted.
In view of the obvious disagreement between the results of Johnson and Barry and other data, in recent years a large number of experiments have been carried out with the aim of measuring the east–west asymmetry at great altitudes \(^{25—28,30—32}\). In 1949 S. N. Vernov, N. L. Grigorov, N. A. Dobrotin and others \(^{26}\) measured the effect of east–west asymmetry in the stratosphere (altitude corresponding to \(\sim 15\ g/cm^{2}\)) in the equatorial region. They found that the asymmetry at \(6—10^\circ\) south geomagnetic latitude reaches \(45—50\%\) for the total intensity and \(\sim 70\%\) for the hard component (penetrating through \(8\ cm\) of lead). This result indicated the manifest erroneousness of the experiment of Johnson and Barry. Similar results were also obtained by other investigators \(^{27,28}\).
If one calculates the expected east–west asymmetry for the conditions under which the experiment was carried out, under the assumption that the integral energy spectrum of the primary particles has the form \(E^{-\gamma}\), then for \(\gamma = 1.2 \div 1.5\) we find **):
\[ A_{\text{E-W}}^{+} = (110—130\%). \]
Comparing this result with the measured asymmetry of the hard component (70%), one can find from formula (4) that the fraction of negative particles in the primary flux is (taking \(A_{\text{E-W}}^{+}=120\%\))
\[ \frac{k}{1+k} \approx 20\%. \]
This means that the results of S. N. Vernov, N. L. Grigorov, N. A. Dobrotin and others do not exclude the possibility of the presence in the primary flux of negative particles in the amount of \(13—20\%\).
Comparison of the observed east–west asymmetry with that expected for the case of total intensity is made difficult by the fact that for
*) As the calculation \(^{87}\) showed, the absence of east–west asymmetry at great altitudes cannot be explained by the deflection of secondary particles in the Earth’s magnetic field.
**) If one takes \(\gamma \simeq 1\), which in the energy region greater than \(10^{10}\ eV\) is known to be an underestimated value, then \(A_{\text{E-W}}^{+} \approx 96\%\) and, correspondingly, the fraction of negatively charged particles will be
\[ \frac{k}{1+k} \approx 13.5\%. \]
For such a comparison it is necessary to know what contribution secondary particles make to the total intensity in measurements at an altitude of \(\sim 15\ \mathrm{g/cm^2}\) in the eastern and western directions. In any case, one may assume that the relative contribution of secondary particles in the eastern direction (where the mean energy of positive particles is higher) will be greater than in the western direction. Introducing a correction for the presence of secondary particles will lead to a decrease in the difference between the measured and expected asymmetry.
Measurements of the total intensity in the western and eastern directions will not require the introduction of corrections for multiplication if they are carried out beyond the boundary of the atmosphere. Such measurements were made\(^{30,31}\) at the geomagnetic equator by means of instruments mounted on rockets. A telescope made of counters, lifted by a rocket beyond the atmosphere, measured the intensity of the primary radiation, and the direction of the counters in space was recorded. The measured east–west asymmetry was \(\sim 40\%\). The expected asymmetry for the apparatus used in these experiments, under the assumption that all primary particles are positive, was \(\sim 84\%\)\(^{31}\). The difference between the measured asymmetry and the calculated value is explained, in the authors’ opinion, by the presence of a return current of particles from the atmosphere (the albedo of the atmosphere for cosmic rays; see Section II), which, according to their measurements, amounts to as much as 35% of the flux of primary particles (for a direction making an angle of \(45^\circ\) with the vertical).
If one assumes that the albedo is \(m\%\) of the total intensity and does not depend on the azimuthal angle, then the asymmetry expected in this case will be determined by the formula
\[ A'_{\mathrm{E-W}} = A_{\mathrm{E-W}}\cdot\left(1-\frac{m}{100}\right) = A^+_{\mathrm{E-W}}\frac{1-k}{1+k}\cdot\left(1-\frac{m}{100}\right). \tag{7} \]
In the case under consideration the expected asymmetry decreases to 54%. However, even taking account of the albedo does not exclude the possibility of the presence of negative particles in an amount of \(\sim 13\%\).
Thus, the experimental data available at present indicate the presence of a noticeable east–west asymmetry at great altitudes, which testifies in favor of a positive sign of charge for the main mass of primary particles. However, the results of direct measurements do not exclude the presence in the primary flux of some fraction of negatively charged particles (\(\sim 13\text{–}20\%\))*).
*) This conclusion, together with the known fact of the absence of primary electrons (see Section III), makes it possible to assume the presence in the primary flux of a certain number of antiprotons (see \(^{147}\)). Bokhumik\(^{28}\), who analyzed the results of his own measurements and those of Winkler et al.\(^{27}\), arrived at an analogous conclusion.
II. PROTONS IN THE COMPOSITION OF PRIMARY COSMIC RADIATION
After the discovery and detailed study in the 1930s of the latitude effect in the physics of cosmic rays, the opinion became established that the primary component consists of electrons (positive and negative). Such an assumption seemed to agree well with the processes observed in the atmosphere and caused by cosmic-ray particles. A large number of investigations were required, both of the primary component itself and of the processes occurring in the atmosphere, in order to establish the non-electronic character of the primary flux of cosmic rays.
Experiments that proved the non-electronic character of the primary particles of cosmic rays. Almost all instruments intended for recording charged particles are based on using the property of fast charged particles to ionize the matter through which they pass. However, at high energies the ionization produced by heavy particles cannot be distinguished from the ionization produced by light particles of the same charge (see Section IV). To determine the nature of particles of high energy, in addition to ionization one must know some other quantity characterizing the motion—for example, the momentum.
In studying the primary component, the apparatus has to be raised to a great altitude, which deprives us of the possibility of using such methods as determining the momentum from the curvature of the track in a magnetic field, since at our disposal there are as yet neither powerful magnets of small weight nor methods for lifting heavy apparatus to the boundary of the atmosphere. Therefore, to determine the nature of primary particles, it is necessary to seek other methods. These methods are based on studying the interaction of high-energy particles with matter. High-energy electrons, when passing through matter, undergo braking in the Coulomb fields of the nuclei (and electrons) of the medium and emit photons, which in turn create electrons and positrons in the process of pair production or in the process of Compton scattering. The theory of such cascade electromagnetic processes has been well developed, and the results of the theory are widely used in the processing and discussion of experimental data. The theory makes it possible, from the number of particles in a shower and from the thickness of the filter in which the shower arose and developed, to estimate the energy of the particle that caused the shower. In contrast to electrons, heavy particles (protons) do not produce bremsstrahlung, since the probability of this process is inversely proportional to the square of the particle mass. Thus, the study of the shower-producing ability of particles makes it possible to distinguish electrons and protons. Further study of the character of the interaction of protons with matter showed that protons cause nuclear disintegrations
(“stars”) and create meson showers, which can be observed in photographic emulsions,^34 whereas electrons create neither mesons nor “stars.”
The assumption of the proton character of the primary component (in any case, of that part of it which creates the penetrating radiation) was made in 1934^35 in explaining the results of measurements of the east–west asymmetry. However, the question of the basic composition of the primary flux remained unresolved for about another 15 years. In 1941 an experiment was carried out whose purpose was to measure the altitude dependence of electron showers in lead.^36 It turned out that at great altitude (pressure \(\sim 3\) cm Hg) the number of showers from lead is small. This gave grounds for supposing that protons constitute the main share in the composition of the primary radiation. To determine the nature of the primary radiation, S. I. Brikker, S. N. Vernov, and others carried out a whole series of experiments.^37, ^38 In these experiments an apparatus was lifted to the boundary of the atmosphere which recorded the number of particles passing through a counter. Measurements were made alternately inside a lead sphere with a wall 1 cm thick and outside the lead, in air. The results of the experiments of S. I. Brikker, S. N. Vernov, and others showed that there is an increase in the number of particles under lead (by a factor of 2.5 at an altitude of 20 km), but above 20 km, with further increase in altitude, no increase in the multiplication efficiency is observed—the number of particles under lead remains all the time 2.5 times greater than the number of particles outside lead. If the primary radiation consisted mainly of electrons, then at the very high energies which they would have to possess in order to pass through the geomagnetic barrier, one would observe, as the ascent proceeded, an ever greater multiplication, far exceeding that measured in the experiment. From this it was possible to conclude that the principal constituent part of the primary flux is not electrons but, apparently, protons.
Confirmation of the proton character of primary radiation is provided by the observation, in plates exposed at great altitude, of nuclear disintegrations and meson showers caused by primary relativistic particles.^34
In the flux of primary cosmic rays one cannot expect an appreciable number of mesons, since they are short-lived particles (their lifetime is less than \(10^{-6}\) sec) and decay spontaneously. For the same reason there cannot be a large number of neutrons in the composition of primary cosmic rays. Although the lifetime of the latter (tens of minutes) is considerably greater than the lifetime of mesons, only in the case of formation of fast neutrons on the Sun could some of them reach the Earth without decaying. At present, however, there are no data on the number of fast neutrons at high altitudes, and the question of their presence in the primary radiation remains open.
The experiments carried out (see Sections III and IV) showed that, in the composition of the primary radiation at this latitude, 14–20% consists of nuclei of various elements (from He to Fe), while electrons account for no more than 0.6%. Since protons apparently constitute more than 80% of the total number of incident particles at this latitude, in this section the flux of primary cosmic rays will be identified with the flux of primary protons.
Flux of the primary component at various latitudes. The flux of the primary component can be determined by direct measurements at the boundary of the atmosphere and beyond it, or from data on measurements of the altitude dependence of cosmic-ray intensity in the atmosphere. The first determinations of the flux of the primary component were made precisely by the second method.
From data on measurements of the latitude effect of cosmic rays, it was possible to find the energy spectrum of the primary radiation and to estimate the particle flux in various energy intervals. Thus, for example, Johnson^39, using the data of Millikan et al.^17 on ionization measurements, as early as 1938 found the form of the energy spectrum of primary particles and the corresponding fluxes at various latitudes. According to^39, the cosmic-ray spectrum has the form \(N(E)\cdot dE=\frac{15\cdot 10^8}{E^3}\,dE\) particles/\(cm^2\cdot sec\); the corresponding fluxes are given in Table I.
Table I
Flux of primary particles, determined from measurements of the ionization produced by them
| Latitude | Threshold energy*), eV | Energy flux, eV/\(cm^2 sec\) | Number of particles per \(cm^2\) per sec, Johnson^39 | Number of particles per \(cm^2\) per sec, Neher^52 |
|---|---|---|---|---|
| 3° | \(15\cdot 10^9\) | \(10^9\) | 0.032 | 0.031 |
| 39° | \(8\cdot 10^9\) | \(1.7\cdot 10^9\) | 0.11 | 0.066 |
| 52° | \(2\cdot 10^9\) | \(3.2\cdot 10^9\) | 0.36 | 0.22 |
*) The threshold energy is taken to be the energy that a proton must have in order to reach the Earth in the vertical direction.
Subsequently, with more accurate measurements, a somewhat different form of the spectrum was found (see below), but the data for the flux,
obtained from measurements of the released energy, are of the same order of magnitude (see \(^{14,52}\)) and are given in the last column of Table I.
Direct measurements of the primary flux of cosmic rays by means of a counter telescope raised to the boundary of the atmosphere \(^{27,40,42,44,50}\), on piloted balloons or beyond the atmosphere on rockets \(^{43,45—48}\), give other, considerably larger values than those obtained from ionization measurements.
Thus, for example, from the measurements of L. T. Baradzei, S. N. Vernov, and Yu. A. Smorodin \(^{40}\), carried out at latitude \(51^\circ\mathrm{N}\), it follows that the flux in the vertical direction at an altitude of \(\sim 13\) g/cm\(^2\) is \(\sim 0.18\) particles/cm\(^2\)·sec·sterad, which corresponds to a total flux of \(\sim 0.56\) particles/cm\(^2\)·sec (as compared with a flux of 0.36 particles/cm\(^2\)·sec or even 0.22 particles/cm\(^2\)·sec, as obtained from the data on energy measurements). In approximately the same relation to the data obtained from measurements of the released energy are the results of other authors \(^{41—48}\), who directly measured the flux of primary particles at the boundary of, or beyond, the atmosphere.
At present there is no exhaustive explanation of the difference between the results of direct measurement of the particle flux and determination of the particle flux from measurements of the ionization produced by it. One can, however, indicate two circumstances which will probably be able to explain this discrepancy completely.
First, measurements of the energy released by cosmic rays may give underestimated results, since part of the energy in the process of interaction with matter passes to unregistered particles—neutrinos—and thus does not enter into the final results.
Second, measurements by means of counter telescopes may, at the boundary of the atmosphere and outside it, give somewhat overestimated results (as compared with the true flux of primary particles) owing to the nonzero albedo of the Earth’s atmosphere, i.e., to the presence of secondary particles which have emerged from the atmosphere and are held by the magnetic field near the Earth \(^{90,91,92}\). Confirmation of the substantial role of the albedo is provided by data from measurements of the particle flux beyond the atmosphere using a single counter and using a counter telescope. It turned out that beyond the atmosphere the flux measured by a single counter \(^{41,45}\) is greater than the flux measured by a telescope \(^{43,45—48}\). At the equator it was found \(^{48}\) that the angular distribution of particles beyond the atmosphere has the form:
\[ j'(\theta)=0.028(1+0.6\sin\theta), \tag{8} \]
where \(\theta\) is the angle between the direction of the telescope axis and the vertical direction. Attempts at direct measurement of the incoming
from below the flux by means of Cherenkov counters[^49] have not yet yielded an unambiguous and sufficiently reliable result.
S. N. Vernov, A. M. Kulikov, and A. N. Charakhchyan[^50] estimated the flux of primary particles at northern latitudes \(51^\circ\), \(31^\circ\), and \(2^\circ\) by measuring the flux of particles penetrating through \(10\ \text{cm}\) Pb. Having determined in a number of experiments that the range absorbing the number of primary particles is \(160\ \text{g}/\text{cm}^2\) Pb, they consider that at the boundary of the atmosphere, through \(10\ \text{cm}\) Pb, half of the protons pass without interaction. Having measured the altitude dependence for particles that have passed through \(10\ \text{cm}\) Pb without multiplication, they extrapolate the curves to the boundary of the atmosphere and take as the primary flux the doubled value obtained as a result of the extrapolation. It should be noted that the extrapolation they perform may raise objections, since already at altitudes of \(\sim 30\ \text{km}\) the telescope in the vertical direction measures the same intensity as beyond the boundary of the atmosphere[^46].
The results of various authors who measured, by means of counter telescopes, the primary flux at the boundary of and beyond the boundary of the atmosphere are brought together in Table II.
Table II
Flux of primary particles at various latitudes, measured by means of a vertical counter telescope
| Geomagnetic latitude \(\lambda\), in ° | Threshold momentum for protons, \(10^9\ \text{eV}/c\) | Particle flux in \(1\ \text{m}^2\cdot\text{sec}\cdot\text{sterad}\) | Depth from the “boundary of the atmosphere,” \(\text{g}/\text{cm}^2\) | Additional absorber | Author |
|---|---|---|---|---|---|
| 0 | 14.9 | \(260\pm10\) | 15 | \(3\ \text{cm}\) Pb | Winkler[^27] |
| 0 | 14.9 | \(270\pm10\) | 15 | \(3\ \text{cm}\) Pb | Winkler[^27] |
| 0 | 14.9 | \(310\pm10\) | 15 | — | Van Allen[^43] |
| 0 | 14.9 | \(280\pm40\) | 0 *) | — | Van Allen[^43] |
| 2 | 14.9 | 150 | extrapolation **) | recalculation ***) | Charakhchyan[^50] |
| 2 | 14.9 | 270 | 15 | recalculation ***) | Charakhchyan[^50] |
| 20 | 11.6 | \(310\pm10\) | 15 | \(3\ \text{cm}\) Pb | Winkler[^27] |
| 28 | 9.1 | \(460\pm10\) | 15 | \(18\ \text{cm}\) Pb | Schein[^27] |
| 28 | 9.1 | \(590\pm10\) | extrapolation **) | — | Vidal[^176] |
| 31 | 8.0 | \(460\pm15\) | 15 | \(3\ \text{cm}\) Pb | Winkler[^27] |
Continuation of Table II
| Geomagnetic latitude $\lambda$, in degrees | Threshold impulse for protons, $10^9\,\mathrm{eV}/c$ | Particle flux, in $1/(m^2\cdot\mathrm{sec}\cdot\mathrm{sterad})$ | Depth from the “atmospheric boundary,” $g/cm^2$ | Additional absorber | Author |
|---|---|---|---|---|---|
| 31 | 8.0 | 300 | extrapolation **) | recalculation ***) | Chakhchyan $^{50}$ |
| 31 | 8.0 | 490 | 15 | recalculation ***) | Chakhchyan $^{50}$ |
| 38.8 | 5.5 | $850\pm30$ | 15 | $3\ \mathrm{cm}$ Pb | Winkler $^{27}$ |
| 39.5 | 5.3 | $680\pm20$ | 15 | $3\ \mathrm{cm}$ Pb | Winkler $^{27}$ |
| 41 | 4.8 | $820\pm20$ | 0 *) | — | Perlow $^{153}$ |
| 41 | 4.8 | $700\pm50$ | 0 *) | — | Van Allen $^{43}$ |
| 41 | 4.8 | $730\pm60$ | 0 *) | — | Singer $^{47}$ |
| 41 | 4.8 | $780\pm100$ | 0 *) | — | Vidal $^{176}$ |
| 41 | 4.8 | $1020\pm100$ | extrapolation **) | — | |
| 50 | 2.5 | $1800\pm200$ | 0 *) | — | Van Allen $^{43}$ |
| 50 | 2.5 | 1500 | 12 | — | Montgomery $^{178}$ |
| 51 | 2.3 | $2200\pm100$ | 15 | $1.9\ \mathrm{cm}$ Pb | Winkler and Stroud $^{27}$ |
| 51 | 2.3 | 1500 | extrapolation **) | recalculation ***) | Chakhchyan $^{50}$ |
| 51 | 2.3 | 1690 | 15 | recalculation ***) | Chakhchyan $^{50}$ |
| 52 | 2.1 | $1680\pm40$ | 18 | $<8\ \mathrm{cm}$ Pb | Pomerantz $^{44}$ |
| 52 | 2.1 | 1858 | 12.5 | $3\ \mathrm{cm}$ Pb | Pomerantz $^{179}$ |
| 52 | 2.1 | 2000 | 11 | — | Pomerantz $^{63}$ |
| 55 | 1.6 | $2960\pm200$ | extrapolation **) | — | Vidal $^{177}$ |
| 56 | 1.5 | 2200 | extrapolation **) | — | — |
| 56 | 1.5 | 2460 | 15 | — | Winkler and Stroud $^{177}$ |
| 58 | 1.2 | $2900\pm300$ | 0 *) | — | Van Allen $^{43}$ |
| 69 | 0.25 | 3000 | 11 | — | Pomerantz $^{63,44}$ |
| 69 | 0.25 | 2500 | 11 | — | Pomerantz $^{66}$ |
) The measurements were carried out on rockets beyond the boundary of the atmosphere.
) The flux values were obtained by extrapolation of the curves of the altitude variation of the intensity to the boundary of the atmosphere.
**) The flux values at zero absorber were obtained from measurements under $10\ \mathrm{cm}$ Pb by means of recalculation to zero absorber thickness (see $^{50}$).
Distribution of primary particles by energy. The results given in the preceding paragraph on the measurement of the flux of primary particles at various latitudes made it possible to find the energy distribution of the primary particles of cosmic rays.
According to the theory of geomagnetic effects, at each latitude \(\lambda\), in the vertical direction only those particles can arrive whose momentum is greater than a certain “threshold” value
\[ p_{\mathrm{vert}}(\lambda)=14.9\cdot 10^9 \cos^4\lambda \ \mathrm{eV}/c . \]
A telescope from counters oriented in the vertical direction will measure the total flux of all particles with momentum exceeding \(p_{\mathrm{vert}}(\lambda)\). Thus, measurements of the vertical intensity of cosmic rays at different latitudes (measurements of the latitude effect) make it possible to find the energy distribution of primary particles (the integral spectrum of primaries) having momentum less than \(\sim 15\cdot 10^9\ \mathrm{eV}/c\). To construct the spectrum in the region of higher energies, data on the energy spectrum of extensive air showers are used, assuming that extensive air showers are produced by primary protons. It should be noted that an objection can be raised against such an assumption: it is not excluded that extensive showers are also produced by multiply charged particles (see Section IV), and the spectrum of extensive showers is, in essence, the spectrum of a mixture of multiply charged particles and protons, and not the spectrum of protons alone. To resolve this question, further investigations of extensive showers are necessary and, in particular, the study of the so-called correlated showers, which, as G. T. Zatsepin\(^{88}\) has indicated, are possibly formed by multiply charged particles.
The spectrum obtained by combining the data of the latitude effect and the data from measurements of extensive showers under the assumptions indicated above is shown in Fig. 1.
Recently a method has been proposed for determining the energy of protons by studying the showers produced by them in photographic emulsions\(^{51}\). For this purpose one measures either the angle of divergence of the particles or the energy of the “soft component” (electrons accompanying these showers). By this method it has been possible to measure proton energies up to \(10^{12}\) eV and to find the flux of particles with energy exceeding \(10^{11}\) eV. The values found agree well with the curve of Fig. 1. However, measurements carried out by this method are still few in number, and the results obtained should be regarded as preliminary.
An analytical expression for the integral spectrum of primary particles can be written in the form\(^{14,52}\)
\[ N(E>E_0)\sim \int_{E_0}^{\infty} \frac{dE}{E^{2/3}\left(1+0.09E^{4/3}\right)^{3/2}}, \tag{9} \]
where \(E\) is the kinetic energy, expressed in \(10^9\) eV. For large-
at higher energies expression (9) behaves as \(\sim \dfrac{1}{E^{1.67}}\), which well reflects the spectrum of extensive air showers\({}^{53}\), while for energy \(E_1\) lying in the interval from \(2\) to \(12\cdot 10^9\) ev it is close to the curve \(\dfrac{1}{E_1^{1.1}}\), passing through the experimental points\({}^{27}\).
Fig. 1. Integral energy spectrum of primary cosmic radiation, obtained by measuring the particle flux at various latitudes (for energies less than \(15\cdot 10^9\) ev). The spectrum obtained is joined at point \(A\) with the spectrum of extensive air showers, given by Hilberry\({}^{53}\) in the form
\[ N(E>E_1)=\frac{A}{E_1^{1.7}}. \]
\(1\) — measurements of Winkler et al.\({}^{27,177}\), \(2\) — measurements of Van Allen and Singer\({}^{43,63,64,66,179}\), \(3\) — measurements of Schein, \(4\) and \(5\) — measurements of Charakhch’yan\({}^{50}\) without extrapolation and with the corresponding extrapolation, \(6\) — measurements of Singer\({}^{47}\), \(7\) — measurements of Montgomery\({}^{178}\), \(8\) — measurements of Perlov\({}^{155}\).
M. I. FRADKIN
Measurements of the latitude effect at high latitudes indicate a “flattening” of the curve of the integral energy spectrum of primary particles: cosmic-ray particles possessing low energies do not reach the Earth. Indications of the disappearance of the latitude effect at the Earth’s surface at high latitudes had already been obtained long ago\(^{16,54,39}\). Such a “threshold” in the latitude effect at the Earth’s surface was explained by absorption of particles in the atmosphere, since this threshold was observed precisely at latitude \(\sim 45^\circ\), where the energy allowed by the Earth’s magnetic field is equal to the energy expended by a relativistic particle on ionization in passing through the atmosphere. However, measurements of the latitude effect at high altitudes\(^{55}\) also revealed the existence of a threshold in the latitude effect, and initially this threshold was placed at \(\sim 50^\circ\) geomagnetic latitude. To explain the observed threshold in the latitude effect, Janossy\(^{5,56}\) advanced the hypothesis that the primary spectrum of particles incident on the Earth is cut off by the Sun’s magnetic field. If the Sun possesses a constant magnetic moment \(\sim 1.3 \cdot 10^{34}\) gauss·cm\(^3\) (the field at the pole \(H_p \sim 77\) gauss), then its magnetic field will not allow particles with momentum less than \(p_0 = 3 \cdot 10^9\) eV/\(c\) (which corresponds to the geomagnetic threshold at \(50^\circ\)) to approach the Earth. At the time when this hypothesis was advanced, it was believed\(^{57,86}\) that the Sun possesses a magnetic moment of the order of \((1.7 \cdot 0.42)\cdot 10^{34}\) gauss·cm\(^3\). Later, however, it was found\(^{58,59,60}\) that the magnetic moment of the Sun is considerably smaller than that measured initially, and indications appeared of the complete absence in the Sun of any appreciable magnetic moment*).
Experiments carried out in recent years with balloon sondes\(^{62—64,168}\) and rockets\(^{43,65}\) have shown that at high latitudes no increase in intensity with increasing latitude is observed, which is precisely evidence for the presence of some cutoff in the primary spectrum. At the present time it may be regarded as established\(^{65—67,168}\) that the threshold in the latitude effect occurs at approximately latitude \(56—58^\circ\).
In view of the fact that present-day astrophysical data indicate rather the absence of a constant magnetic moment in the Sun**) than its existence, it was assumed—
*) The determination of the magnitude of the Sun’s magnetic moment was made on the basis of measurements of the Zeeman broadening of absorption lines in the optical spectrum of the Sun. However, doubts were expressed\(^{61}\) concerning the possibility of applying this method to the measurement of comparatively small fields (tens of gauss) on the surface of the Sun.
**) The presence of a constant magnetic moment of the Sun may be a cause of diurnal variations in cosmic-ray intensity\(^{53,70,71}\). The absence of such variations in measurements\(^{64,72,74}\) was interpreted as an additional indication of the absence in the Sun of a constant mag-
...that the cutoff of the spectrum is explained by the absorption of low-energy particles as they move from the region of the source to the Earth. If the cause of the cutoff is absorption, then different particles will be absorbed differently, and the cutoff of the spectrum for them will occur at different values of the momentum and, consequently, at different latitudes. Although at present there are few experimental data, there are indications^68 that the cutoff for protons and for α-particles occurs at approximately the same latitude. These indications testify in favor of a magnetic cutoff. V. L. Ginzburg^69 pointed out that a magnetic cutoff may occur even in the absence of a constant magnetic field of the Sun: it may occur owing to the existence of the magnetic field of the solar system as a whole, arising from the motion of a conducting interplanetary medium.
In summary, one may say that the integral spectrum of protons (primary particles) cannot be approximated in the form of a power function with a constant exponent. Only in separate energy intervals does such an approximation agree well with the experimental data. In the region of low energies the integral spectrum flattens, which corresponds to a “cutoff” in the primary flux of particles of low energy.
III. ELECTRONS AND PHOTONS IN THE COMPOSITION OF THE PRIMARY COMPONENT OF COSMIC RADIATION
In the preceding sections experiments have already been described which proved that the primary radiation consists predominantly of positively charged particles, not electrons. However, from the results of these experiments no conclusions could be drawn about a possible upper limit for the electron component in primary cosmic radiation. In connection with this, a number of attempts were undertaken to measure the flux of primary electrons and photons in various energy intervals.
1. Electrons and photons of high energies
To separate from the total mass of cosmic-ray particles electrons and photons of high energy, use is made of the property of multiplication of the electron-photon component when passing through matter. This property makes it possible to measure the intensity of the electron-photon component in various
magnetic moment. However, Singer^73 showed that, with proper allowance for the particle spectrum and a number of other circumstances, the results of the measurements^72 do not contradict the presence at the Sun of a constant magnetic moment \(\sim 0.65 \cdot 10^{34}\) gauss·cm\(^3\), corresponding to a threshold in the latitude effect at \(56^\circ\). See also^183.
in energy intervals. First of all, investigators were interested in the question of the number of electrons and photons with energy \(>10^9\) eV. A number of experiments were carried out using an ionization chamber\(^{75,76}\) and a Wilson chamber\(^{77,78}\), raised on balloon sondes to the boundary of the atmosphere.
The first crude results were obtained with the aid of an ionization chamber. The ionization chamber used had the form of a cylinder 5 cm in diameter and 15 cm long. It was made of brass of thickness \(\sim 0.7\) mm \((0.6\ \mathrm{g/cm^2})\). The chamber was filled with pure argon to a pressure of 6 atmospheres. Above the chamber there was mounted a semicylindrical lead filter 2.5 cm thick and 10 cm long. In this lead block an electron-photon shower was produced; when its particles passed through the sensitive volume of the chamber they produced ionization proportional to the number of particles (all the particles had approximately the same velocity, close to the velocity of light, and all were singly charged, so that the ionization produced by individual particles was practically the same). The number of “bursts” exceeding a certain minimum, chosen differently in different experiments, was measured.
In the first experiments\(^{75}\) the threshold corresponded to the passage through the chamber of 80 relativistic singly charged particles. An estimate\(^{76}\) of the energy of an electron producing, under 2.5 cm of Pb, a shower of 80 relativistic particles gives a value \(\sim 10^{10}\) eV. During the flight, the entire system was calibrated with the aid of a Po \(\alpha\)-particle source, which periodically irradiated the chamber. Such calibration made it possible to monitor the operation of the apparatus and to exclude from consideration the data of those flights in which the system functioned incorrectly.
To determine the number of electrons and photons with energy greater than \(10^{10}\) eV, flights were made with chambers with an absorber and without an absorber. There were 2 successful flights at great altitude. The data obtained in these flights are given in Table III.
Table III
Results of experiments measuring the electron-photon component
| Pressure | Number of bursts per hour | Observation time (in hours) | Notes |
|---|---|---|---|
| \(20\ \mathrm{g/cm^2}\) | 313 | 1.2 | absorber above the chamber |
| \(45\ \mathrm{g/cm^2}\) | 183 | 0.6 | without absorber |
For comparison of the results of the two flights the authors extrapolated the data of the second flight to an altitude of \(20\ \mathrm{g/cm^2}\) (using-
obtained additional data for an altitude of \(306\ \text{g}/\text{cm}^2\) and found that the presence of lead leads to an increase in the number of bursts by \(\sim 1.5\) times. Undoubtedly, the method of comparing the results of different flights, moreover carried out at different altitudes, can lead to erroneous conclusions, but for rough estimates it is quite applicable. If one assumes that the entire difference is explained by electrons and photons (some fraction of the effect may, generally speaking, be associated with nuclear disintegrations in the walls of the chamber and in the absorber layer adjacent to the chamber), then the flux of these particles will be \(\sim 5\) particles/\(\text{m}^2\cdot\text{sec}\cdot\text{sterad}\) (the effective area of the chamber is \(19\ \text{cm}^2\), the solid angle is equal to \(\pi\)). Taking for the flux of all primary particles the value \(700\) particles/\(\text{m}^2\cdot\text{sec}\cdot\text{sterad}\), which corresponds to a flux of particles with \(E \gtrsim 5\cdot 10^9\ \text{eV}\), the authors find that electrons and photons of the energies measured by them constitute no more than \(1\%\) of the total number of particles\(^*\). Subsequently the same measurements were carried out, but the threshold was chosen to be 30 relativistic particles, which corresponds\(^{76}\) to an energy of the incident particle \(\sim 5\cdot 10^9\ \text{eV}\). As a result of flights of the apparatus at an altitude corresponding to a pressure of \(\sim 27\ \text{g}/\text{cm}^2\), it was found that the number of recorded bursts is \(\sim 4580 \pm 100\) per hour. This gives\(^{76}\), for the flux of the component causing bursts in the chamber, the value \(84\) particles/\(\text{m}^2\cdot\text{sec}\cdot\text{sterad}\). The data on measurements in the chamber without lead with a threshold of 30 particles have not been published, and therefore it is impossible to estimate the fraction of bursts caused by the electron-photon component. However, assuming that all bursts in the chamber are caused by showers from electrons and photons, we find, as a greatly overestimated upper limit for the fraction of the electron-photon component with energy \(E > 5\cdot 10^9\ \text{eV}\), the value \(\sim 12\%\).
The estimate made in work\(^{77}\) of the fraction of the electron-photon component as \(\sim 4\%\) is incorrect, since the flux of electrons and photons with energy \(E \gtrsim 5\cdot 10^9\ \text{eV}\) was compared with the flux of all particles with energy \(E \gtrsim 10^9\ \text{eV}\).
Undoubtedly, part of the bursts in the ionization chamber was caused not by electrons (nuclear disintegrations, meson showers), and some part of the “electronic” bursts was caused not by primary electrons but by secondary ones formed in lead. Thus, the value given above (12%) for the content of high-energy electrons in the primary radiation is obviously overestimated.
Measurements\(^{89,92}\) by means of telescopes with lead absorbers of different thicknesses, raised on rockets beyond the boundary
\(^*\) If one takes into account that the flux of particles with energy \(E > 10^{10}\ \text{eV}\) is \(400\) particles/\(\text{m}^2\cdot\text{sec}\cdot\text{sterad}\) (see \(^{27}\)), then the upper limit for the fraction of primary electrons will be \(1.5\%\) of the total number of particles with energy \(E > 10^{10}\ \text{eV}\).
of the atmosphere, also made it possible to estimate approximately the fraction of electrons in the primary cosmic-ray flux. According to the measurements\(^{92}\), primary electrons at latitude \(41^\circ\) constitute no more than 14% of the primary radiation. In work\(^{89}\) it was established that the flux of primary photons and electrons with energy greater than \(5\cdot 10^9\) eV amounts to less than 5% of the flux of primary particles.
Further investigations\(^{77,73}\) made it possible to reduce appreciably the upper limit for the fraction of high-energy electrons and photons in the primary cosmic-ray flux. The experiments were carried out at latitude \(55^\circ\) with Wilson chambers lifted by balloon probes to the boundary of the atmosphere (\(\sim 20\ \text{g}/\text{cm}^2\)). Lead plates \(0.6\ \text{cm}\) thick (1.2 \(t\)-units) were placed in the Wilson chamber; in them electron multiplication and the formation of showers occurred. In all six flights at least two lead plates were placed inside the chamber. 1000 photographs were selected on which electron showers are visible. In the selection they were guided by the requirement that the number of particles with minimum ionization be not less than 10. The latter requirement imposes restrictions on the minimum energy of the recorded electron. A careful analysis\(^{78}\) showed that this minimum energy \(E_0\) is \(\sim 0.73\cdot 10^9\) eV, and even in the least favorable case \(E_0\) is not more than \(1.1\cdot 10^9\) eV. Measurement of the sensitive time of the chamber (by means of a radioactive source) and calculation of the effective area of the chamber and the effective solid angle made it possible to determine an upper limit for the flux of electrons with energy greater than at least \(1.1\cdot 10^9\) eV. This flux was \(\sim 12\) particles/\(\text{m}^2\cdot\text{s}\cdot\text{sterad}\), i.e. \(\sim 0.6\%\) of the primary flux of particles with momentum \(p > 1.1\cdot 10^9\ \text{eV}/c\)*). The value of the fraction of the electron-photon component (\(\sim 0.2\%\)) given in work\(^{77}\) differs from that given in the later work\(^{73}\) because in work\(^{77}\) only those showers were taken into account which were not accompanied by penetrating particles. In addition, in work\(^{73}\) a more careful determination of the sensitive time of the chamber and of the effective solid angle was made.
It may be considered that in the primary cosmic-ray flux electrons with energy \(E \gtrsim 10^9\) eV, if they exist at all, constitute no more than 0.6% of the number of all primary particles. This corresponds to a density of high-energy electrons near the Earth of less than \(7\cdot 10^{-13}\) electrons/\(\text{cm}^3\). At the same time, from data on the radio emission of the Galaxy it follows\(^{79}\) that electrons with energy \(\sim 10^9\) eV exist in galactic space, and the dens—
*) It is possible that the flux found, \(\sim 12\) particles/\(\text{m}^2\cdot\text{s}\cdot\text{sterad}\), refers to electrons with energy greater than \(0.73\cdot 10^9\) eV. In that case the flux of electrons with energy \(E > 1.1\cdot 10^9\) eV will be still smaller.
... their density\(^{69}\) is of the order of \(10^{-14}\)—\(10^{-13}\) per \(\mathrm{cm}^3\). It is essential to determine whether such a coincidence of the values of the electron density is accidental or whether electrons really exist near the Earth in an amount corresponding to the number of relativistic electrons that produce galactic radio emission. From this point of view, it is very important to carry out further experiments on measuring electrons in the primary flux, with the aim of establishing a more accurate limiting value for the number of electrons with energy \(\sim 10^9\ \mathrm{eV}\) in the flux of cosmic particles arriving at the Earth.
2. Electrons and photons of low energies
The experiments described above established an almost complete absence of primary electrons and photons with energy \(E \gtrsim 10^9\ \mathrm{eV}\). The question arises whether there are electrons and photons in the primary radiation with energies less than \(\sim 10^9\ \mathrm{eV}\). According to the available data\(^{63}\), charged particles with momentum less than \(1.2 \cdot 10^9\ \mathrm{eV}/c\) do not reach the Earth at all, i.e. electrons with energy less than \(1.2 \cdot 10^9\ \mathrm{eV}\) do not arrive either*). With regard to photons of low energies, however, no conclusions of this kind can be drawn without carrying out special experiments.
Experiments to search for primary photons were carried out with the aid of rockets that lifted the corresponding installations beyond the boundary of the atmosphere (at geomagnetic latitude \(41^\circ\))\(^{80,81}\). Ascent to great heights was necessary because at lower altitudes (at altitudes attainable by means of balloon sondes) there is a large number of secondary photons, which complicate and confuse the whole picture. The apparatus for measuring photons consisted of a group of counters connected in coincidence. The counters were surrounded by lead half-cylinders, which in turn were surrounded by groups of counters (Fig. 2). Coincidences of the counters inside the lead blocks and anticoincidences of this group with any peripheral counter were recorded. The anticoincidences corresponded to photons that produced electrons in the lead, whose energy
*) The maximum percentage of electrons with energy greater than \(2.5 \cdot 10^8\ \mathrm{eV}\) can be roughly estimated from the following considerations. The fluxes of primary particles measured at \(69^\circ\) N latitude \((p_{\mathrm{vert}}\cdot c = 2.5 \cdot 10^8\ \mathrm{eV})\) and at \(58^\circ\) N latitude \((p_{\mathrm{vert}}\cdot c = 1.2 \cdot 10^9\ \mathrm{eV})\) are respectively \(0.25 \pm 0.02\) particles/\(\mathrm{cm}^2\cdot\mathrm{sec}\cdot\mathrm{sterad}\) and \(0.29 \pm 0.03\) particles/\(\mathrm{cm}^2\cdot\mathrm{sec}\cdot\mathrm{sterad}\)\(^{43}\). If the maximum possible difference in the fluxes at \(69^\circ\) N latitude and at \(58^\circ\) N latitude is taken as the flux of electrons with momentum \(2.5 \cdot 10^8\ \mathrm{eV}/c < p < 1.2 \cdot 10^9\ \mathrm{eV}/c\), then the percentage of such electrons will be no more than
\[ \frac{\Delta I_{\max}}{I_{69^\circ,\max}} = \frac{0.01}{0.27} \sim 3.7\%. \]
It is clear that in reality there are still fewer such electrons, if they are present at all in the primary flux.
of which was less than that necessary for passage through the second absorber. Coincidences in the central counters gave the total number of particles (ionizing and nonionizing). The absorbers used selected photons in the energy interval from 3.4 to 90 MeV (photons with energy less than 3.4 MeV produced electrons that could not pass through a copper plate 1.9 mm thick placed between the two central counters; photons with energy greater than 90 MeV produced electrons that passed through the lower filter and caused a discharge in the lower group of counters).
The number of coincidences registered above the atmosphere was \(2.30 \pm 0.11\) per second, and the number of anticoincidences was \(0.20 \pm 0.04\) per second (\(\sim 8.7\%\) of the number of coincidences)\(^{80}\).
Fig. 2. Schematic representation of the apparatus for registering photons with energies in the interval from 3.4 to 90 MeV: \(C_1\) and \(C_2\)—lead half-cylinders of thickness 0.63 cm and 2.42 cm, respectively; \(A\), \(B\)—Geiger–Müller counters with Al walls 0.15 mm thick; \(B\) and \(G\)—groups of Geiger–Müller counters with walls 0.8 mm thick, Cu; \(M_1\)—a copper plate 1.9 mm thick, absorbing low-energy electrons.
If, however, one takes into account (approximately) the difference between surfaces collecting photons and those collecting charged particles, then the percentage constituted by neutral particles relative to charged ones will be only \(\sim 2.5\%\), and if the necessary corrections for random coincidences, counter dead time, stars, etc., are introduced, this percentage will decrease to 1%.
It is more reasonable to compare not the number of photons with the number of all particles, but the energy carried by the photons with the energy carried by all cosmic radiation. The energy carried by photons in the energy interval from 3.4 to 90 MeV is\(^{80}\) \(1.4 \cdot 10^6\) eV/cm\(^2\)·sec. The energy of the total radiation at the same latitude (41° N. lat.) is\(^{82,83}\) \(1.8 \cdot 10^9\) eV/cm\(^2\)·sec. Thus, the energy carried by photons with energies in the interval \(3.4 \div 90\) MeV constitutes
only 0.08% of the total energy carried by cosmic radiation at northern latitude \(41^\circ\)*).
We thus see that the contribution of photons with energies from 3.4 to 90 MeV to the energy flux of the total cosmic radiation is negligible.
To determine the photon flux in the energy interval from 0.1 to 15 MeV, a similar apparatus\(^{81}\) was lifted, but without additional absorbers. The only absorbers were the copper counter walls, \(0.9\) mm thick. The apparatus, consisting of seven counters, is shown in Fig. 3. Coincidences were recorded between the central counter \(A\) and the peripheral
Fig. 3. Schematic diagram of an apparatus for recording photons with energies in the interval from 0.1 to 15 MeV: \(A\)—central counter; \(B\)—peripheral counters connected in parallel. Wall thickness of all counters \(\sim 0.09\) mm Cu.
counters, which formed one ring \(B\). At the same time, anticoincidences \(A-B\) were recorded. Coincidences gave the number of charged particles, energetic \(\gamma\)-rays, and energetic neutrons. Anticoincidences gave the number of low-energy \(\gamma\)-rays and low-energy neutrons. As a result of the measurements it was found that the number of coincidences was \((28.3 \pm 0.4)\) per second, and the number of anticoincidences (after the corresponding corrections had been introduced) was \(1.0 \pm 0.1\) per second. The energy flux carried by photons in the energy interval from 0.1 to 15 MeV is \(0.9\ \text{MeV}/\text{cm}^2\cdot\text{s}\), which is comparable with the energy flux carried by photons in the energy interval from 3.4 to 90 MeV.
Thus, the results of measurements of the photon intensity in the energy interval from 0.1 to 90 MeV show that the flux of energy carried by photons constitutes a negligible fraction (less than 0.1%) of the energy flux carried by charged particles of cosmic rays.
* If the measured energy flux carried by \(\gamma\)-rays in the energy interval \(3.4\text{–}90\) MeV is referred to the energy flux carried by cosmic rays at latitude \(60^\circ\) (owing to the presence of a “cutoff” of the primary spectrum, this flux may be regarded as the flux of cosmic rays in the Earth’s orbit), equal to \(2.4\cdot 10^9\ \text{eV}/\text{cm}^2\cdot\text{s}\), then the fraction of energy carried by \(\gamma\)-rays will be less than 0.06%.
3. Significance of the Absence of Primary Electrons and Photons for Theories of the Origin of Cosmic Rays
The results set forth in the preceding sections show that in the primary flux of cosmic rays electrons are almost completely absent (over the entire energy interval from low energies to very high ones), as are photons with energy \(0.1\ \mathrm{MeV} \ll E \ll 90\ \mathrm{MeV}\) and with \(E \gtrsim 10^9\ \mathrm{eV}\). There are no direct experimental data on photons in the energy interval from 90 to 1000 MeV, but it is highly improbable that in this narrow energy interval the intensity of the photon flux greatly exceeds its intensity in the neighboring intervals.
Without dwelling on the question of how various theories of the origin of cosmic rays explain this experimental fact, we shall note only several points indicating the nontriviality of the assertion that an electron-photon component is absent in the primary flux of cosmic rays.
Since most modern theories of the origin of cosmic rays are based on electromagnetic mechanisms of acceleration, in the general case there is no reason to suppose that electrons will not be accelerated in the same way as protons and complex nuclei. Moreover, protons, moving in interstellar space from the source region to the Earth, will undergo nuclear interactions, thereby producing mesons which, on decaying, will create energetic electrons and \(\gamma\)-rays. Thus we see that there is a sufficiently large number of sources of electrons, and it is necessary to explain why these electrons are not observed on Earth.
Most authors of theories of the origin of cosmic rays either do not consider the question of electrons at all, or confine themselves to indicating those mechanisms of electron energy losses which may bring about the removal of energetic electrons from the cosmic-ray flux. However, as was pointed out in a number of papers \(^{69,84,85}\), a detailed and careful analysis of the processes of energy loss is necessary for each specific acceleration mechanism. Otherwise it may turn out that the absence of a primary electron component does not follow at all from the given theory.
The absence of an appreciable fraction of photons in the primary radiation is explained much more simply. According to modern views, the flux of cosmic rays observed on Earth is the result of the “accumulation” of charged cosmic-ray particles held by interstellar magnetic fields. It is clear that \(\gamma\)-radiation will not “accumulate,” but will leave the source
unlimitedly far. For this reason, the fraction of $\gamma$-radiation in comparison with the fraction of charged particles will decrease very strongly*). It is necessary, however, to analyze whether the upper limit for the intensity of $\gamma$-radiation derived from theoretical considerations corresponds to that established by experiment.
The question of the energy carried away by $\gamma$-radiation also remains unclear: whether it returns in some form to the Galaxy; whether there is an equilibrium between the outgoing $\gamma$-radiation and the $\gamma$-radiation arriving from other galaxies; or whether, through $\gamma$-radiation, there is a constant leakage of energy from the Galaxy.
Further experimental and theoretical investigations will make it possible to clarify the questions posed and will allow us to broaden and deepen our knowledge not only of cosmic rays, but also of the Galaxy, of intergalactic space, and of the entire universe.
IV. COMPLEX NUCLEI
IN PRIMARY COSMIC RADIATION
Assumptions concerning the presence of complex nuclei in the composition of primary cosmic radiation were made long before the discovery of these nuclei in the primary flux $^{101,102,149—151}$. Thus, for example, Alfvén $^{101}$, developing his theory of the acceleration of charged particles in the induction fields of binary stars, indicated that the cosmic rays emitted by such a generator should constitute a mixture of atomic nuclei of various elements, and that the ratio in which the various nuclei are represented in the composition of cosmic rays should reflect the chemical composition of the source. The same conclusion was also reached by Ya. P. Terletskii $^{102}$, who developed the theory of acceleration of charged particles in the fields of stars with noncoinciding magnetic and mechanical moments. Reliable reports of experimental confirmation of such an assumption ap-
*) As an illustration of the assertion made, one may give a simple estimate. Suppose that for a long time ($\gg 10^8$ years) there is continuous production of photons and charged particles of high energy, and that both are formed in one and the same energy interval, not differing by the same amount. The charged particles will be retained by magnetic fields and, over the course of $\sim 5\cdot 10^8$ years $\simeq 1.5\cdot 10^{16}$ sec, will “wander” inside the Galaxy, creating the intensity of cosmic rays registered by us. The photons emitted together with the charged particles, moving with the speed of light, will leave the Galaxy after a time less than
$$ \frac{4.5\cdot 10^{22}}{3\cdot 10^{10}} \simeq 1.5\cdot 10^{12}\ \text{sec}. $$
It is therefore evident that the “accumulation factor” of charged particles is greater than $10^4$, i.e., under the assumptions we have made about the character of the sources of cosmic rays, there should be 10,000 times fewer photons than charged particles.
appeared in 1948.*) In the paper of a group of researchers\(^{103}\), examples were given of microphotographs of tracks with increased ioniza-
Fig. 4. One of the first photographs of the track of a multiply charged particle. A large number of tracks of \(\delta\)-electrons accompanying the particle track is visible.
tion left in the photographic emulsion by cosmic-ray particles at high altitude (Fig. 4). Comparison of the ionization produced by these parti-
*) In 1936, a photograph was published\(^{137}\) of a track attributed to a primary \(\alpha\)-particle, and several brief reports appeared\(^{145}\) on multiply charged particles. However, another report was soon published\(^{144}\), whose authors did not observe tracks of \(\alpha\)-particles. In that work the primary character of the previously registered \(\alpha\)-particle was called into question, and subsequently no reports of observations of primary complex nuclei appeared.
by the amounts of ionization and their ranges showed that these tracks cannot be attributed to slow protons or other singly charged particles. Tracks of this kind of particles were also recorded in a Wilson chamber (Fig. 5). Thus it was established that cosmic radiation contains nuclei of various atoms, including atoms with large \(Z\). At the present time there is a large amount of information, obtained by various methods, on the composition and energy distribution of nuclei in the primary flux of cosmic rays, but, unfortunately,
Fig. 5. Stereophotograph of a Wilson chamber showing the passage through a lead plate of a particle with high ionizing power (a multiply charged particle).
there is still no complete agreement among the results of different authors who used different investigative techniques. In order to be able to discuss critically the available results and draw sufficiently reliable conclusions from them, it is necessary to become more closely acquainted with the various methods used in studying the nuclear component of primary cosmic rays.
1. Methods for determining the charge and energy of nuclei by means of photographic emulsions
The principal method used for studying the composition of the nuclear component is the method of thick-layer photographic emulsions. This method, proposed in 1927 by L. V. Mysovskii \(^{104}\), has found very wide application in investigations connected with nuclear interactions, including the study of cosmic rays. The fundamentals of this method have been set forth in various articles and a number of books \(^{105, 106, 181}\), and therefore here only briefly will be
described methods for determining the charge and energy of cosmic-ray particles from the tracks they leave in emulsion (Fig. 6).
Determination of charge. The basic phenomenon that made it possible to use photoemulsions (as well as most other instruments of nuclear physics) to study energetic charged
Fig. 6. Tracks of relativistic nuclei with \(1 \leq Z < 23\) in Ilford photoemulsion with track width and large
particles, is a property of charges moving in matter: they produce ionization of the atoms of the medium. The process of ionization has been well studied; theory \({}^{107}\) gives, for describing this process, formulas,
Fig. 65. Tracks of multiply charged nuclei are characterized by a significant number of \(\delta\)-electrons.
the correctness of which has been verified experimentally. The basic conclusions of the theory are as follows: the energy losses per unit path due to ionization are proportional to the square of the charge of the particle and, moreover, depend only on the particle velocity.
Thus, one may write that the specific ionization (the ionization produced by the particle per unit path), which is proportional to the ionization losses, is equal to:
\[ j = Z^{2}\cdot f_{1}(v), \tag{10} \]
where \(j\) is the specific ionization, \(v\) is the velocity of the particle.
By ionizing, as it passes through the emulsion, the atoms that enter into its composition, the particle creates centers which, after the emulsion is developed, are visible in the form of silver “grains.” The density of grains (the number of grains per unit path) depends on the specific ionization, this dependence having the form
\[ g = D\left[1-e^{-\frac{a}{D}j}\right], \tag{11} \]
where \(g\) is the grain density, \(D\) is the density of AgBr molecules, and \(a\) is a constant determined from experiment. It is precisely the grain density \(g\) that is the quantity measured in experiments.
Another method for determining the charge of a particle is based on the fact that, in ionizing atoms in the emulsion, a charged particle imparts to some atomic electrons an energy so large that these electrons, moving in the emulsion, themselves ionize atoms and leave characteristic tracks (tracks of \(\delta\)-electrons)\(^{108}\). The density of \(\delta\)-electrons (the number of \(\delta\)-electrons per unit length of the particle track), like the specific ionization, is proportional to \(Z^{2}\) and depends only on the velocity \(v\). We may write
\[ N_{\delta}=Z^{2}\cdot f_{2}(v), \tag{12} \]
where \(N_{\delta}\) is the density of \(\delta\)-electrons.
Still another method for determining the charge of a complex nucleus is based on the fact that a nucleus moving at high velocity, while losing part of its energy to the ionization of atoms in the emulsion, is slowed down; its velocity decreases, and when the velocity of motion of the nucleus becomes close to the velocity of motion of the orbital electrons in a nonionized atom, the nucleus begins to “capture” electrons and its effective charge decreases. The decrease in effective charge leads to a sharp decrease in the ionization produced, which is manifested in the gradual narrowing of the track in the direction toward the stopping point of the particle in the emulsion. An example of such a narrowing track is shown in Fig. 7. Theoretical consideration\(^{121}\) has shown that the length of that part of the track where distinct narrowing occurs is uniquely related to the charge of the nucleus and can serve for determining the magnitude of the charge.
A rough estimate of the nuclear charge can also be made by counting the total charge of all the “fragments” emitted when the primary complex nucleus is split by one of the atoms in the emulsion. This method is applied^153 in the case of recording the splitting of nuclei with large \(Z\).
The described methods for determining the charge from the tracks left by charged particles in a photographic emulsion are applied in different ranges of values of the charge \(Z\), and each of them has its positive and negative aspects.
The grain-counting method makes it possible to distinguish well between close values of charges (when the specific ionization is not very large), and the results obtained in this way are sufficiently objective, while the specific ionization is determined with an accuracy of up to \(\sim 5\%\)^110. However, in order to apply this method it is necessary that the particle track consist of separate grains that are distinguishable from one another and can be counted. For this purpose one has to use low-sensitivity emulsions and apply special methods of processing these emulsions (underdevelopment)^110. As a consequence of using low-sensitivity emulsions, there arises the danger, when examining exposed plates, of missing the tracks of a number of nuclei (especially nuclei with small \(Z\)), all the more so since in such emuls—
Fig. 7. Track of a phosphorus nucleus (\(Z=15\)) stopped in the emulsion. On the right is the track of this nucleus upon entering the emulsion (nuclear velocity \(\beta = 0.7\)); on the left is the track of the same nucleus after passing through \(9.6\ \text{g}/\text{cm}^2\) of glass and emulsion. The widening of the track is clearly visible as a result of the increase in ionizing power as the nucleus slows down, and subsequently the narrowing of the track caused by the capture of orbital electrons by the nucleus, which has already lost its energy.
traces of complex nuclei are accompanied by a small number of tracks of δ-electrons. A shortcoming of this method is also the circumstance that, in a photoemulsion of a given sensitivity, the grain density can be measured only for tracks in which the specific ionization changes by a factor of 10–15 (a change of charge by a factor of 3–4).
In contrast to the grain-counting method, when determining the charge by counting δ-electrons, the use of sensitive emulsions is permissible and even desirable[^109_110]. Because of this, when such a method is used there is little probability of failing to notice a track left by a multiply charged particle, since it stands out among other tracks by the large number of accompanying δ-electrons. When determining the charge by this method, one can measure, in one and the same plate, charges from tracks whose specific ionization differs by a factor of 100. In addition, the results of the count do not depend on the quality of the processing of the plate after exposure.
A substantial shortcoming of this method should be considered its comparatively low accuracy (~15–20%). The low accuracy is mainly a consequence of poor statistics (a small number of δ-electrons, especially for small \(Z\)) and of a certain subjective element that appears during counting. The latter circumstance is connected with the fact that it is necessary to set some criteria with respect to the length and direction of the track of the δ-electron that is to be counted. When the charge of particles with small \(Z\) is determined by this method, there arises the danger of taking tracks of background electrons for tracks of δ-electrons. However, data from various investigators[^109_111] indicate that this circumstance apparently does not exert a significant influence on the results obtained.
In order, as far as possible, to eliminate the shortcomings inherent in each of the methods under discussion and to make fuller use of the possibilities they provide, a combination of both methods is used[^135]. For this purpose, a plate with a low-sensitivity emulsion is placed between plates with a sensitive emulsion. From such elements a whole stack of plates is assembled. After exposure and development of the emulsions, they are examined in order to find the tracks of multiply charged particles. When such a track is found, it is observed in all the plates through which the particle has passed; for this purpose the plates are assembled into exactly the same stacks as those subjected to exposure. In this way the charge of the particle can be determined by counting the density of δ-electrons in the sensitive emulsions and by counting grains in the low-sensitivity emulsions.
The method of determining the charge from the length of the narrowing part of the track has, in comparison with the two methods described above, low accuracy, especially in the case of nuclei with small \(Z\). In the case of identification of nuclei with comparatively large \(Z\) (\(Z > 15\)), the accuracy is 20–30%. This is explained by the fact that in the case of large
PRIMARY COMPONENT OF COSMIC RADIATION
...for large \(Z\) the measured quantity has appreciable dimensions (more than \(100\,\mu\)) and therefore can be determined with greater accuracy. The application of this method is also limited by the fact that the number of tracks in which the narrowing end of the track can be clearly noted is relatively small, since most often the particles either stop in glass, which has a considerably greater thickness, or leave the plate altogether.
Determination of energy. As was already indicated above, and as follows from formulas (10), (11), and (12), in order to determine the charge it is necessary, simultaneously with measuring the specific ionization or the density of \(\delta\)-electrons, to measure the velocity of the particle \(v\). At high energies, when the velocity of the particle is close to the speed of light \(c\), the ionization losses depend only weakly on the velocity and reach a minimum value at \(v=0.96\,c\). Thus, if it is known that the particle moves with relativistic velocity, then to determine its charge it is sufficient to count the grain density or the density of \(\delta\)-electrons and compare it with the corresponding values for the track of a relativistic nucleus with known \(Z\) (for example, for the track of an \(\alpha\)-particle).
The situation is different for nuclei moving with nonrelativistic velocity. In this case the velocity of the particle must be determined. One of the most widespread methods for determining the velocity of a particle is the measurement of the mean angle of deflection in multiple Coulomb scattering of the particle by atoms in the emulsion.
To determine the mean angle of deflection of a particle, its track in the emulsion is divided into a number of sections of length \(t\) (“measuring element”), and, having measured the deflection in each segment (the angle \(\alpha\) between chords or tangents in neighboring sections), the mean value of the angle \(\langle \bar{\alpha}\rangle\) is calculated.
The theory of multiple scattering\(^{112-113,180}\), by means of the formula
\[ \langle \bar{\alpha}\rangle=\frac{KZ\sqrt{1-\beta^2}}{A\beta^2} \tag{13} \]
relates the values of the mean scattering angle \(\langle \bar{\alpha}\rangle\), the charge \(Z\), the atomic weight \(A\), and the velocity \(\beta=\frac{v}{c}\), with
\[ K=f(t,Z,\beta)\cdot \sqrt{t}, \tag{14} \]
where \(f(t,Z,\beta)\) is a function depending only weakly on \(Z\), \(\beta\), and the length of the “measuring element” \(t\), and determined mainly by the composition of the emulsion\(^{113}\). The quantity \(K\), which for a given \(t\) is almost constant, can be determined either from measurements of the mean scattering angle in tracks of particles with known \(\frac{Z}{A}\) and known velocity, or by calculation from the corresponding formula (see, for example,\(^{113}\)).
Thus, by measuring \(\overline{\langle \alpha \rangle}\) with the ratio \(\dfrac{Z}{A}\) known, one can determine the velocity of the particle and, consequently, its energy.
In Fig. 8 the solid curves are lines of constant \(Z\). The dashed curves are lines of constant range. The numbers placed in the upper part of the diagram give the energy per nucleon corresponding to the given mean scattering angle. The light and dark circles represent the results of measurements of the density of \(\delta\)-electrons and of the mean scattering angle in 857 tracks of particles observed in G5 photographic plates exposed at northern geomagnetic latitude \(55^\circ\).
Often, instead of measuring the velocity, one uses a measurement of the particle range. In the case when energy losses occur exclusively through ionization, and in the case of heavy particles this holds up to quite high energies, the range of a particle in matter depends on the charge and velocity in the following way:
\[ R=\frac{A}{Z^2}\,\psi(v), \tag{15} \]
where \(R\) is the range and \(A\) is the atomic weight. From this relation we can find the velocity
\[ v=\varphi\left(\frac{RZ^2}{A}\right) \tag{16} \]
and, substituting this expression into formulas (10) and (12), we obtain the dependence of the specific ionization and of the density of \(\delta\)-electron tracks on the range, or rather on \(\dfrac{RZ^2}{A}\):
\[ j=Z^2 F_1\left(\frac{RZ^2}{A}\right) \tag{17} \]
and
\[ N_\delta=Z^2 F_2\left(\frac{RZ^2}{A}\right). \tag{18} \]
If the form of these functions is found for a particle with known \(Z\) and \(A\) (for example, for the proton), then the corresponding dependences can be constructed graphically for particles with various \(Z\) and \(A\) (Fig. 9). By measuring in the track left by the particle \(j\) or \(N_\delta\) and the corresponding \(R\), one can, knowing the ratio \(\dfrac{Z}{A}\), find \(Z\) from the nomogram and determine the energy of the particle.
In the case where the energy of the particle is so large that its velocity is close to the speed of light, in order to determine the energy (when studying the distribution of particles by energy) it is necessary to apply some other methods. In this case the range in the photoemul-
Fig. 8. Curves of the dependence of the density of δ-electrons on the mean scattering angle \(\langle \theta \rangle\) (i.e., on the particle velocity).
...and the specific ionization and the density of δ-electrons practically do not depend on the energy, whereas to measure the mean angle of deflection in multiple Coulomb scattering one must (as is seen from formula (15) for \(\beta \to 1\)) choose sufficiently large \(t\), which is possible only for sufficiently long tracks. However, in the case of complex nuclei, whose flux, as will be seen below, is small, sufficiently long tracks are observed very rarely and, moreover, the track of a multiply charged particle is so wide that it is difficult to measure the angles of deflection.
Fig. 9. Curves of the dependence of specific ionization on range. Along the abscissa is plotted the range in \(\mathrm{g/cm^2}\) Al. Along the ordinate is the ratio \(\dfrac{I}{I_0}\), where \(I\) and \(I_0\) are respectively the specific ionization of the particle and the minimum specific ionization of a singly charged particle.
A new method for determining the energy of the primary nucleus is the measurement of the angle of divergence of fragments formed when this nucleus is split by an atom nucleus in the emulsion\(^{114–115}\).
When a proton collides with a complex nucleus, various processes may take place, and the particles thereby formed will produce in the emulsion various kinds of “stars.” In those cases where the primary proton, colliding with the nucleus, excites it, after which the excited nucleus “evaporates,” characteristic tracks of evaporation products are observed, consisting of approximately equal numbers of tracks of protons and \(\alpha\)-particles with energies of several \(M_{38}\) and a small number of heavier nuclei\(^{116}\).
The particles emitted from the nucleus are distributed isotropically in space (Fig. 10).
If one considers the interaction of a heavy nucleus moving at high speed with a stationary proton, then in the emul—
Fig. 10. Disintegration of a heavy nucleus belonging to the emulsion, caused by a cosmic-ray particle. The four $\alpha$-particles emitted in the disintegration of the nucleus have an isotropic distribution, and their total energy is 64 MeV.
a completely different picture will undoubtedly be observed. It is, however, easy to imagine the appearance of a “star” in the case of the “evaporation” of a complex nucleus of high energy in a collision with one of the stationary nucleons (in particular, with a proton) in an emulsion. For this it must be taken into account that, in the coordinate system associated with the rapidly moving nucleus, excitation of the stationary nucleus by a nucleon of high energy will occur. In this coordinate system there will be an isotropic scattering of the “fragments” of the nucleus (protons and $\alpha$-particles). On passing to the laboratory coordinate system, the spatial distribution of the “fragments” will change: in the emulsion there will be observed a very narrow beam of protons, $\alpha$-particles, and heavier nuclei, moving with approximately the same energy per nucleon as that possessed by the primary nucleus (Fig. 11). It should be noted that the stars observed in emulsions from the evaporation of fast heavy nuclei have a considerably more complex appearance, since in fact the collision is not nucleus—nucleon, but nucleus—nucleus, and, in addition, a large number of mesons and other particles may be emitted in the process.
The mean angle of scattering of $\alpha$-particles emitted during the “evaporation” of a fast complex nucleus is determined by the following relation$^{11}$:
$$ \sqrt{\langle \theta^2\rangle}=\sqrt{\frac{\langle T^*\rangle M}{3p_0^2}}, \tag{19} $$
where $M$ is the mass of the proton; $\langle T^*\rangle$ is the mean kinetic energy of the $\alpha$-particle in the system associated with the nucleus; $p_0$ is the momentum of the nucleus in the laboratory system. For a known value of $\langle T^*\rangle$, one can, by measuring the mean angle of scattering, determine the momentum of the primary nucleus.
In the coordinate system associated with the nucleus, the $\alpha$-particles scatter isotropically, and their mean energy lies between 10 and 15 MeV; only very rarely are $\alpha$-particles encountered with energies exceeding 30 MeV. In determining the energy of the incident nucleus from the angle of scattering of the fragments one takes $\langle T\rangle = 12$ MeV. In this case
$$ \sqrt{\langle \theta^2\rangle}=\frac{0.06}{\varepsilon_0}, \tag{20} $$
where $\varepsilon_0$ is the total energy of the primary nucleus, measured in $10^9$ eV/nucleon, and $\theta$ is the angle, measured in radians.
To determine the energy of the nucleus from the angle of scattering of the particles emitted by it, one uses mainly the tracks of $\alpha$-particles ($Z>1$), since the tracks of relativistic protons cannot be distinguished from the tracks of relativistic mesons moving in the same cone.
The correctness of the data obtained by this method can be checked by measuring the mean angle of scattering along the track of an $\alpha$-particle that has emerged from a “star.” In the coordinate system associated with—
Fig. 11. Splitting of a primary Al nucleus ($Z=13$) upon collision with the nucleus of an atom in the emulsion. The bundle of six $\alpha$-particles formed as a result of the disintegration of the Al nucleus has a sharply defined forward direction. The presence of tracks of strongly ionizing particles emitted at large angles to the direction of the primary particle indicates that, in this case, in addition, there occurred the splitting of a nucleus belonging to the emulsion.
bonded to the nucleus, all $\alpha$-particles have approximately the same and, moreover, comparatively small kinetic energy, and consequently, in the laboratory coordinate system the velocities of all $\alpha$-particles emitted will also be approximately the same and equal to the velocity of the primary nucleus. Thus, measurement of the velocity of the $\alpha$-particles emitted from the nucleus makes it possible to determine independently the velocity (energy) of the primary nucleus. The measurements carried out$^{115}$ showed that both methods of determining the energy of a complex nucleus (measurement of the angle of scattering in fission and measurement of the mean angle of scattering) give concordant results.
Let us briefly note the sources of errors that arise when measuring energy by various methods, and the ranges of applicability of these methods.
When measuring the mean angle of scattering there are a number of factors that distort the results and limit the accuracy of the measurements. First of all, the so-called “noise level” sets a lower limit to the accuracy of angle measurement at $1.5—2$ seconds of arc ($\sim 10^{-5}$ radians). The cause of such a background is the insufficient accuracy of the microscope (determined by the mechanical properties of the system), the insufficient accuracy of measuring the individual deflection (which can be improved by repeated measurement of one and the same section of the track), and fluctuations in the arrangement of grains along the track (the influence of fluctuations can be reduced by increasing the length of the measuring element). A substantial error can be introduced by distortion of the emulsion during processing. In order to avoid errors of this kind, a number of precautions are taken in processing emulsions (development in a horizontal position, constancy of temperature and of solution density during development, etc.).$^{113}$ As a rule, this method is used to determine particle energies if this energy is less than $\sim 2\cdot 10^9$ ev/nucleon, since application of this method in the region of higher energies requires the use of larger “measuring elements.” Thus, for example, if for measuring the mean angle of scattering in the track of a particle with energy $\sim 2\cdot 10^9$ ev/nucleon one uses “measuring elements” of length $300\,\mu$, then in the case of a particle with energy $\sim 2\cdot 10^{10}$ ev/nucleon, with the same accuracy of angle measurement, it is necessary to use “measuring elements” of length $3$ cm.
The velocity of a particle can usually be determined from its range only in those cases when its energy is not very great, and therefore the particle stops within the stack of measuring plates. If a system of plates with interlayers of a dense absorber (for example, copper) is used, it becomes possible to determine the velocity from the range also in the case of more energetic particles$^{115}$. However, as the energy of the particles under study increases, the probability of nuclear fissions increases
PRIMARY COMPONENT OF COSMIC RADIATION
...which determines the upper limit for range measurements. Thus, using experimental data on the range for the interaction of various nuclei, one can calculate\(^{117}\) that fewer than 10% of the particles will reach the end of their ionization range if the particle energy is greater than
\[ 0.425\cdot 10^9\ \text{eV/nucleon for He}, \]
\[ 0.74\cdot 10^9\ \text{eV/nucleon for O}, \]
\[ 0.91\cdot 10^9\ \text{eV/nucleon for Si}, \]
\[ 1.05\cdot 10^9\ \text{eV/nucleon for Fe}. \]
Measurement of the range makes it possible to determine particle energies smaller than \((0.3—0.7)\cdot 10^9\ \text{eV/nucleon}\).
The principal error in range measurements is associated with the fact that some particles stop not in the emulsion, but in the glass of the photographic plates or in the absorber plates, as a result of which the exact value of the range remains unknown. At the same time it is also unknown whether the particle stopped as a result of ionization losses or underwent nuclear disintegration.
In determining the energy of a multiply charged particle by the method of measuring the emission angle of the disintegration products, the principal sources of error may be errors in measuring the angle and an error in the choice of the value of \(\langle T\rangle\) in formula (19). Errors in measuring the emission angle arise from distortions of the emulsion, from displacement (tilt, rotation, etc.) of the separately developed photographic plates relative to one another after they have been reassembled into the measuring stack, and from multiple Coulomb scattering. In order to avoid errors connected with distortion of the emulsion and relative displacement of the individual plates, the necessary precautions are observed during development\(^{113}\), and a frame for placing the plates is carefully and precisely constructed. This makes it possible\(^{117}\) to reduce the errors introduced into the determination of the angle to \(1/2\)%. Estimates show that the error introduced by multiple scattering does not exceed 10%; usually it is considerably smaller\(^{117}\). An incorrect choice of the value of \(\langle T\rangle\) may lead to a substantial error in determining the energy. If the charge of the primary nucleus is small, then the number of emitted \(\alpha\)-particles is small (two or three). In this case it may happen that the energies of all the particles are less than the chosen mean value \(\langle T\rangle\). This will lead to an overestimate of the energy of the primary particle. The same result will be obtained if a small number of \(\alpha\)-particles are emitted, if by chance they are emitted in one and the same direction (in the coordinate system connected with the nucleus). However, as the charge of the incident nucleus increases, the number of emitted \(\alpha\)-particles increases, and the probability of obtaining an erroneous
the result decreases sharply. This method gives the most reliable results in the case of particles with \(Z>8\)—10.
One can estimate the maximum error caused by the fact that, in measurements by this method, the energy of all \(\alpha\)-particles is taken to be equal to the mean energy \(\langle T\rangle\). We shall assume, in accordance with experiment \(^{116}\), that in fragmentation \(\alpha\)-particles with energy greater than \(30\) MeV (\(\beta \simeq 0.12\)) do not fly out of the nucleus. The maximum angle between the axis of the shower and an \(\alpha\)-particle with energy \(30\) MeV, according to the relation
\[ \varepsilon_0 \operatorname{tg}\theta_{\max} = \beta_{\max}\left(\beta_0^2-\beta_{\max}^2\right)^{-\frac12} \]
will be
\[ \theta_{\max}\simeq \frac{0.12}{\varepsilon_0}. \tag{21} \]
Comparison of relation (21) with formula (20) shows that the quantity determined by formula (20) can differ from the true value of the energy by no more than a factor of two.
The angle of dispersion can be measured down to angles of the order of \(10^{-4}\) radian. This means that estimates of the energy of heavy particles by the method described can be carried out up to energies of \(6\cdot 10^{11}\) eV/nucleon \(^{117}\). Up to now the maximum energy measured in this way has been \(4.5\cdot 10^{10}\) eV/nucleon \(^{115}\).
2. Other methods for studying the nuclear component of primary cosmic radiation
The study of primary cosmic radiation by means of photographic emulsions, for all its advantages, has a substantial drawback. The tracks observed in the emulsion after development are the result of the action of all particles that have passed through the emulsion from the moment of its preparation to the moment of development. As a consequence of this circumstance, it is not always possible to assert that the tracks observed in the plates were left by particles that passed through the emulsion while it was at altitude. This is especially important for the study of nuclei with small \(Z\), since at lower altitudes such nuclei may appear as a result of the fragmentation of heavier nuclei that occurred at greater altitude. To reduce this kind of background, efforts are made to minimize the relative time of ascent and descent (in relation to the time spent at altitude). It is desirable, however, to have methods for investigating multiply charged particles which, while giving results referring to a definite altitude, would make it possible to investigate the distribution of different groups of nuclei with altitude*). Below is a brief description of these methods.
* Recently a method \(^{183}\) has been proposed which makes it possible, from the displacement of the tracks of one and the same particle in two plates shifted relative to one another, to determine the moment of registration.
Wilson chamber. Using a Wilson chamber, it is possible, as is known, to determine the nature of an individual charged particle that has left a track inside the chamber[^118]. In the case of multiply charged particles, measurement of the ionization along the track makes it possible to find the charge of the particle, if (as in the case of photographic emulsions) it is known with what velocity it was moving. Measuring particles by the mean scattering angle in the chamber is, as a rule, not possible because of the comparatively small length of the track inside the gas-filled chamber. Measurements of the range also cannot serve as a reliable method of determining the velocity, since the amount of matter inside the chamber is small and the ionization losses are slight. Placing absorber plates inside the chamber somewhat improves the situation, but increases the probability of nuclear disintegration. The method of determining the velocity (momentum) of a particle from its deflection in a magnetic field is inapplicable to problems of studying the primary component because of the difficulty of raising a magnet to great altitudes.
Already in the first experiments on the study of the nuclear component of primary cosmic radiation, Wilson chambers were raised to the boundary of the atmosphere with the aid of balloon-sondes[^103]. Among the photographs obtained there are some in which tracks of multiply charged particles are visible (see Fig. 5). However, determination of the charge could be carried out only for part of the tracks and, moreover, with very low accuracy.
Attempts to use the Wilson chamber for the study of multiply charged particles beyond the boundary of the atmosphere yielded no results. A Wilson chamber raised on a rocket registered during the entire flight (~250 sec.) only one case of the passage of an \(\alpha\)-particle[^119] (the expansion was carried out once every 25 sec.). In addition, when the Wilson chamber was used on a rocket, an additional technical difficulty appeared, connected with the fact that after the end of combustion the rocket flies as a freely falling body. As a result, the droplets formed inside the chamber do not fall to the bottom, but float in the chamber, creating a fog background that becomes denser as the number of droplets in the chamber volume increases. Toward the end of the flight this background becomes so dense that any possibility of distinguishing the tracks of individual particles disappears[^119].
The principal inherent shortcomings of the Wilson-chamber method are the low efficiency*) of particle registration and the comparatively small “sensitive” time of the chamber.
*) In notes[^154,^161] it is pointed out that it is possible to use, for the study of complex nuclei, a Wilson chamber controlled by a telescope of proportional or scintillation counters. Such a chamber will undoubtedly have a higher efficiency for registering multiply charged particles.
The use of a Wilson chamber confirmed the presence of multiply charged particles in the composition of the primary radiation\(^{120,121}\) and, in a certain sense, justified the need for a broad study of the primary nuclear component.
Counters with low efficiency. In contrast to the methods described above for studying the nuclear component of the primary flux of cosmic rays, the use of counters with low efficiency gives no information about individual particles, but makes it possible to draw conclusions about the ionizing power of the incident radiation and about the percentage content of particles with different specific ionization.
The use of low-efficiency counters is based on the fact that the probability of producing a discharge in such a counter depends on the specific ionization \(j^{122,121,162}\). This probability (the efficiency of the counter) \(\eta\) is determined by the relation\(^{124,162}\)
\[ \eta = 1 - e^{-jlp}, \tag{22} \]
where \(\bar l\) is the mean path length traversed by the particle in the counter, and \(p\) is the pressure. If one takes a counter with low pressure, then, for not very large \(j\), the efficiency will depend substantially on the magnitude of the specific ionization. The use of telescope arrangements consisting of such counters\(^{123}\), or of a combination of low-efficiency counters with ordinary ones\(^{46}\), makes it possible to determine the fractions of particles with single and multiple ionization. If all particles entering the counter have relativistic velocities, then the percentage content of particles with different ionizing power gives information about the content of particles with different \(Z\). As we see, this method (as also the next two) can give information about the distribution of primary particles by charge only in the case of measurements at such latitudes where the Earth’s magnetic field admits only those particles whose velocities are close to the speed of light.
A substantial shortcoming of this method is that the results obtained with its help may be distorted by an admixture of low-energy singly charged particles of secondary origin, which will produce increased ionization and thereby imitate the presence of multiply charged particles.
In addition, the difficulty of carrying out the experiments, associated with the fact that, in order to separate \(n\) groups of particles, it is necessary to make measurements with \(n - 1\) types of telescopes (see \(^{123}\)), sharply reduces the value of this method.
The results that were obtained with the aid of low-efficiency counters are in quantitative agreement with the results obtained by other methods.
Pulse ionization chambers and proportional counters. The use of pulse ionization-
PRIMARY COMPONENT OF COSMIC RADIATION
... chambers \[125—129, 170\] and proportional counters \[158, 159, 167\] makes it possible to measure both the total flux of multiply charged particles and their charge distribution. In essence, a pulse ionization chamber measures the ionization produced in the gas when an individual particle or group of particles passes through the chamber volume. By recording, in a chamber raised to a great altitude, the number of pulses of a given magnitude, one can obtain a “spectrum of jolts” produced by the passage of multiply charged particles and by nuclear disintegrations that are produced in the chamber walls by primary protons, $\alpha$-particles, and, in part, heavier nuclei. In a thin-walled chamber the number of jolts corresponding to nuclear disintegrations is small, and such a chamber at the boundary of the atmosphere will register chiefly primary particles. The use of such an instrument makes it possible to register multiply charged particles at a given altitude, where the pressure and temperature are known, and for each individual “jolt” the instant of time is precisely known. This makes it possible to study variations in the intensity of the nuclear component. Moreover, unlike the Wilson chamber, a large statistical body of material can be obtained in a single flight; and, unlike a rather inefficient counter, the pulse ionization chamber measures the ionization produced by an individual particle.
The principal shortcoming of the pulse ionization chamber is that, when the results are processed, it becomes necessary to introduce a correction for nuclear disintegrations.
For separating pulses corresponding to nuclear disintegrations and to the passage of multiply charged particles through the chamber, it is probably possible to use analysis of the pulse shape in the ionization chamber \[154, 155, 157\]. From the calculations of L. A. Razorenov \[157\] and G. M. Avak'yants \[165\] it follows that the form of the pulse corresponding to “ionization along a chord” (the flight of a particle through the chamber) differs from the form of the pulse corresponding to “local ionization” (a nuclear disintegration in the wall or in the gas of the chamber). However, an experimental test of the effectiveness of this method in the case of multiply charged particles has not been carried out.
Another substantial shortcoming of the ionization chamber is the dependence of the magnitude of the pulse obtained in the chamber on the length of the path that the particle traverses inside the chamber. This circumstance limits the accuracy of determining the specific ionization and thereby the accuracy of determining the charge. However, this inaccuracy can be appreciably reduced if one uses a combination of an ionization chamber and a telescope of counters that would permit registration only of particles with a definite path length inside the chamber. In this case the principal source of error will be fluctuations in the magnitude of the ionization produced over a definite segment of the path. Pulse ionization chambers can...
to use for determining the charge spectrum for particles with \(Z \gg 2\), since for particles with lower ionizing ability the pulse amplitude becomes comparable with the noise level of the radio-engineering circuit*).
In the study of multiply charged particles, proportional counters possess, in essence, the same advantages and disadvantages as pulsed ionization chambers. Unlike chambers, proportional counters make it possible, with greater reliability, to distinguish relativistic singly charged and doubly charged particles. The most reasonable application of proportional counters should be considered to be in the form of a telescope or together with a telescope made of ordinary counters.
Scintillation counters. In connection with the development of the comparatively new technique of counting charged particles by means of scintillation counters, attempts have been made\({}^{130}\) to apply this technique to the study of multiply charged particles in primary cosmic radiation.
The passage of an energetic charged particle through a scintillation counter (a crystal or a corresponding liquid) produces a flash, which is detected by a photomultiplier and, in the form of an electrical pulse, is fed to the input of an amplifier. In the work mentioned above\({}^{130}\), the scintillation counter consisted of a glass T-shaped tube, blackened on the outside with magnesium oxide, filled with a solution of pyrene in xylene. A photomultiplier was mounted in one branch of the tube. Such a counter was placed in a telescope of ordinary counters, and the pulse from the scintillation counter was recorded only in the event that a discharge occurred in the telescope of ordinary counters.
This method has the same shortcomings as the method of ionization chambers: the indistinguishability of nuclear disintegrations and multiply charged particles, and a certain uncertainty in the magnitude of the pulse associated with the difference in the length of the particle’s path inside the scintillator.
In addition, a role is played by inaccuracies caused by fluctuations in the amount of light collected and by fluctuations in the number of photoelectrons in the photomultiplier. Another circumstance reducing the value of applying this method to the study of multiply charged particles is that the scintillator itself represents a comparatively large amount of matter, in which the primary particles produce nuclear disintegrations that distort the true charge distribution of the primary nuclei of cosmic radiation. Scintillation counters have the advantage that,
*) As is seen from the work of N. L. Grigorov, I. D. Rapoport, and G. P. Shlyupov\({}^{155}\), a pulsed ionization chamber with a telescope of counters makes it possible to register even singly charged relativistic particles.
that they have a low noise level, and therefore particles with minimal \(Z\) can be measured.
The results obtained by this method\(^{130}\) agree in the main with those obtained by other methods.
3. Experimental Results
The application of the methods described in the preceding section has made it possible to obtain much diverse information on the nuclear component of cosmic radiation. The principal results concern the charge distribution of the atomic nuclei of various elements entering into the composition of cosmic rays, the energy spectrum of various groups of nuclei, variations in the intensity of the nuclear component, and questions connected with the behavior of nuclei in interstellar space. Unfortunately, some of the results do not agree with one another, and at present it is impossible to decide unambiguously which of them are more reliable.
Charge distribution. The most reliable conclusion is the presence in the primary flux of a considerable fraction of helium nuclei. As early as 1948, analyzing photographs in a Wilson chamber lifted at \(55^\circ\) northern geomagnetic latitude to the boundary of the atmosphere \((14 \div 25 \text{ g}/\text{cm}^2)\), Freier et al.\(^{121}\) found that the ratio of the number of He nuclei to the number of energetic protons at this latitude was \(1:4\). Subsequent measurements, carried out at various latitudes, confirmed this value, and more accurate experiments made it possible to find the absolute value of the flux of \(\alpha\)-particles. Thus, from the measurements of Pomerantz and Gyrford\(^{123}\), who raised on balloon sondes a telescope of low-efficiency counters \((\lambda = 50^\circ)\), it followed that approximately \(1/3\) of the cosmic-ray particles at an altitude corresponding to a pressure of \(20 \text{ g}/\text{cm}^2\) are \(\alpha\)-particles. Singer’s measurements\(^{46,31}\) on rockets, using a telescope of 4 counters, one of which was low-efficiency, showed that at northern geomagnetic latitude \(41^\circ\) the efficiency of the counter with reduced pressure increases from \(\eta_3 = 0.585 \pm 0.019\) at the Earth’s surface to \(\eta_{\text{prim}} = 0.670 \pm 0.027\) beyond the boundary of the atmosphere. From formula (22) it follows that, if the primary particles are assumed to be singly charged, and the particles registered at the Earth’s surface to possess minimum specific ionization, then the specific ionization of the particles registered beyond the boundary of the atmosphere will be equal to approximately \(1.30\) times the minimum. If one assumes that the primary radiation consists of a mixture of protons and \(\alpha\)-particles, then on the basis of formula (22) one can write the following relation:
\[ \eta_{\text{prim}} = \frac{n_p \eta_3^p + n_\alpha \eta_3^\alpha}{n_p + n_\alpha} = \frac{n_p \eta_3^p + n_\alpha \left[1 - \left(1 - \eta_3^p\right)^4\right]}{n_p + n_\alpha}. \tag{23} \]
where \(n_p\) and \(n_\alpha\) are, respectively, the numbers of protons and \(\alpha\)-particles that passed through the counter, and \(\eta_3^\alpha\) is the efficiency of the low-pressure counter with respect to relativistic \(\alpha\)-particles. From relation (23) one can find the fraction constituted by primary \(\alpha\)-particles in the total flux of protons and \(\alpha\)-particles. Schein’s measurements \(^{46}\) correspond to the presence in the primary flux of \((20\pm 8)\%\) \(\alpha\)-particles. It should be mentioned, however, that the result obtained by him \(^{31}\) at the equator on the almost complete identity of the efficiency of a counter with reduced pressure on the Earth and beyond the boundary of the atmosphere \((\eta_3^p=0.356\pm 0.015;\ \eta_{\text{prim}}=0.378\pm 0.043)\), which should be interpreted as an indication of the absence of \(\alpha\)-particles and heavier nuclei, is in contradiction with plate data. In plates exposed in the equatorial region at the boundary of the atmosphere, tracks of \(\alpha\)-particles and heavier nuclei were found \(^{171}\). There are as yet no reliable data on the flux of \(\alpha\)-particles in the equatorial region.
Using photographic plates registering relativistic singly charged particles, it proved possible to determine \(^{111,136}\) the fraction of \(\alpha\)-particles relative to the total number of particles. It also amounted to approximately 20%. From these same data, taking into account possible changes in the flux of \(\alpha\)-particles in the atmosphere, the flux of primary \(\alpha\)-particles was found at two latitudes, namely at \(30^\circ\) N latitude \(80\pm 30\) \(\alpha\)-particles/\(m^2\cdot sec\cdot sterad\) and at \(51^\circ\) N latitude \(340\pm 120\) \(\alpha\)-particles/\(m^2\cdot sec\cdot sterad\). In this calculation it was assumed \(^{117}\) that the mean free path of \(\alpha\)-particles for disintegrations is \(\lambda_{\mathrm{He}}=50\ \text{g}/\text{cm}^2\). The large error in the results is explained by the uncertainty in the number of secondary particles.
Measurements carried out with the aid of a proportional counter at \(41^\circ\) and \(55^\circ\) N latitude made it possible to find the ratio of the flux of \(\alpha\)-particles to the flux of protons, which proved to be in the first case \(^{158}\sim 5.5\), and in the second case \(^{159}\sim 6\). The absolute values of the fluxes measured by this method were: at \(41^\circ\) N latitude \(I_{\mathrm{pr}}=580\pm 50\) particles/\(m^2\cdot sec\cdot sterad\) and \(I_{\mathrm{He}}=110\pm 20\) particles/\(m^2\cdot sec\cdot sterad\), at \(55^\circ\) N latitude \(I_{\mathrm{pr}}=2100\pm 100\) particles/\(m^2\cdot sec\cdot sterad\) and \(I_{\mathrm{He}}=340\pm 40\) particles/\(m^2\cdot sec\cdot sterad\).
At \(55^\circ\) N latitude, Ney and Toon \(^{130}\) raised on balloon-borne probes a telescope in which one of the counters was a scintillation counter. The flux of \(\alpha\)-particles measured by them proved to be \((280\pm 9)\) \(\alpha\)-particles/\(m^2\cdot sec\cdot sterad\). The indicated error is a statistical error. Apparently, the true error is considerably larger, since the instrument did not make it possible to distinguish with certainty particles with close \(Z\). A further indication of the possibility of a large error is the circumstance that, in contrast to the data of other authors, the ratio found in this work of the number of \(\alpha\)-particles
to the number of protons is \(1:7\). Therefore the quoted value of the flux of \(\alpha\)-particles at \(55^\circ\) N latitude should be treated with caution, since it may be somewhat underestimated.
The flux of \(\alpha\)-particles at various latitudes is presented in Table IV:
Table IV
Flux of \(\alpha\)-particles and the total flux of cosmic particles
at latitudes \(30^\circ\), \(41^\circ\), \(51^\circ\), and \(55^\circ\)
| Geomagnetic latitude | Flux of \(\alpha\)-particles in \(1/m^2\cdot sec\cdot sterad\) | Flux of all particles in \(1/m^2\cdot sec\cdot sterad\) |
|---|---|---|
| \(30^\circ\) | \(60 \pm 10^{117}\) | \(460^{27}\) |
| \(41^\circ\) | \(110 \pm 20^{158}\) | \(790 \pm 50^{158}\) |
| \(51^\circ\) | \(340 \pm 120^{136}\) | \(2200^{27}\) |
| \(55^\circ\) | \(280 \pm 8^{130}\) | \(2300^{27}\) |
| \(55^\circ\) | \(340 \pm 40^{159}\) | \(2440 \pm 140^{153}\) |
Nuclei of other elements, heavier than He, are encountered in significantly smaller numbers. Taken all together, they constitute \(\sim 1\%\) of the total number of primary particles.
The charge distribution has been studied in sufficient detail for nuclei with \(Z > 6\). Measurements carried out by various authors and at different latitudes give concordant results both for the group of nuclei C, N, O, F and for nuclei with \(28 > Z > 10\).
The study of photographic plates exposed at the boundary of the atmosphere showed that the fluxes of nuclei of the groups C, N, O, F and \(28 > Z > 10\) at various latitudes can be represented in the form of Table V on p. 51.
Measurements of the flux of particles with \(Z > 6\), carried out\(^{130}\) with a scintillation counter at latitude \(55^\circ\), also gave results in good agreement with those obtained by the photographic-plate method: the flux of C, N, O nuclei is \((16 \pm 1.8)\) particles/\(m^2\cdot sec\cdot sterad\); the flux of nuclei \(Z > 9\) is \((4.3 \pm 0.2)\) particles/\(m^2\cdot sec\cdot sterad\). (The errors given here are statistical; it is possible that the true errors are larger.)
Nor do the data\(^{127}\) from a thin-walled pulsed ionization chamber, lifted at \(52^\circ\) N latitude to an altitude corresponding to \(16\ g/cm^2\), contradict the measured flux.
Measurements beyond the boundary of the atmosphere, carried out by the method of photographic plates lifted on a rocket, agree within the limits of error with the results obtained at the boundary of the atmosphere. The flux of particles with \(Z \geqslant 6\), measured by Igoda and Kaplon\(^{134}\) at \(41^\circ\) N latitude, is \(310 \pm 180\) particles/\(m^2 \cdot min\), instead of \(170 \pm 20\) particles/\(m^2 \cdot min\) according to Bradt and Peters.
Table V
Flux of various groups of nuclei at geomagnetic latitudes
\(3^\circ,\ 30^\circ,\ 41^\circ,\ 51^\circ,\ 55^\circ\)
| Latitude | Flux (particles/\(m^2 \cdot sec \cdot sterad\)) \(3 \leqslant Z < 5\) | Flux (particles/\(m^2 \cdot sec \cdot sterad\)) \(6 \leqslant Z \leqslant 9\) | Flux (particles/\(m^2 \cdot sec \cdot sterad\)) \(Z \geqslant 10\) |
|---|---|---|---|
| \(3^\circ\) | — | \(1.30 \pm 0.25^{171}\) | \(0.30 \pm 0.07^{171}\) |
| \(3^\circ\) | — | \(1.45 \pm 0.30\) | \(0.33 \pm 0.08^{184}\) |
| \(30^\circ\) | — | \(3.4 \pm 0.5^{117}\) | \(1.0 \pm 0.3^{117}\) |
| \(30^\circ\) | — | \(2.7^{133}\) | \(0.85^{133}\) |
| \(41^\circ\) | — | \(5.8 \pm 0.7^{117}\) | \(2.5 \pm 0.5^{117}\) |
| \(51^\circ\) | — | \(12 \pm 3^{117}\) | \(3.5 \pm 0.7^{117}\) |
| \(55^\circ\) | — | \(15 \pm 1.5^{117}\) | \(4.5 \pm 1.0^{117}\) |
| \(55^\circ\) | \(15 \pm 1^{109}\) | \(12 \pm 1^{109}\) | \(4.2 \pm 0.9^{109}\) |
| \(55^\circ\) | — | — | \(5.8^{133}\) |
The results obtained with the aid of a pulsed ionization chamber lifted at northern geomagnetic latitude \(41^\circ\) beyond the boundary of the atmosphere\(^{128}\) (the chamber was installed on a rocket) also agree with the data from plates lifted at the same latitude on balloon soundings. If one considers particles with \(Z \geqslant 6\) and assumes that in the primary flux they are represented in the same proportion in which the corresponding elements are represented in the universe (see below), then from the ionization-chamber data the following values of the fluxes at latitude \(41^\circ\) are obtained:
\[ 6 \leqslant Z < 9 \quad \text{flux } 6 \ \text{particles}/m^2 \cdot sec \cdot sterad, \]
\[ 10 \leqslant Z < 28 \quad \text{flux } 1.1 \ \text{particles}/m^2 \cdot sec \cdot sterad. \]
Comparison with Table V shows good agreement for \(6 \leqslant Z < 9\) and only a small difference for \(Z \geqslant 10\).
In contrast to the results set forth above, at present there is no clarity regarding the presence in the primary flux of cosmic rays of the nuclei Li, Be, B. This situation is connected above all with the difficulty of detecting this group of nuclei.
The point is that in electron-sensitive emulsions the tracks of Li, Be, B have such a high grain density that it is impossible to use the grain-counting method for determining the charge. On the other hand, the number of \(\delta\)-electrons along the tracks of these particles is small, and the method of determining the charge from the density of \(\delta\)-electrons may, in the opinion of some authors \(^{110,111}\), give erroneous results because of the inclusion of background electrons. In those cases where low-sensitivity emulsions are used and the charge is determined by the grain-counting method, the tracks of Li, Be, B nuclei may be missed when the plates are examined, since these tracks are very thin, with a low grain density and a small number of \(\delta\)-electrons. Another reason making it difficult to decide whether Li, Be, B nuclei are present in the primary flux is the relative smallness of the number of these nuclei in comparison with protons and \(\alpha\)-particles. In addition, when measuring the flux of primary Li, Be, B nuclei, one must take into account the circumstance that, in the fragmentation of heavier primary nuclei, “fragments” are formed, among which there may be relativistic Li, Be, B nuclei. Therefore, in determining the true flux of these nuclei, a correction must be introduced for the possible admixture of secondary particles.
Numerous determinations of particle charges by measuring the grain density in their tracks seemed to indicate the absence of any appreciable quantity of primary Li, Be, B nuclei. Thus, at latitude \(30^\circ\) it was found \(^{110,135}\) that the maximum value of the flux of Li, Be, B nuclei does not exceed \(0.4\) particles/\(\text{m}^2\cdot\text{sec}\cdot\text{sterad}\). This amounts to less than \(10\%\) of the number of nuclei with \(Z>6\). For a number of years it was considered that the absence of Li, Be, B nuclei in the primary flux of cosmic rays was a firmly established fact. However, in 1951 a paper was published \(^{131}\) whose results indicated the presence of a considerable fraction of Li, Be, B nuclei in the cosmic-ray flux at an altitude of \(32\) km at geomagnetic latitude \(55^\circ\). In this work the value of the charge was determined by measuring the density of \(\delta\)-electrons \(N_\delta\). Although in this case considerable errors are possible because of the inclusion of background electron tracks, the careful investigation of the method used and the large number of control measurements carried out by the authors \(^{109}\) apparently confirm the correctness of the conclusions drawn. According to their results, the flux of Li, Be, B nuclei at latitude \(55^\circ\) is approximately \(15\pm1\) particles/\(\text{m}^2\cdot\text{sec}\cdot\text{sterad}\), i.e., more than \(80\%\) of the number of all heavier nuclei. This result cannot in any way be reconciled with the result obtained by Bradt and Peters \(^{110,135}\), but Dainton et al.’s results \(^{109}\) coincide with those of Bradt and Peters in the region of nuclei with \(Z>6\). The observed number of Li, Be, B nuclei cannot be explained by secondary particles formed in the fragmentation of heavier nuclei. As shown by
calculations, the number of nuclei of the Li, Be, B group formed at an altitude of 20 g/cm² amounts to \(\sim 30\%\) of the number of C, N, O, F nuclei. Even if one assumes that, of the indicated 80%, secondary particles account for 30%, there still remains a significant fraction of particles that should be attributed to the number of primary ones. A substantial error could have been introduced into the results if, in the flights carried out, the time of ascent and descent was not small in comparison with the time the plates remained at an altitude of 30 km. In this case a large fraction of the particles of the Li, Be, B group could be explained by secondary particles collected from the entire height of the atmosphere. However, the published paper does not give a flight graph, and consequently this questionable point cannot be clarified completely.
A confirmation of the results of Dainton et al.\(^{109}\) is provided by the data reported in the work of Gottstein\(^{175}\). The measurements were made at latitude 55° by raising photographic emulsions to an altitude of \(\sim 29\) km. In the photographic emulsions, stars formed in the disintegration of various complex nuclei of high energy were studied. The charge was determined both by measuring the grain density and by measuring the density of \(\delta\)-electrons. In some cases these determinations were checked by summing the charges of all particles emitted in the disintegration of the primary nucleus. Various methods were used to determine the energy of the primary particles. Measurements of a large number of tracks of primary complex nuclei showed that the ratio between the intensities of the individual groups agrees with that found in work\(^{109}\). A comparison of the data of work\(^{175}\) with work\(^{109}\) and with Peters’s data\(^{135}\) is given in Table VI.
Table VI
Relative content of various groups of nuclei in the primary flux
| Author | Charge groups | Charge groups | Charge groups |
|---|---|---|---|
| Author | \(3 \leq Z \leq 5\) | \(6 \leq Z \leq 9\) | \(Z > 9\) |
| Gottstein (latitude 55°) . . . . | 36.5% | 40.5% | 23% |
| Dainton (” 55°) . . . . | 49% | 42% | 9% |
| Peters (” 30°) . . . . | \(\leq 8\%\) | \(\geq 71\%\) | \(\geq 21\%\) |
Measurements carried out with the aid of a scintillation counter\(^{130}\) give, for a flux of particles with \(3 \leq Z \leq 5\), a value of 84 particles/m²·sec·sterad. This improbably large value of the flux of Li, Be, B nuclei is explained by the fact that the scintillation counter cannot distinguish multiply charged particles from nuclear disinte-
...events (stars) produced in the scintillator itself. The authors of this work, proceeding from the results of Bradt and Peters on the absence of Li, Be, B nuclei in the primary flux, attribute all these cases to stars and obtain, for the effective cross section for the production of stars by primary protons, a value equal to one half of the geometrical cross section. If, however, the effective cross section is reduced by (14–15)%, which corresponds to a cross section \(\sim 0.43\) of the geometrical one, then the results of experiments with the scintillation counter will not contradict the conclusions concerning the presence of a primary flux of Li, Be, B nuclei equal, at \(55^\circ\) N latitude, to (12–15) particles/\(m^2\cdot sec\cdot sterad\).
Measurements carried out with a pulse ionization chamber on rockets\({}^{128}\) made it possible to estimate an upper limit for the flux of particles with \(3 \leq Z \leq 5\). In order to make this estimate, it was necessary to compare the results obtained with the pulse ionization chamber with those obtained with photographic plates. Using the charge distribution of particles found in the photographic plates, one calculates the spectrum of pulses that these particles will produce in the chamber used. Comparison of the spectrum calculated in this way with the experimentally measured one shows a definite discrepancy in the region of small pulses. If all this discrepancy is ascribed to the appearance of a group of primary Li, Be, B nuclei, which are absent in the distribution used, then, as an upper limit for the flux of these nuclei at \(41^\circ\) N latitude, a value \(\sim 18\) particles/\(m^2\cdot sec\cdot sterad\) is obtained. If one takes into account that a definite contribution to the difference between the pulse spectrum in the ionization chamber and the spectrum of nuclei according to the plate data is made by nuclear disintegrations in the walls of the ionization chamber, then, undoubtedly, the limiting value for the flux of Li, Be, B nuclei is greatly reduced.
Assuming that the entire difference is due to nuclear disintegrations, one finds for the mean range of nuclear disintegrations \(270\,g/cm^2\) (the geometrical cross section corresponds to a range of \(100\,g/cm^2\)). However, a ratio \(\sim 1:1\) between the numbers of Li, Be, B nuclei and C, N, O, F nuclei can also be satisfied in this case. In this case the mean range will increase only to \(360\,g/cm^2\). In any event, it may be said that the data obtained with the pulse ionization chamber do not refute the conclusion concerning the presence of Li, Be, B nuclei in the primary flux.
Measurements carried out beyond the boundary of the atmosphere with proportional counters\({}^{136}\), owing to their low statistical accuracy, can serve neither as confirmation nor as refutation of Dainton et al.’s results. During the entire flight only one particle with charge greater than 2 was recorded (a carbon nucleus, \(Z=6\)).
The final resolution of the question of the presence of nuclei of the Li, Be, B group in the primary radiation, and the determination of the magnitude of the flux of these particles, require further experiments using different methods that check and complement one another.
At present the question of the presence in the primary radiation of nuclei heavier than nickel nuclei remains unresolved. In most works109—111, 131 it is asserted that nuclei with \(Z\) greater than \(\sim 28\) are not encountered in the primary radiation. In Peters’ paper117 doubt is cast on the correctness of the charge determination in the early works103, 121, where tracks of nuclei with \(Z > 28\) had been found. However, reports later appeared as well132, 133, 152 on the discovery, in photographic emulsions exposed at very high altitudes, of tracks of nuclei with \(Z > 28\). Yagoda153, who carried out experiments at an altitude of \(\sim 37\) km, found a comparatively large flux of nuclei with \(Z > 34\). According to his measurements, the flux of nuclei with \(Z > 34\) amounts to 0.3 of the flux of Fe, Co, Ni nuclei; moreover, tracks of particles were encountered whose charge, determined by the method of measuring the length of the narrowing part of the track, reached \(Z \sim 53\). The fact that in earlier works no noticeable number of nuclei with \(Z > 28\) had been recorded is possibly explained by the fact that these nuclei are very strongly absorbed even in a small layer of residual atmosphere. Further measurements at the greatest possible altitudes will make it possible to find out whether nuclei with very large \(Z\) are present in the primary flux.
Energy spectra of various groups of nuclei. The principal method for determining the energy spectrum, as in the case of protons, is the measurement of the fluxes of separate groups of nuclei at different latitudes163. Assuming that multicharged particles approach the Earth in a completely ionized state (this assumption is confirmed by a number of measurements; see below), we may take for these particles (with charge \(Z\) and atomic weight \(A\))
\[ \frac{Z}{A} = \frac{1}{2} \qquad (Z \leqslant 20). \]
In this case, according to the theory of motion of charged particles in the magnetic field of a dipole13, only those particles will arrive at a given latitude \(\lambda\) in the vertical direction whose momentum per nucleon \(p\) satisfies the relation
\[ pc \geqslant 7.45 \cos^{4}\lambda \cdot 10^{9}\ \text{eV}. \tag{24} \]
In the region of low energies (up to \(0.7 \cdot 10^{9}\ \text{eV/nucleon}\)) the spectrum can be obtained if one uses the data of the distribution by ranges173. For energies less than \(\sim 2 \cdot 10^{9}\ \text{eV/nucleon}\), in constructing the spectrum of nuclei with not very large \(Z\), one may use the measurement of the mean deflection angle in multiple scattering. To find the spectrum in the energy region exceeding \(7 \cdot 10^{9}\ \text{eV/nucleon}\)
(for \(Z \gg 10\)), the method of measuring the mean scattering angle of the \(\alpha\)-particles formed in the breakup of the primary nucleus (see above) can be applied. In this case, however, it is necessary to assume that the probability of splitting is independent of the energy\(^*\), and depends only on the atomic number of the primary nucleus and on the impact parameter of the collision with a nucleus in the emulsion. Such an assumption is justified if the observed shower of \(\alpha\)-particles is the result of the “evaporation” of the incident nucleus excited by a nucleus in the emulsion.
The application of all these methods made it possible to find the spectra of different groups of particles in the energy range from \(0.3 \cdot 10^9\) (for He) to \(\sim 50 \cdot 10^9\) eV/nucleon (for nuclei with \(Z \gg 10\))\({}^{115}\). The spectra of the different groups of nuclei are shown in Fig. 12. An analytical expression that well describes the dependence on energy for all particle groups has the form:
\[ N(E>\varepsilon)=\frac{K}{(1+\varepsilon)^{1.2}}, \tag{25} \]
where \(\varepsilon\) is the kinetic energy of the nucleus in \(10^9\) eV per nucleon, and \(K\) has the following values:
\[ 380\ \frac{\text{particles}}{m^2\cdot \text{sec}\cdot \text{sterad}} \quad \text{for He;} \]
\[ 20\ \frac{\text{particles}}{m^2\cdot \text{sec}\cdot \text{sterad}} \quad \text{for the group of nuclei C, N, O;} \]
\[ 6\ \frac{\text{particles}}{m^2\cdot \text{sec}\cdot \text{sterad}} \quad \text{for the group of nuclei with } Z \gg 9. \]
Fig. 12. Integral energy spectrum of various components of primary cosmic radiation. Along the abscissa is plotted the kinetic energy in \(10^9\) eV/nucleon. Along the ordinate is the flux in particles/\(m^2\cdot\)sec\(\cdot\)sterad. Curves 1, 2, 3, 4 represent, respectively, the spectra of protons, \(\alpha\)-particles, nuclei of the C, N, O group, and nuclei of the group with \(Z \gg 10\). The ordinates of curves 3 and 4 have been increased by a factor of 10. The vertical bars are data from measurements of the flux at different latitudes. Crosses and circles are results of energy measurements by the magnitude of the scattering angle of the secondary particles and by the mean scattering angle; they are normalized to the data of direct flux measurements at the point \(3\cdot 10^9\) eV/nucleon.
\[ {}^*\ \text{In Ref. }{}^{175}\text{ it is indicated, however, that when a complex nucleus of high energy collides with a nucleus of a light atom in an emulsion, the probability of emission of fragments with charge } Z>2 \text{ depends on the energy. This assertion requires verification.} \]
Comparison with the proton spectrum shows that in the energy region \(\lesssim 7 \cdot 10^{10}\) eV/nucleon the spectra are very close to one another*). This circumstance apparently points to a common source of acceleration of protons and more complex nuclei.
For particles in the energy interval from \(0.35 \cdot 10^{9}\) to \(8 \cdot 10^{9}\) eV/nucleon, the number of nucleons of the same energy brought by different groups of nuclei can be represented in the form of Table VII.
Table VII
Relative number of nucleons brought to the Earth by different groups of primary nuclei
| Nuclei | Fraction of nucleons under the assumption that there are no Li, Be, B (in %) | Fraction of nucleons under the assumption that \(N(\mathrm{Li}, \mathrm{Be}, \mathrm{B}) \approx N(\mathrm{C}, \mathrm{N}, \mathrm{O})\) (in %) |
|---|---|---|
| Protons | 66 | 64 |
| \(\alpha\)-particles | 26 | 25 |
| Li, Be, B group | — | 3 |
| C, N, O group | 5 | 5 |
| \(Z \geqslant 9\) | 3 | 3 |
Variations in the intensity of the nuclear component of primary cosmic radiation. The question of changes with time in the intensity of the primary flux of multiply charged particles attracted attention after the work of Lord and Schein\(^{138}\) was published in 1950. In this work a 2–3-fold decrease was reported in the flux of nuclei with \(Z > 10\), measured at night at the boundary of the atmosphere, in comparison with the flux measured in the daytime. At the same time the flux of protons and \(\alpha\)-particles, determined from the number of “stars” produced in plates, did not change. In the same year, the same authors\(^{139}\), as well as others\(^{140}\), obtained confirmation of the initial result. The experiments they carried out gave a decrease of the flux at night, compared with the daytime flux, by a factor of \((2.55 \pm 0.26)\). In experiments already mentioned, using a scintillation counter\(^{130}\), a change with time in the frequency of occurrence was observed
* There are indications\(^{171,172}\) that the similarity in the character of the spectrum is preserved also at higher energies, up to \(10^{12}\) eV/nucleon. Further experiments are necessary, however, in order to make this assertion sufficiently reliable.
large pulses corresponding to heavy particles, whereas the frequency of pulses corresponding to protons and $\alpha$-particles changed only slightly, although the fraction of $\alpha$-particles apparently increased somewhat. In the authors’ opinion, it is possible that the increase in the intensity of the nuclear component by $\sim 45\%$ is explained by diurnal variations or is connected with solar activity.
These are the facts that indicated the existence of diurnal variations.
However, later works $^{129,133,160,171}$ proved the erroneousness of the conclusions made earlier. Thus, in the work of Freier et al. $^{133}$ it is pointed out that, of the two night flights carried out by them, the results of the first can be interpreted as indicating the presence of diurnal variations $^{140}$, while the results of the second show the absence of any noticeable variations. The authors themselves consider the results of the second night flight more reliable, since a greater altitude was reached ($\sim 14 \text{ g}/\text{cm}^2$) and it was maintained during the flight better than in the first case. In the first flight the altitude varied from 23 to 35 $\text{g}/\text{cm}^2$, and at an altitude of 30 $\text{g}/\text{cm}^2$ the apparatus was located for $\sim 10\%$ of the flight time. It is possible that the diurnal effect measured in 1950 $^{138}$ is also explained by some unaccounted-for experimental errors.
Another experimental proof of the absence of diurnal variations is provided by the results obtained with pulse ionization chambers raised on balloon sondes at 52 and 55° N latitude to an altitude of 27 km $^{129}$. In the chamber, bursts exceeding the threshold corresponding to the passage of a particle with $Z > 8$ were measured. Comparison of the data obtained at night at 55° N latitude with the corresponding values of the number of bursts at the given altitude during the day, determined from the averaged results of four daytime flights at 52° N latitude, shows the absence of a noticeable diurnal effect. The change in the intensity of the nuclear component during the course of a day, consistent with the results of the measurements, does not exceed 13%.
Thus, there is every reason to believe that the intensity of the nuclear component of primary cosmic rays is not subject to substantial diurnal fluctuations. The results that indicated the presence of diurnal variations are apparently erroneous, or the observed changes were caused by some other reasons*).
At present it does not seem possible to say anything about variations in the intensity of the nuclear component,
*) Recently a report appeared $^{183}$ in which, on the basis of data from one flight, it is asserted that at 12–14 hours a maximum is observed in the intensity of the flux of nuclei with $Z > 10$. This conclusion requires verification.
having other periods (annual variations, 27-day variations, etc.). Such observations have not been carried out systematically, and the statistical material available is still insufficient for drawing any conclusions whatsoever.
It may only be noted that an attempt\(^{133}\) to find a connection between solar flares and the intensity of the nuclear component did not give reliable results, but showed that if the effect exists, it is very small.
Ionization of multiply charged particles. A very important question is the state in which particles of primary cosmic radiation arrive at the Earth—whether they are completely or only partially ionized. The solution of this question should make it possible to judge the conditions of motion of a heavy nucleus in interstellar space, and also the place and nature of the acceleration process.
A rapidly moving atom, when passing through matter, undergoes ionization, i.e. loses electrons. Calculations show\(^{110}\) that, in order for an atom moving with velocity \(\beta \simeq 0.3\) to become completely ionized, an amount of matter \(\sim 1.5\ \mathrm{mg}/\mathrm{cm}^{2}\) is sufficient, and in the case \(\beta \sim 1\) only \(\sim 1\ \mathrm{mg}/\mathrm{cm}^{2}\) is sufficient. Therefore it was quite justified to assume, in processing data obtained by means of photographic plates, Wilson chambers, and other instruments (see above), that we are dealing with “bare” nuclei, since under all conditions (even in observations beyond the boundary of the atmosphere) the particle, before the moment of its registration, passes through a layer of matter exceeding \(15\ \mathrm{mg}/\mathrm{cm}^{2}\). However, this does not exclude the possibility that atoms not fully ionized enter the region of the Earth’s magnetic field. The Earth’s magnetic field will act on these partially ionized atoms to a lesser degree than on the same atoms that have undergone complete ionization. The appearance of such partially ionized atoms should therefore lead to the observation on Earth of nuclei with energies below the threshold determined, in the case of completely ionized atoms, by formula (24). The simplest estimates show that if a relativistic particle traverses a distance of the order of the dimensions of the Galaxy (\(\sim 5 \cdot 10^{22}\ \mathrm{cm}\), which corresponds to \(10^{-24}\ \mathrm{g}/\mathrm{cm}^{3} \cdot 5 \cdot 10^{22}\ \mathrm{cm} = 5 \cdot 10^{-2}\ \mathrm{g}/\mathrm{cm}^{2} = 50\ \mathrm{mg}/\mathrm{cm}^{2}\)), then in doing so it is completely ionized and enters the region of action of the Earth’s magnetic field in the form of a “bare” nucleus. If, however, the particles arrive from regions of space close to the Earth (for example, directly from the Sun; \(R \sim 10^{13}\ \mathrm{cm}\)), then they may retain part of their electron shells and may penetrate to the Earth with energies below the threshold for the given latitude.
Experiments\(^{111,115}\), carried out on Earth at high altitudes, showed that complex nuclei enter the region of action
of the Earth’s magnetic field already completely stripped of their electron shells.
In experiments with photographic plates\(^{111,143}\) at \(55^\circ\) N latitude, where the threshold produced by the Earth’s magnetic field for “bare” nuclei is \(0.35 \cdot 10^9\) eV/nucleon, out of 30 tracks not a single one was found corresponding to an energy less than \(0.37 \cdot 10^9\) eV/nucleon. At the same time, for particles of the C, N, O group to reach the plates an energy of \(\sim 0.25 \cdot 10^9\) eV/nucleon was required, while for quadruply ionized carbon nuclei the geomagnetic threshold is \(\sim 0.15 \cdot 10^9\) eV/nucleon. In measuring the flux of heavy particles at \(30^\circ\) N latitude, out of 150 particles not a single one was found that stopped in the stack of plates. If particles of the C, N, O group arrived incompletely ionized, then heavier nuclei would retain a large fraction of their electrons and would penetrate to the Earth with energies much smaller than the limiting one. The facts cited indicate that at least light nuclei \((Z < 10)\) arrive at the Earth completely stripped of their electron shells. With respect to heavy nuclei, direct experiments at high latitudes cannot be carried out, since, in order to clarify at latitude \(54^\circ\) the question of whether nuclei—say, iron nuclei—with energy less than that determined by the Earth’s magnetic field arrive at the Earth, it would be necessary to raise the plates to an as yet unattainable altitude of \(\sim 5\) g/cm\(^2\). However, measurements at latitude \(30^\circ\), where the threshold corresponds to \(3.5 \cdot 10^9\) eV/nucleon, showed that particles with energy less than \(3.5 \cdot 10^9\) eV/nucleon do not arrive.
More careful measurements\(^{115}\) at \(41^\circ.7\) N latitude, after comparison with data obtained at \(55^\circ\) N latitude, confirmed the conclusion that cosmic-ray particles enter the Earth’s magnetic field in a completely ionized state. Having measured the flux of primary particles at \(55^\circ\) N latitude in the region of low energies, one calculates the expected decrease in the number of particles at \(41^\circ.7\) N latitude (due to cutoff by the magnetic field) under three different assumptions: 1) the nuclei are completely freed of electrons; 2) the \(K\)-shell remains; 3) the \(K\)- and \(L\)-shells remain. After this, the expected number of particle stops in the emulsion is calculated.
The results of the calculations and the measurement data may be presented in the form of Table VIII (p. 62).
It is seen from the table that, in all probability, even heavy atoms arrive at the Earth in a completely ionized state.
4. Evolution of nuclei in interstellar space
The results of studying the component of cosmic rays consisting of nuclei of various elements make it possible to draw a number of conclusions about the sources of these particles and about the character of their motion from
Table VIII
Comparison of the number of particles stopped in the emulsion with the expected number of stops under different assumptions about the degree of ionization of primary nuclei with large \(Z\)
| \(Z\) | Element | Number of stopped particles in case 1 | Number of stopped particles in case 2 | Number of stopped particles in case 3 | Number of observed stops | Number of tracks with energy below threshold |
|---|---|---|---|---|---|---|
| 26 | Fe | 3.8 | 5.4 | 17 | 3 | 0 |
| 20 | Ca | 1.5 | 2.8 | 13 | 1 | 0 |
| 14 | Si | 0.6 | 4.4 | 53 | 2 | 0 |
| 12 | Mg | 0 | 2.3 | 65 | 0 | 0 |
| Total | 5.9 | 14.9 | 148 | 6 | 0 |
Case 1: a completely ionized atom.
Case 2: a nucleus with electrons in the \(K\)-shell.
Case 3: a nucleus with electrons in the \(K\)- and \(L\)-shells.
of the source to the Earth. If one takes into account that, in interaction with interstellar gas, the composition of the nuclear component can, generally speaking, change, then one should not expect the distribution of the primary component from complex nuclei by charge observed on Earth to coincide with their distribution in the source. Such agreement can occur only when the source of cosmic rays is very close to the Earth, and the cosmic rays formed in it reach the Earth directly from the source, without any more or less prolonged wandering in interstellar (or interplanetary) space. However, the observed isotropy in the distribution of cosmic rays argues against such an assumption. In the case where cosmic rays travel sufficiently long paths from the source to the Earth, the relative fraction of light nuclei (protons, \(\alpha\)-particles, nuclei of Li, Be, B) should increase in comparison with the fraction of the corresponding nuclei in the source. This should occur for two reasons: first, in the fragmentation of heavy nuclei, light “fragments” will be formed, which will contribute to the component of cosmic rays consisting of light nuclei; second, the cross section for the interaction of heavy nuclei is larger than the cross section for the interaction of light nuclei, and therefore heavy nuclei will be absorbed by interstellar hydrogen more rapidly than light ones.
From this point of view, a certain similarity between the charge distribution of nuclei in cosmic radiation and the relative abundance of the various elements in nature is quite unexpected and surprising. If we combine the data on the relative average abundance of the elements in nature \(^{141-142}\) and the data on the relative content of various nuclei in cosmic radiation, taking the hydrogen content in both cases to be \(3.5 \cdot 10^8\), then we obtain Table IX.
Table IX
Average abundance of the elements in nature and the charge spectrum of the nuclear component of the primary flux of cosmic rays
| Element | \(Z\) | On average in nature | In the primary flux of cosmic rays*) |
|---|---|---|---|
| H | 1 | \(3.5 \cdot 10^8\) | \(3.5 \cdot 10^8\) |
| He | 2 | \(3.5 \cdot 10^7\) | \(3.5 \cdot 10^7\) |
| Li | 3 | \(\sim 1.4\) | |
| Be | 4 | \(\sim 1.4\) | \(190 \cdot 10^4\) |
| B | 5 | \(\sim 1.4\) | |
| C | 6 | \(8 \cdot 10^4\) | \(182 \cdot 10^4\) |
| N | 7 | \(16 \cdot 10^4\) | \(182 \cdot 10^4\) |
| O | 8 | \(22 \cdot 10^4\) | \(182 \cdot 10^4\) |
| Ne | 10 | \((9\text{—}24)\cdot 10^4\) | \(10.5 \cdot 10^4\) |
| Mg | 12 | \(8.8 \cdot 10^3\) | \(140 \cdot 10^3\) |
| Si | 14 | \(10^4\) | \(10.5 \cdot 10^4\) |
| Fe | 26 | \(1.8 \cdot 10^4\) | \(10.5 \cdot 10^4\) |
| Other elements \(Z<30\) | \(<30\) | \(9.3 \cdot 10^3\) | \(105 \cdot 10^3\) |
| Elements with \(30<Z\leq 92\) | \(30\text{—}92\) | \(10^4\) | \(<3.5 \cdot 10^3\) |
*) The normalization of both distributions was carried out with respect to hydrogen.
It is not difficult to see that the ratio of the number of helium nuclei to the number of hydrogen nuclei and the ratios among the other groups of nuclei (not counting the group Li, Be, B) are approximately the same both in the case of cosmic rays and in the case of abundance in nature. However, the relative fraction of hydrogen and helium nuclei in cosmic rays is smaller than in the universe. As we shall see from
furthermore, this circumstance is very essential for theories of the origin of cosmic rays.
The observed parallelism in the distribution of elements in the universe and in cosmic rays, in the opinion of some investigators, could be regarded as evidence in favor of those theories which took stars as the sources of cosmic rays, since the emission of protons and other nuclei under one and the same acceleration mechanism should, at first glance, lead to an identity of the distributions by nuclear charge in cosmic rays and in the source \({}^{101,102}\). However, taking into account the disintegration of complex nuclei occurring in interstellar space leads, as was said, to the conclusion that the composition of cosmic rays must differ strongly from the composition of the source.
A very characteristic question in this respect is the presence, in the primary component of cosmic rays, of nuclei of the group Li, Be, B. As is seen from Table IX, in nature these elements are present in negligible quantities. The abundance curve of the elements in the region Li, Be, B has a “gap.” If the particles arriving at the Earth have traversed a comparatively short path from the source, then we may expect that among them there will be no Li, Be, B nuclei if there were none in the source. A different picture will occur if the cosmic-ray particles have traversed a long path in interstellar space. In this case, owing to the disintegration of heavy nuclei, an appreciable fraction of Li, Be, B nuclei will appear.
Let us estimate the expected fraction of Li, Be, B nuclei for the case when equilibrium has been established and the number of particles of a given kind does not change on the average, while in the flux emitted by the source the group of Li, Be, B nuclei was completely absent. Denote the group of Li, Be, B nuclei by \(A\), the group of C, N, O, F nuclei by \(B\), and the group of nuclei with \(Z>10\) by \(C\). If \(N_A\), \(N_B\), and \(N_C\) denote, respectively, the numbers of nuclei of types \(A\), \(B\), and \(C\) in the primary flux, \(\sigma_A\), \(\sigma_B\), \(\sigma_C\) the effective cross sections for the disintegration of nuclei \(A\), \(B\), \(C\) by interstellar hydrogen, and \(P_H(B)\) and \(P_H(C)\) the probability that, in the disintegration of a nucleus of type \(B\) or \(C\), a nucleus of type \(A\) is emitted, then at equilibrium we may write
\[ \sigma_A N_A = \sigma_B N_B P_H(B) + \sigma_C N_C P_H(C) \]
or
\[ R = \frac{N_A}{N_B} = \frac{\sigma_B}{\sigma_A} P_H(B) + \frac{\sigma_C}{\sigma_A}\frac{N_C}{N_B} P_H(C). \tag{26} \]
Measurements \({}^{115,135}\), carried out with the aid of photographic emulsions, give values for the effective interaction cross sections that are well described by the empirical relation
\[ \sigma_{1,2} = \pi (r_1 + r_2 - 2\Delta r)^2, \tag{27} \]
where \(r_i = 1.45\cdot 10^{-13} A_i^{1/3}\ \text{cm}\); \(\Delta r = 0.85\cdot 10^{-13}\ \text{cm}\) (\(A_i\) is the atomic weight of the \(i\)-th nucleus; the subscripts 1 and 2 refer to the two interacting nuclei). The values of the mean free path for collisions found experimentally are given in Table X.
Table X
Mean free path of energetic nuclei in various substances, determined by energy losses in nuclear collisions
| Atomic number | Mean free path in glass \((\text{g}/\text{cm}^2)^*)\) | Mean free path in brass \((\text{g}/\text{cm}^2)^*)\) | Mean free path in air \((\text{g}/\text{cm}^2)^{**})\) | Mean free path in hydrogen \((\text{g}/\text{cm}^2)^{**})\) |
|---|---|---|---|---|
| \(Z=2\) | 50 | 80 | 44.5 | 12.5 |
| \(3 \leq Z \leq 5\) | 47.5 | — | 32.0 | 7.5 |
| \(6 \leq Z \leq 9\) | 34.5 | 58.5 | 27.0 | 4.8 |
| \(10 \leq Z \leq 26\) | 25.5 | 49 | 21.0 | 3.1 |
| \((Z\sim 14)\) |
* The mean free path was measured experimentally.
** Calculated from formula (27).
In the case of interaction with hydrogen one may approximately assume that, for \(A_i > 8\), \(\sigma_i \simeq \pi r_i^2\).
This gives us the following values for the quantities entering formula (26):
\[ \frac{\sigma_B}{\sigma_A} \simeq \frac{\pi r_B^2}{\pi r_A^2} \simeq \left(\frac{15}{8}\right)^{2/3} \simeq 1.52, \]
\[ \frac{\sigma_C}{\sigma_A} \simeq \frac{\pi r_C^2}{\pi r_A^2} \simeq \left(\frac{30}{8}\right)^{2/3} \simeq 2.41. \]
There are no direct experimental data for determining \(P_{\mathrm{H}}(Z)\), but there are data for \(P_{\mathrm{air}}(Z)\)—the probability of formation of nuclei of group \(A\) in the collision of a nucleus of charge \(Z\) with one of the atoms making up air\(^{1,5}\).
These data are as follows:
\[ P_{\mathrm{air}}(B)=P_{\mathrm{air}}(C)=0.23. \]
Observations showed that, when a hydrogen nucleus collides with a nucleus in the emulsion, fewer tracks appear than when heavier energetic nuclei collide with the nucleus of an atom in the emulsion (less complete disintegration takes place). Therefore one may expect,
that, when nuclei of group \(B\) move in hydrogen, the relative fraction of nuclei of group \(A\) formed in nuclear collisions will be greater than when moving in air. On this basis one may assume:
\[ P_{\mathrm H}(B)>P_{\text{air}}(B)=0.23. \]
In the case of nuclei of group \(C\) the same phenomenon will occur, although in this case the probability of formation of a nucleus of group \(A\), possibly, will depend to a lesser degree on the atomic number of the nucleus colliding with the nucleus of group \(C\), and one may assume:
\[ P_{\mathrm H}(C)>P_{\text{air}}(C)=0.23. \]
If we take \(P_{\mathrm H}(Z)\approx 0.23\), then relation (26) will give the minimum value for \(R\). There are indications\(^{13}\) that one may put:
\[ P_{\mathrm H}(B)>0.6. \]
For the above-indicated values of the cross sections and \(P_{\mathrm H}(Z)\), from equation (26) we shall find, taking in accordance with experiment
\[ \frac{N_C}{N_B}\approx \frac{1}{3}, \]
that
\[ R>0.5,\quad \text{if } P_{\mathrm H}(B)=P_{\mathrm H}(C)>0.23 \]
and
\[ R>1.0,\quad \text{if } P_{\mathrm H}(B)>0.6 \text{ and } P_{\mathrm H}(C)>0.23. \]
Thus, we see that even in the case when the source does not emit nuclei of the group Li, Be, B at all, these nuclei must arrive at the boundary of the atmosphere in approximately the same quantity as the nuclei of the group C, N, O, F, if, during motion in interstellar space, the particles traverse sufficiently large paths.
The fragmentation of heavy nuclei in interstellar space also leads to an increase in the number of protons and helium nuclei. Even if one does not take into account the appearance of an additional number of protons as a result of the fragmentation of complex nuclei, then, because of the difference in the effective cross sections of interaction with interstellar hydrogen of heavy nuclei and protons, at equilibrium the ratio of the number of protons to the number of nuclei with \(Z>10\) in the primary flux will not reflect the ratio between them in the region of the source.
Let us consider in somewhat more detail the influence of nuclear fragmentations on the relation between the various components. In the case of equilibrium one may write, denoting by \(\Phi_i\) and \(N_i\), respectively, the fluxes of the \(i\)-th component from the source and at the Earth, the following relation between the fluxes of the individual components of cosmic rays:
\[ \frac{N_i}{t_i}=\Phi_i+\sum_{j>i} P_{ij}\frac{N_j}{t_j}, \tag{28} \]
where \(t_i\) is the mean “lifetime” of a particle of the \(i\)-th type when moving in interstellar hydrogen, and \(P_{ij}\) is the probability of formation of a nucleus of the \(i\)-th type in a collision with interstellar hydrogen of a nucleus of the \(j\)-th type. Since the lifetime is inversely proportional to the interaction cross section \(\sigma_i\), relation (28) can be rewritten in the form
\[ k\Phi_i=\sigma_i N_i-\sum_{j>i} P_{ij}N_j\sigma_j, \tag{29} \]
where \(k\) is a proportionality coefficient.
For the ratio of the fluxes of the \(i\)-th and \(l\)-th components in the source we find:
\[ \frac{\Phi_i}{\Phi_l}= \frac{\sigma_i N_i-\sum_{j>i}P_{ij}N_j\sigma_j} {\sigma_l N_l-\sum_{j>l}P_{lj}N_j\sigma_j}. \tag{30} \]
In the particular case of the relation between the proton flux \((\Phi_p)\) and the flux of nuclei with \(Z>10\) \((\Phi_C)\), it may be assumed that the contribution to the number of nuclei with \(Z>10\) from the disintegration of still more complex nuclei is small \((P_{C,j}\ll 1)\). Therefore
\[ \frac{\Phi_p}{\Phi_C}\approx \frac{\sigma_p N_p-\sum_{j>1}P_jN_j\sigma_j} {\sigma_C N_C}. \]
It is known from experiment that
\[ \frac{N_p}{N_C}\approx \frac{3800}{6}. \]
If we want to estimate, for the ratio \(\dfrac{\Phi_p}{\Phi_C}\), an upper limit consistent with experiment, then, neglecting the contribution to the number of protons from “fragments” formed in the disintegration of heavy nuclei and taking for the cross sections \(\sigma_p\) and \(\sigma_C\) the values obtained from formula (27)*), we find for the ratio of the fluxes of protons and nuclei with \(Z>10\) in the source
\[ \frac{\Phi_p}{\Phi_C} < \frac{\sigma_p}{\sigma_C}\cdot\frac{N_p}{N_C} < \frac{4.5\cdot10^{-26}}{7\cdot10^{-25}}\cdot\frac{3800}{6} \approx 40, \]
in comparison with the mean ratio 1400, derived from data on the abundance of elements in the universe. The found
*) For \(\sigma_p\) one should in fact take a smaller value, since, in order to reduce the number of annihilated particles, it is necessary that both protons have low energy, whereas the value we have taken refers to the loss of energy by only one incident proton (this circumstance is accounted for by substituting an inequality sign for the equality sign).
the value obtained by us for the fraction of hydrogen atoms in the source means that either the actual composition of the source is such^[182], or the acceleration mechanism is selective: it preferentially accelerates heavy nuclei, rather than the more numerous hydrogen and helium nuclei*). This interesting question evidently requires further investigation.
From the available experimental data on the flux of various groups of nuclei at the boundary of the atmosphere, one can, by making a number of assumptions, draw certain conclusions about the distances traversed by cosmic-ray particles, about the character of the distribution of sources in space, etc. The lower limit for the distance traversed by particles can be determined on the basis of the assumption that equilibrium has been established. This distance must be greater than the free path of nuclei in hydrogen, i.e., according to Table X, greater than approximately \((5 \div 8)\ \mathrm{g/cm^2}\) of hydrogen.
An estimate of the upper limit for the distance traversed by cosmic-ray particles was made by Dainton^[109]. Assuming that all particles with charge less than 20 are of secondary origin and are not accelerated by the cosmic-ray source, he found that the amount of matter traversed by the particles after acceleration is less than \(10\ \mathrm{g/cm^2}\). Indeed, if one assumes that all nuclei with \(Z > 20\) appear as a result of fragmentation in collisions with interstellar hydrogen of heavier nuclei accelerated in the source, then the number of nucleons \(N_{Z>20}(x)\), carried by nuclei with \(Z > 20\), after traversing a distance \(x\ \mathrm{g/cm^2}\) of hydrogen, will be
\[ N_{Z>20}(x)=\sum_{Z>20} N_Z A_Z e^{-\frac{x}{\lambda_Z}}, \]
where \(N_Z\) is the number of nuclei with charge \(Z\), \(A_Z\) is the number of nucleons in a nucleus with charge \(Z\), and \(\lambda_Z\) is the mean free path for fragmentation of such a nucleus by interstellar hydrogen. Assuming that, for particles with \(20 < Z < 30\), \(\lambda_Z\) depends only weakly on the atomic number, we find:
\[ N_{Z>20}(x)=e^{-\frac{x}{\lambda}}\cdot \sum_{Z>20} N_Z A_Z. \]
It is known from experiment that in the primary flux the ratio of the number of nucleons carried by nuclei with \(Z > 20\), \([N_{Z>20}(x)]\), to the total number of nucleons \(N\), equal under our assumption to the number
*) Thus, for example, in the case considered by V. L. Ginzburg^[1] of acceleration of particles in the envelope of a supernova, heavy nuclei are accelerated more easily than protons and \(\alpha\)-particles.
of nucleons in the heavy nuclei emitted by the source is \(1:150\). Then one can find that
\[ \frac{N_{Z>20}}{N} = \frac{ e^{-\frac{x}{\lambda}} \sum\limits_{Z>20} N_Z A_Z }{ \sum\limits_{Z>20} N_Z A_Z } = e^{-\frac{x}{\lambda}} = \frac{1}{150}. \]
Hence, taking according to formula (27) \(\bar{\lambda}_{Z>20} \simeq 2\ \mathrm{g/cm^2}\), we find \(x=\bar{\lambda}\ln 150 \simeq 10\ \mathrm{g/cm^2}\).
There is no doubt that the assumption that only particles with \(Z>20\) are accelerated in the source is entirely arbitrary and, generally speaking, unjustified. But in that case, if light nuclei are nevertheless accelerated by the source in a noticeable quantity, the ratio observed on Earth, \(N_{Z>20}:N=1:150\), means that the particles traverse from the source a path even smaller than \(10\ \mathrm{g/cm^2}\), corresponding, for an interstellar hydrogen density equal to \(\sim 10^{-25}\ \mathrm{g/cm^3}\), to a distance \(\sim 10^{26}\ \mathrm{cm} \simeq 10^8\) light-years.
It must, however, be noted that estimates of this kind are still far too uncertain, since on the basis of the information known to us about complex nuclei in the primary flux of cosmic rays it is not yet possible to draw an unambiguous conclusion as to which of the registered particles were accelerated directly by the source and which have a secondary origin, what distance the particles traveled before reaching the Earth, etc. To clarify all these questions, further persistent work by physicists and astrophysicists—both experimentalists and theorists—is necessary.
CONCLUSION
The main information about primary radiation that we possess at the present time may be briefly formulated as follows:
-
The primary component of cosmic rays consists almost entirely of charged particles of high energy. The distribution of cosmic rays in space is isotropic to a high degree.
-
The main fraction of primary radiation consists of singly charged nuclei (protons and, possibly, a small percentage of antiprotons). Singly charged nuclei account for \(\sim 90\%\) of the particles with a given energy per nucleon (or \(\sim 80\div 85\%\) of all particles at a given latitude). This group of primary particles carries \(\sim 65\%\) of the total energy of cosmic rays, and it contains approximately the same percentage of all nucleons.
-
Besides protons, nuclei of various elements constitute a noticeable fraction of the primary radiation. The most widespread
are He nuclei, which in the given energy interval constitute \(\sim 9\%\) of all particles (10 times fewer than protons) and \(\sim 20\text{–}15\%\) of all particles at this latitude. Nuclei with \(Z>2\) together constitute \(\sim 1\%\) of the number of particles with the given energy per nucleon. The ratio between the fluxes of different nuclei may be expressed as:
\[ N_{\mathrm{He}} : N_{\mathrm{Li, Be, B}} : N_{\mathrm{C, N, O, F}} : N_{Z>10} \simeq 60 : 3 : 3 : 1 . \]
-
The ratio between the number of nuclei with \(Z>2\) and the number of singly charged particles in cosmic rays is approximately 10 times greater than the average ratio between the corresponding elements in nature.
-
The electron–photon component in the primary flux constitutes no more than \(0.6\%\) of the particles in the corresponding energy interval.
-
The integral spectrum of singly charged nuclei in the region of momenta \(>10^{9}\ \mathrm{eV}/c\) has an approximately power-law form, but the exponent changes from 1.1 at lower energies to 1.7 at higher energies. In the region of small momenta the curve of the integral spectrum becomes flattened, and accordingly a sharp drop is observed in the differential spectrum. The cause of such a dependence is apparently the influence of the magnetic field of the Sun or of the solar system.
-
The integral energy spectra of various groups of complex nuclei also have a power-law form; moreover, the exponent for all groups in the energy region below \(3\cdot 10^{10}\ \mathrm{eV}/\)nucleon is the same and is equal to \(\sim 1.2\). It has not yet been established whether the energy spectrum of complex nuclei is cut off in the region of low energies, but there are indications that such a cutoff does occur.
All these properties of primary cosmic radiation impose definite restrictions on theories of the origin of cosmic rays, since any at least somewhat satisfactory theory of their origin must explain the principal experimental facts.
One such fact, whose explanation requires a careful analysis of the conditions for the propagation of cosmic rays from the source to the Earth, is the absence of an electron–photon component in the primary flux of cosmic rays.
No less substantial a role for theories of origin is played by the observed distribution of the nuclear component by charge. For example, the presence in the primary flux of cosmic rays of Li, Be, and B nuclei, which are rarely encountered in nature, indicates that cosmic-ray particles wander in the universe for a rather long time.
Data on the relative abundance of singly charged and multiply charged nuclei in the primary flux of cosmic rays, and allowance for the process of fragmentation of complex nuclei in interstellar space, show that the sources emit heavy nuclei in considerably greater—
higher than the average abundance in the universe, than singly charged nuclei.
At the present time, unfortunately, there is still no theory of the origin of cosmic rays that would be able to explain all the experimentally established facts without resorting to various kinds of assumptions, often insufficiently justified. The creation of such a consistent theory of the origin of cosmic rays is a task for the near future.
In conclusion I consider it a pleasant duty to express my gratitude to Corresponding Member of the Academy of Sciences of the USSR V. L. Ginzburg for the attention and assistance he gave in the writing of this review, and also to N. L. Grigorov, L. V. Kurnosova, and M. I. Podgoretsky for the valuable advice and comments they made after reading the manuscript.
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