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HEAVY PARTICLES AND NUCLEAR DISINTEGRATIONS (“STARS”) IN COSMIC RAYS
V. L. Ginzburg
The composition of cosmic rays, besides mesotrons, electrons, positrons, and photons, also includes heavy particles—protons and neutrons. At sea level the role of this third, proton-neutron component is relatively small. However, as one ascends upward, the third component becomes ever more significant. Moreover, at present it is considered most probable that protons are the primary cosmic particles[^1]. If this point of view is correct, then protons must in any case be assigned a place no less important than that of mesotrons and electrons. Therefore the study of the proton-neutron component and of its connection with mesotrons and light particles is becoming ever more urgent and at present may be regarded as one of the principal, if not the principal, tasks in the field of cosmic-ray research.
The information now available on protons and neutrons in cosmic rays is still very incomplete, especially with regard to fast particles and great altitudes. At the same time there can be no doubt that increasing attention will be devoted in the near future to the question of heavy particles and nuclear disintegrations. It therefore seems useful to discuss and compare the experimental material available in this field, which is the purpose of the present article.
§ 1. Protons
Fast protons are of the greatest interest. They are constituents of the primary cosmic particles or, in any case, traverse a considerable part of the atmosphere. However, at energies \(\gtrsim 10^9\) eV protons ionize practically in the same way as relativistic mesotrons and electrons, and therefore it is extremely difficult to identify them.
As a result, direct information on the number of protons in the hard component of cosmic rays is at present lacking. In experiment
only nonrelativistic protons are observed, distinguished by their relatively large ionization. The corresponding measurements were made with the aid of photographic plates2,3,4, proportional counters5, and a Wilson chamber6–10.
In the photographic-plate method, special plates with a thick layer of bromosilver emulsion are used, in which ionizing particles leave tracks. In the case of protons this method is applicable for particles with energies less than approximately 60–100 MeV11,12, since at higher energies the ionization becomes already too small, and the particle does not leave a sufficiently clear track. With the aid of plates one can determine the flux and the energy spectrum of slow protons in air, and also under various coverings. The most complete work in this field belongs to Vidhalm2, to whose results we shall now turn.
Table 1
| Altitude above sea level in meters | Atmospheric pressure | $S^p = \dfrac{\text{number of protons}}{cm^2 \cdot \text{day}}$ |
|---|---|---|
| 200 | 0,98 | 0,13 |
| 954 | 0,89 | 0,65 |
| 1600 | 0,82 | 1,5 |
| 2173 | 0,76 | 2,1 |
| 3106 | 0,68 | 4,7 |
| 3465 | 0,65 | 8,0 |
| 2300 | 0,75 | 3,0 |
| 3400 | 0,65 | 4,6 |
The proton flux $S^p$, i.e. the number of particles crossing an area of $1\ cm^2$ in a definite time, depends strongly on altitude; the corresponding data are given in Table 1. The last two values were obtained with plates of a different type than the preceding ones. In addition, the conditions at the different altitudes differed somewhat from one another (the difference consists in the different thickness and type of covering above the plates; the coverings were the ceilings and roof). A very approximate allowance for this circumstance leads to a displacement of some of the values, and as a result one obtains the curve shown in Fig. 1. This curve is well described by an exponential function, if the pressure is taken as the independent variable:
\[ S^p = \mathrm{const}\cdot e^{-\mu p}, \qquad \mu = 9-10\ \mathrm{atm}^{-1}, \tag{1} \]
where $p$ is measured in atmospheres.
The observed protons have a range of the order of $1\ m$ of air and thus are formed near the plate. Formula (1) evidently refers to the particles generating these protons. From (1) one can determine the effective cross section for absorption of these particles by oxygen and nitrogen nuclei
\[ \left(\frac{dS}{dp} = -\mu S = -N_0\sigma S,\ \text{where } N_0 \text{ is the number of nuclei in the atmosphere above } 1\ cm^2 \text{ of the earth’s surface}\right). \]
This cross section is equal to:
\[ \sigma=\frac{\mu}{N_0}\simeq 2.2\cdot 10^{-25}\ \text{cm}^2, \tag{2} \]
where it has been taken into account that the height of the reduced atmosphere is \(8\ \text{km}\) and the number of nuclei in \(1\ \text{cm}^3\) of air at \(p=1\) and temperature \(1^\circ\text{C}\) is \(2\cdot 2.7\cdot 10^{19}\).
At an altitude of \(3465\ \text{m}\), where the value given in Table 1 does not need correction\(^2\), the proton flux is
\[ S'_{3465}\simeq 5.6\cdot 10^{-3}\ \frac{\text{protons}}{\text{cm}^2\cdot\text{min}} . \tag{3} \]
For comparison, let us point out that at sea level the flux of all ionizing particles is \(1.5\ \frac{\text{particles}}{\text{cm}^2\cdot\text{min}}\), with mesotrons accounting for approximately \(75\%\) of the particles. At an altitude of \(\sim 3400\ \text{m}\) the mesotron flux
Fig. 1.
increases by approximately \(1.7\) times and the flux of soft particles by \(4\)—\(5\) times, so that the total flux is \(4\ \frac{\text{particles}}{\text{cm}^2\cdot\text{min}}\), and the intensities of the soft and hard components are approximately the same\({}^{3,4,12}\). Let us note, however, that the question of the relation of the soft component to the hard one at an altitude of \(\sim 3400\ \text{m}\) is still under discussion\({}^{13,14,15}\). For definiteness we shall take the above value of the intensity of the soft component, equal to \(2\ \frac{\text{particles}}{\text{cm}^2\cdot\text{min}}\) at an altitude of \(3400\ \text{m}\). In this case the flux of slow protons is 300 times smaller than the flux of soft particles [see (3)].
The proton flux was also determined by the photographic-plate method in the work of Heitler et al.\({}^{3,4*}\). At an altitude of \(3400\ \text{m}\), according to these data, the flux
\(*\) Let us note that the first communication on this work\({}^3\) somewhat contradicts the second\({}^4\). We shall mainly use the second communication.
is equal to \(S^p_{3400} \simeq 2.7 \cdot 10^{-3}\ \dfrac{\text{proton}}{\text{cm}^2\cdot\text{min}}\). At sea level the number of protons is smaller by 10–20 times. The discrepancy between the values of Heitler and Wildhalm is partly explained by the different allowance made for very soft particles; the errors, apparently, are considerably greater than the 20% indicated by the authors.
The interpretation of the results obtained with proportional counters\(^5\) is somewhat difficult, but nevertheless this method leads to quite definite results. The variation in the number of protons with altitude in the pressure interval \(p=0.2—0.6\ \text{atm}\) is in approximate agreement with formula (1), where \(\mu\) is closer to \(7\ \text{atm}^{-1}\) than to \(9\ \text{atm}^{-1}\). The proton flux is in good agreement with the value (3). Indeed, for a pressure of about \(0.6\ \text{atm}\), according to Korff’s data\(^5\), there are formed \(q \sim 5\cdot 10^{-6}\ \dfrac{\text{protons}}{\text{cm}^3\cdot\text{sec}}\). Further, the proton flux \(S \sim qR\), where \(R\) is the range of the fastest protons registered by the counter, equal to approximately \(20\ \text{cm}\). Hence \(S^p \sim 5\cdot 10^{-3}\ \dfrac{\text{protons}}{\text{cm}^2\cdot\text{min}}\), in complete agreement with (3). At a pressure \(p=0.2\ \text{atm}\) the flux is approximately 10 times larger.
According to other data obtained with counters\(^ {19}\), at an altitude of \(3860\ \text{m}\), the flux of protons with energy less than 80—100 MeV is
\[ S^p_{3860} < 10^{-2}\ \frac{\text{proton}}{\text{cm}^2\cdot\text{min}}. \]
The information on the number of protons obtained in a Wilson chamber\(^ {6-10}\) is rather indefinite. The percentage of thick tracks reaches 1—5% of the number of tracks of hard particles at an altitude of \(\sim 3—4\ \text{km}\). At sea level the percentage of thick tracks decreases by approximately a factor of 10.\(^6\) These data, however, may be very strongly complicated, first, by the presence of the chamber walls and, in a number of cases, by the presence in it of lead plates, and also by the different efficiency of the chamber with respect to strongly and weakly ionizing particles. It would therefore be inadvisable to dwell on a discussion of the data obtained with chambers. We shall indicate only that, according to observations in chambers, apparently, one may consider that
\[ S^p_{3000} < 5\cdot 10^{-2}\ \frac{\text{protons}}{\text{cm}^2\cdot\text{min}}. \]
Johnson et al.\(^7\) observed at sea level proton tracks in a Wilson chamber under conditions in which these protons entered the chamber still relativistic, but were then slowed down in a lead plate. Such protons constitute 15% of all delayed, non-shower-producing particles indicated in this way. Assuming that the observed slow particles, before slowing down, formed part of the hard component, and taking into account that the range of a proton is 10 times greater than the range of a mesotron of the same velocity, the authors come to the conclusion that protons constitute 1—2% of the particles of the hard component.
In this case, obviously, it is assumed that the numbers of observed slow protons and mesotrons are proportional to their ranges;
this will be the case if the particles are generated throughout the entire thickness of the atmosphere and, moreover, the probability of their creation does not depend on energy. However, for protons that are part of the primary cosmic rays or are formed in the upper part of the atmosphere, there is no proportionality of flux to range. Therefore, from the results of Johnson et al. one cannot draw quantitative conclusions about the proton content in the hard component.
Analogous experiments by Leprince-Ringuet et al.⁵⁴, carried out at an altitude of 1000 m under 12 cm of lead, lead to the conclusion that the number of protons among non-shower-producing particles with momentum less than
\[ 7 \cdot 10^{8}\,\frac{\mathrm{eV}}{c}, \]
is equal to \(2—3\%\).
Alikhanov, Alikhanyan, and Nikitin¹³,²⁸,²⁹, on the basis of a whole series of experiments, asserted that at an altitude of 3250 m the soft component includes a large number of protons, constituting about one third of all soft particles.
The energy of these protons is of the order of 150 MeV; one of the main arguments in favor of their existence consists in a comparison of data from Geiger counters and an ionization chamber. The question of whether the effects observed by the authors are explained by protons with energy \(\sim 150\) MeV or by narrow showers, as the authors admit (see also¹⁴), is not yet clear. Therefore it seems inadvisable to analyze the corresponding results here. However, regardless of whether the observed effects¹³ are caused by protons or by narrow showers, they are of great interest and, apparently, are connected with the component generating nuclear disintegrations (see § 4).
The protons recorded by photographic plates (the fact that mainly protons are observed was subjected to a special check²,¹¹) are distributed isotropically in space. Their energy spectrum at an altitude of 3465 m is shown in Fig. 2. The mean energy at this altitude is 14 MeV; such protons have a range in air (at atmospheric pressure) equal to 200 cm. The mean energy in the altitude interval 959—1600 m is 12.7 MeV. Using the spectrum shown in Fig. 2 and the value of the total flux (3), one can calculate the ionization produced by the protons in comparison with the ionization of the entire soft component. As a result, it turns out that the mean specific ionization of a proton is 25—30 times greater than the ionization of a relativistic particle*) and, since at an altitude of 3400 m there are 300 times fewer protons than particles of the soft component, the total ionization of the protons considered is of the order of
\[ \frac{1}{10} \]
of the ionization of the soft electron-
*) For protons with energy \(E = 10\) MeV, \(I = 30 I_{\mathrm{rel}}\), where \(I_{\mathrm{rel}}\) is the specific ionization of a relativistic particle; over a broad interval the ionization is inversely proportional to the energy: at \(E = 15\) MeV, \(I = 20 I_{\mathrm{rel}}\); at \(E = 20\) MeV, \(I = 15 I_{\mathrm{rel}}\); at \(E = 60\) MeV, \(I = 5.5 I_{\mathrm{rel}}\).
component:
$$ I^{p}_{3400} \leq \frac{1}{10} I^{m}_{3400}. \tag{4} $$
This value is in agreement with the data obtained with an ionization chamber at approximately the same altitude[^16]. The total ionization in the chamber corresponding to the passage of a particle with ionization greater than 10-fold amounts to 13% of the ionization of the hard
Fig. 2.
component and, as follows from the figures given above, is \(\sim 10\%\) of the ionization of the soft component. Of course, the comparison made is of a very approximate character, owing to the entirely different methods of observation (in the chamber, for example, a transition effect in its walls may occur).
The question of the dependence of proton production and of the absorption of the component generating them on the material located above the registering apparatus is of especially great interest and at the same time has been studied very little. The influence of coating the plates with paraffin[^17] will be discussed in § 2. The change in the number of protons in the emulsion as a function of the thickness of lead above the plate was investigated by Heitler et al.[^4]. The corresponding results (altitude 3400 m) are given in Fig. 3. The influence of the material of the walls of a proportional counter was discovered by Ivanova[^18]. In the case of lead walls the ionization effect from strongly ionizing particles (with \(I > 5 I_{\mathrm{rel}}\)) proved to be 3 times greater than for aluminum walls (altitude 3860 m). In Young’s experiments[^16], placing 6.7 cm Pb above the chamber reduced-
the ionization effect from strongly ionizing particles from 13 to 10% of the ionization of the hard component. Other quantitative data on the influence of an absorber on the number of protons are unknown to us.
Placing above the emulsion (for definiteness we shall speak of the photographic-plate method) some dense material leads, generally speaking, to two effects. As indicated, the mean energy of the recorded protons is of the order of 15 MeV and their range \(R\) is approximately 200 cm of air, 0.035 cm Pb, and 0.1 cm Al. Only particles from distances of the order of \(R\) reach the emulsion. Therefore placing
Fig. 3.
above the emulsion a thin coating with thickness greater than \(R\) will have no effect on the particles generating the protons (their absorption coefficient is very small), but will make it possible to determine the dependence of proton production on the material. According to Heitler’s data\(^4\), the effect of a thin Pb layer is imperceptible (see the point corresponding to approximately 0.4 cm Pb in Fig. 3); according to Ivanova’s data\(^ {18}\), for a counter, lead increases the number of particles by a factor of 3. It is very difficult to compare a plate with a counter, and the question of the influence of a thin coating must be considered open. If the flux of protons from Pb and from air is the same, this means that the cross section for the formation of protons on a Pb nucleus is 10 times greater than on an oxygen or nitrogen nucleus (the range in Pb in grams is 1.5 times greater than in air; the number of nuclei in a gram of Pb is 14.3 times smaller than in a gram of air). We note that if the cross section is assumed proportional to \(A^{2/3}\) (\(A\) is the atomic weight), then the cross section \(\sigma\) of the Pb nucleus should be \(\sim 6\) times greater than the cross section of the \(N\) or \(O\) nuclei.
Placing thick layers of material above the emulsion or proportional counter makes it possible to determine the absorption coefficient of the particles generating protons as a function of atomic number. Absorption in air is determined by the values of \(\mu\) and \(\sigma\) given above (see (1) and (2)). For lead the data are very inaccurate; as is clear
from Fig. 3, 12.2 cm of Pb reduce the proton flux by at most a factor of 1.5. It follows that the cross section for absorption of the generating particles is \(\sigma < 1 \cdot 10^{-24}\) per Pb nucleus. Young’s data\(^{16}\) lead to a cross section \(\sigma = 1.2 \cdot 10^{-24}\) per Pb nucleus. The resulting cross section cannot be regarded as anomalously small, and there is as yet no basis for concluding that the absorption\(^{3}\) of the generating particles by lead is weak.
The presence, on the curve of Fig. 3, of a maximum situated at the position of the maximum of Rossi’s curve argues in favor of the supposition that the observed protons are generated in part by the soft component. We shall discuss the question of the nature of the generating particles in more detail in § 4, but here we shall already note that at least the overwhelming majority of the protons are produced by nonionizing particles different from photons; these particles are either neutrons or neutral mesotrons (neutrettos)*). If the neutretto plays the principal role and if these particles are unstable, then the variation of intensity with altitude could be connected to a considerable extent with their decay. This supposition may be tested by comparing the absorption curve in air with the absorption curve at a given altitude under the condition that, above the plate, a dense absorber similar in its properties to air (carbon, aluminum) is placed.
The investigation of the influence on the proton intensity of various thin and thick coatings seems to us the most urgent task of further work. At the same time it is desirable to determine the proton spectrum. It is also necessary to continue the study of the proton spectrum in the energy region not registered by the plates\(^{13,19}\).
§ 2. Neutrons
Measurements of the number of neutrons in cosmic rays have been carried out chiefly in the thermal region by using counters with \(\mathrm{BF}_3\), in which the reaction \(\mathrm{B}_{10}(n\alpha)\mathrm{Li}_7\) is used. In this case the counter responds not only to thermal neutrons but also to faster particles; however, the efficiency is maximal in the thermal region\(^{20}\). According to Montgomery\(^{21}\), at sea level the flux of slow neutrons is equal to
\[ S_0^n = 0.09 \frac{\text{neutrons}}{\text{cm}^2 \cdot \text{min}}, \tag{5} \]
i.e., 16 times smaller than the flux of all ionizing particles at the same altitude.
*) If the generating particles were mainly neutral mesotrons, then in cosmic rays one would have to speak of four components.
The dependence of the neutron flux on altitude was determined by Fünfer[^22], whose results are given in Table 2.
Table 2
| Altitude above sea level, in meters | Pressure, in atmospheres | $\dfrac{S^n}{S^n_{160}} = \dfrac{\text{Flux}}{\text{flux at altitude }160\ \text{m}}$ | $\dfrac{S^n}{S^n_{160}} = e^{\mu(0.99-p)}$ $\mu = 7\ \mathrm{atm}^{-1}$ |
|---|---|---|---|
| 160 | 0.99 | 1.00 | 1.00 |
| 780 | 0.91 | 1.65 | 1.75 |
| 1,280 | 0.85 | 2.52 | 2.66 |
| 1,500 | 0.82 | 3.15 | 3.29 |
| 2,650 | 0.71 | 7.71 | 7.10 |
| 17,000 | 0.1 | 650 | 548 |
The last line in this table reproduces Korff’s data[^23]; for a number of reasons, the experimental value 650 cited is of a very approximate character.
At an altitude of $\sim 17\ \text{km}$ the neutron flux becomes approximately the same as the flux of ionizing particles.
As is seen from Table 2, with fairly good accuracy (see (1) and (2)):
\[ \left. \begin{aligned} S^n &= \mathrm{const}\cdot e^{-\mu p}, \qquad \mu \simeq 7\ \mathrm{atm}^{-1},\\ \sigma &= \frac{\mu}{N_0} = 1.6\cdot 10^{-25}\ \text{cm}^2 \end{aligned} \right\}. \tag{6} \]
The absorption of slow neutrons occurs as a result of the reaction $N_{14}(np)C_{14}$, for which the cross section in the thermal region is $\sigma = 1.3\cdot 10^{-24}\ \text{cm}^2$[^20]. The protons produced in this reaction have an energy of $0.7\ \mathrm{MeV}$ and a range of the order of $1\ \text{cm}$ of air. The absorption coefficient for thermal neutrons is equal to the cross section multiplied by the number of nitrogen nuclei in $\text{cm}^3$, i.e. is equal to $\mu' = 5.5\cdot 10^{-5}\ \text{cm}^{-1}$; the “range” of the neutrons is
\[ R = \frac{1}{\mu'} \simeq 200\ \text{m}. \]
Furthermore, the neutron flux is equal to their number $q$, produced in $\text{cm}^3$, divided by two and multiplied by the range1.
Using the values
\[ S^n_0 = 0.09\ \frac{\text{neutrons}}{\text{cm}^2\cdot\text{min}} \]
and $R = 200\ \text{m}$, we arrive at the conclusion that at sea level $q$ is equal to
\[ q^n_0 = \frac{2S^n_0}{R} \simeq 1.5\cdot 10^{-7}\ \frac{\text{neutrons}}{\text{cm}^3\,\text{sec}} \simeq 10^{-4}\ \frac{\text{neutrons}}{\text{g}\,\text{sec}}. \tag{7} \]
At an altitude corresponding to 1 meter of water (altitude \(\sim 17\) km), according to other data \(^{20}\):
\[ q_{1700}^{n} > 5 \cdot 10^{-2}\ \frac{\text{neutrons}}{\text{g}\cdot \text{sec}} . \tag{8} \]
The values (7) and (8) agree with the assertion that \(S_{1700}^{n}/S_{0}^{n} \sim 500\) (see Table 2).
Let us note that by \(q^{n}\) is meant the number of slow neutrons arising by any means, for example as a result of the slowing down of fast neutrons.
The total number of neutrons formed in the atmosphere in a column with a base of \(1\ \text{cm}^{2}\) is \(^{20}\):
\[ Q > 10\ \frac{\text{neutrons}}{\text{cm}^{2}\cdot \text{sec}} . \tag{9} \]
Assuming that the primary particle expends on the formation of one neutron an average of 20 MeV (it is assumed that the binding energy and kinetic energy are on the average of the order of 10 MeV), from (9) we see that the losses of primary particles for neutron production are greater than
\[ 200\ \frac{\text{MeV}}{\text{cm}^{2}\cdot \text{sec}} . \]
This figure is about \(1/12\) of the energy expended by cosmic rays on ionization of an atmospheric column with cross-section \(1\ \text{cm}^{2}\) (see \(^{20}\)). The energy of the neutrons is ultimately spent on ionization and on the formation of various nuclei (neutrons are absorbed as a result of the reactions \(\mathrm{N}_{14}(n\alpha)\mathrm{B}_{11}\) and \(\mathrm{N}_{14}(np)\mathrm{C}_{14}\)). About
\[ 50\ \frac{\text{MeV}}{\text{cm}^{2}\cdot \text{sec}} \]
goes into ionization, which constitutes \(2\%\) of the total ionizing effect of cosmic rays. The calculation given \(^{20}\) is, of course, of a highly approximate character.
Table 3
| Altitude | \(S = \dfrac{\text{protons}}{\text{cm}^{2}\cdot \text{hour}}\) 1 mm paraffin |
\(S = \dfrac{\text{protons}}{\text{cm}^{2}\cdot \text{hour}}\) 1 mm Pb |
|---|---|---|
| 200 m | 0.07 | — |
| 3,400 m | 0.28 | 0.06 |
| 18,000 m | 5.1 | — |
Fast neutrons are recorded by proportional counters filled with a gas containing hydrogen \(^{20,24}\), and with the aid of photographic plates coated with a layer of paraffin \(^{17,25}\). We shall not discuss the results of measurements with counters (see \(^{20,5,24}\)), since they are still of a rather approximate character. The latter, however, also applies to the work carried out with paraffin-coated plates. Nevertheless, it is advisable to discuss the relevant results of Shoper \(^{17}\); the corresponding data are given in Table 3. Unfortunately, the author gives only the values of the flux in the case of coating the emulsion with 1 mm of paraffin and, for one altitude, in the case of coating with 1 mm Pb; the proton flux without any coating is not indi-
is produced. Under lead, \(S_{3400}^p = 10^{-3}\,\dfrac{\text{protons}}{\text{cm}^2\cdot\text{min}}\), i.e. 5–6 times less than for plates without coating according to Widhalm’s data and 3 times less than according to Heitler’s data (see § 1). Since the plates are different, no conclusions can, of course, be drawn from this except that the various data agree in order of magnitude. The flux of protons knocked out by neutrons from paraffin at an altitude of \(3400\,m\) is
\[ S' = 0.22\,\frac{\text{protons}}{\text{cm}^2\cdot\text{hour}}; \]
on the other hand, \(S' = S_{3400}^n \sigma_{pn}N_p\), where \(S_{3400}^n\) is the flux of fast neutrons, \(\sigma_{pn}\) is the cross section for collisions of neutrons with protons, and \(N_p\) is the number of hydrogen nuclei in a paraffin layer \(1\,mm\) thick and of area \(1\,cm^2\). The principal effect must apparently be produced by neutrons with energies of several MeV, since for more energetic neutrons the cross section \(\sigma_{pn}\) decreases. Taking \(\sigma = 10^{-24}\,cm^2\) and noting that \(N_p = 9\cdot 10^{21}\), we obtain\(^ {26}\):
\[ S_{3400}^n = 0.4\,\frac{\text{neutron}}{\text{cm}^2\cdot\text{min}} . \tag{10} \]
The flux given refers to fast neutrons in a broad interval of energies greater than, approximately, 1–2 MeV, for slower recoil protons cannot be registered. As follows from (5) and (6), at the same altitude the flux of slow neutrons is equal to
\[ S_{3400}^n \simeq 1\,\frac{\text{neutron}}{\text{cm}^2\cdot\text{min}} . \]
Discussion of the question of the degradation and diffusion of neutrons in the atmosphere has been undertaken in the works of Bethe, Korff, and Placzek\(^ {27}\) and of Flugge\(^ {27}\), on which we shall not dwell.
It may be thought that both protons and neutrons with energies up to several tens and even hundreds of MeV are formed as a result of nuclear disintegrations (see § 3). In this case the numbers of protons and neutrons produced must be approximately the same, and their fluxes must be proportional to their ranges. The range of protons with energy 15 MeV is 2 meters of air; the range of neutrons depends only weakly on the energy and is approximately 200–300 meters (if the absorption cross section is \(\sigma \sim 10^{-24}\,cm^2\), then
\[ R \sim \frac{1}{10^{-24}\cdot 2\cdot 2.7\cdot 10^{19}} \sim 200\,m \]
). Hence it is clear that the neutron flux must be greater than the proton flux by a factor of 100–150; as is clear from (3) and (10), this is indeed the case, since
\[ \frac{S_{3400}^n}{S_{3400}^p} \simeq 100^*). \]
Thus the quanti-
\(^*\) If one compares the flux (10) with the value \(S_{3400}^p = 10^{-3}\,\dfrac{\text{protons}}{\text{cm}^2\cdot\text{min}}\) obtained from Table 3 for a plate coated with lead, then \(S^n/S^p \sim 400\). The accuracy of the calculations, however, is such that all comparisons can be made only in order of magnitude.
...the number of protons and neutrons generated in the atmosphere is approximately the same. In the future it would be of interest to investigate the influence of an absorber above the paraffin, the spectrum of the protons knocked out of the paraffin, and the dependence of the effect on altitude; for comparison it is necessary to have identical plates exposed without paraffin, but otherwise with exactly the same coating as the plates with paraffin.
§ 3. Nuclear disintegrations (“stars”)
In addition to proton tracks, in the emulsion of photographic plates and in the Wilson chamber there are observed the so-called “stars”—several particles emerging from a single center (a photograph of a “star” in the emulsion is reproduced in Fig. 4). There is no doubt that the “stars” are nuclear disintegrations caused by certain particles that are constituents of cosmic rays. By the method of photographic plates the “stars” have been investigated in a large number of works11, 32–37 (reviews26, 30, 31). This method makes it possible to obtain abundant statistical material, but it has a very substantial drawback, since it does not make it possible to register relativistic particles.
Fig. 4.
In the Wilson chamber, if episodic observations are not counted, “stars” have been studied comparatively little, and, properly speaking, there is here only one detailed work, by Hazen40; the details of Powell’s work38, unfortunately, have not been published.
The dependence of the number of stars on altitude is presented in Fig. 538. The exponential dependence cannot be regarded as being obeyed especially...
particularly well. In particular, the point corresponding to sea level stands out noticeably; the same applies to the altitude dependence of the number of protons (see Table 1). Thus one may conclude that at altitudes less than approximately \(1000\ \text{m}\), absorption of the generating component is stronger. This may be explained by an increase in the absorption cross section for the slower generating particles. The same result will be obtained if these particles are unstable, since the effective lifetime \(\tau\) decreases with decreasing energy,
\[ \tau=\frac{\tau_0 E}{\mu c^2}, \]
where \(\tau_0\) is the lifetime in the system associated with the particle, \(E\) is the energy, and \(\mu\) is the rest mass of the particle.
Fig. 5.
If the lower point in the curve of Fig. 5 is disregarded, then the dependence of the number of stars on altitude is satisfactorily represented by an exponential law:
\[ \left. \begin{aligned} N&=\mathrm{const}\cdot e^{-\mu p}, \qquad \mu \simeq 7\ \text{atm}^{-1},\\ \sigma&=1.6\cdot 10^{-25}\ \text{cm}^2. \end{aligned} \right\} \tag{11} \]
At an altitude of \(3400\ \text{m}\),
\[ N=0.03\ \frac{\text{stars}}{\text{cm}^2\cdot\text{day}} \]
for an emulsion \(100\ \mu\) thick, and apparently only “stars” with a number of particles not less than three are counted\(*\). The density of the emulsion is approximately equal to unity, and it contains Ag and Br nuclei in an amount 8 times smaller than C, O, and N nuclei. Assuming that the formation of “stars” per unit mass in air is the same as in the emulsion, it is easy to obtain the number of “stars” formed in \(1\ \text{cm}^3\) of air:
\[ N_{3400}=3\ \frac{\text{stars}}{\text{g}\cdot\text{day}} =4\cdot 10^{-3}\ \frac{\text{stars}}{\text{cm}^3\cdot\text{day}}. \tag{12} \]
The distribution of “stars” according to the number \(n\) of particles entering into their composition is presented in Fig. 6 (altitude \(2300\ \text{m}\), total number of observed stars equal to 109). The number of “stars” consisting of 2 particles is not determined exactly; the same applies to the number of nuclear disintegrations in which only one particle emerges. Apparently, the number of disintegra-
\(*\) According to the approximate data of Windhalm\({}^{2}\), at the same altitude \(N\simeq 6\)—\(8\cdot 10^{-2}\ \dfrac{\text{stars}}{\text{cm}^2\cdot\text{day}}\). According to the approximate data of Zhdanov\({}^{55}\), at sea level
\[ N<0.2\ \frac{\text{stars}}{\text{cm}^2\cdot\text{day}}. \]
Such an enormous value seems incredible.
ones with \(n<3\) by more than the number of disintegrations with \(n \ge 3\). Extrapolation of the dependence \(N(n)\) from \(n \ge 3\) to \(n = 1\) leads to the conclusion that the number of disintegrations with \(n \ge 1\) is 5 times greater than the number of “stars” with \(n \ge 3\). Hazen’s data\({}^{10}\) with a Wilson chamber show that the number of disintegrations with \(n = 1\) is approximately 7 times greater than the number of disintegrations with \(n \ge 2\). If, moreover, one takes into account that in the photographic-plate method fast particles are not recorded, it becomes clear that the total number of disintegrations is several times greater than the value 12.
The average number of particles in a “star,” as is seen from Fig. 6, is approximately four. The particles observed in “stars,” if
Fig. 6.
one disregards the fast particles not recorded by the plates, in the overwhelming majority of cases are protons\({}^{11,30}\). The number of \(\alpha\)-particles in “stars” amounts to only about 6% of the total number of observed particles\({}^{37}\).
The distribution of particles in “stars” by energy is presented in Fig. 7 for an altitude of 2300 m\({}^{11}\). The dependence of the mean energy of all particles visible in a “star” on altitude is shown in Fig. 8\({}^{86}\); from Fig. 9 the dependence of the mean energy per particle on the number of particles in a “star” is clear\({}^{26}\). Fig. 10 shows the distribution of “stars” as a function of the total energy of all visible particles, i.e., protons\({}^{11}\).
The total energy released in nuclear disintegration is equal to the sum of the energies of all emitted particles plus their binding energy. It is natural to think that in nuclear disintegration, in addition to protons, neutrons appear in approximately the same number,
moreover, their energy distribution is analogous to the proton distribution.
Taking this circumstance into account and assuming the binding energy to be approximately 8 MeV per particle, we obtain approximately the total energy released in the disintegration.
The distribution of stars according to the energy released is shown in Fig. 11³⁶.
It should, however, be borne in mind that, since plates do not register fast particles, the determination of the energy given here may be greatly underestimated; it is enough to say that, according to Fig. 11, “stars” with an energy release of \(\sim 100\) MeV are encountered most often, while at the same time the energy required for the production of a mesotron is also 100 MeV; therefore, if mesotrons are produced in a “star”¹⁰, then the average energy release may be considerably greater than follows from Fig. 11.
Fig. 7.
The particles in the “stars” have a rather weakly expressed preferential direction from top to bottom. The distribution of particle tracks in “stars” by direction is clear from Fig. 12, where along the abscissa is plotted the angle of the tracks with the direction of the plumb line.
“Stars” are of undoubted interest for the physics of the atomic nucleus, since up to the present there is still no possibility of bombarding the nucleus with particles having energies \(> 100\) MeV. Therefore only in cosmic rays are nuclear disintegrations observed with the emission of a large number of particles (sometimes even the complete breakup of the nucleus into protons and neutrons³⁴ is observed). The present state of the theory of the nucleus and of nuclear forces does not at present
... at the present time, the possibility of correctly considering the interaction of a nucleus with a fast neutron, proton, or mesotron. This applies in particular
Fig. 8.
Vertical axis: “Average total energy of all protons in a star.”
Horizontal axis: “Altitude above sea level.”
Fig. 9.
Vertical axis: “Average energy of one particle, MeV.”
Horizontal axis: “Number of particles in a star.”
to particles with energies greater than several tens of MeV, since in this case the notions of an intermediate nucleus (“compound nucleus”) become poorly applicable.
Fig. 10.
Vertical axis: “Number of stars.”
Horizontal axis: “Sum of proton energies in MeV.”
Therefore the attempts by Heisenberg, Bhabha, and others \(^{26,40,41}\) to treat nuclear disintegrations theoretically lack persuasiveness (see, for example, \(^{42}\)), and we shall not dwell on them.
Fig. 11.
Vertical axis: “Number of stars.”
Horizontal axis: “Energy release,” MeV.
Despite the impossibility of a reliable theoretical ...
interpretation and, if desired, precisely because of this impossibility, the study of nuclear disintegrations in cosmic rays is of great interest. In this field one can already point to one feature which remains entirely unclear. As follows from the distribution of particles by energies (see Fig. 7), in the “stars” there is a large number of particles with energy less than 2–3 MeV. At the same time, among the low-energy particles there are also present in “stars” with a number of particles greater than 8 those which are associated with the disintegration of Br or Ag nuclei. Meanwhile the height of the potential barrier for Br is, approximately, 8 MeV, and for Ag still higher. Therefore it would seem that, in the disintegration of Br and Ag nuclei with the emission of a not very large number of protons, these protons should have an energy not much smaller than the height of the barrier. In experiment, however, as a detailed analysis shows\(^{11}\), in the disintegration of Br and Ag nuclei (“stars” with \(n > 8\)) at least 1–2 and probably even 4 particles with energy less than 4 MeV are emitted, i.e. less than half the height of the barrier.
Fig. 12.
At large excitations intense oscillations arise in the nucleus, leading to an increase of its effective radius and to a lowering of the barrier\(^{43}\). However, it is hardly possible to explain the observed effect by this circumstance.
If the observed “sub-barrier” particles are not protons and are negatively charged, then their energy may be arbitrary. It may also be assumed that the particle passes through the barrier in a neutron state, and that this neutron is excited and, emitting an electron, turns into a proton*).
Finally, one cannot regard as wholly excluded the possibility that the nucleus actually disintegrates into a much larger number of particles than the number of observed tracks; the unobserved particles could have too large or too small energies and therefore not act on the emulsion. All these assumptions, of course, are as yet based on nothing, and the mechanism of emission of “sub-barrier” particles must be regarded as entirely unclear.
Further study of this question should, in particular, be carried out with a Wilson chamber, and it may prove convenient
*) A neutron in the ordinary state has a half-life for transformation into a proton equal to approximately one hour (if the calculations are considered correct). Therefore the neutron will decay very rapidly only in the case that it can be in some excited state.
to use a high-pressure chamber, since the “stars” must be observed in gas.
Observation of “stars” in a Wilson chamber has one great advantage, namely the possibility of detecting relativistic particles. Hazen \(^{10}\), at an altitude of \(3050\) m, found in his photographs 58 “stars,” of which 2 were produced in gas, and the rest in metal plates placed in the chamber. In addition, about 400 tracks of single strongly ionizing particles were observed. About one-third of the particles making up the “stars” had an ionization close
Fig. 13.
to the relativistic one and were, apparently, protons, mesotrons, and more rarely electrons. Owing to the chamber’s lower efficiency for relativistic particles than for slow particles, it may be thought that the relative number of relativistic particles is in fact greater than that observed. It is not yet possible to determine precisely the number of mesotrons in the “stars”; this question is of great interest in view of the possible connection of nuclear disintegrations with the formation of penetrating mesotron showers. It can already be said that in disintegrations, penetrating particles sometimes appear (with a range greater than centimeters of lead \(^{10,44,45}\)). A Wilson-chamber photograph of a disintegration with the formation of penetrating particles is shown in Fig. 13 \(^{45}\).
Naturally, the thought arises of linking the appearance of individual protons and neutrons, which were discussed in §§ 1 and 2, with the formation of a “star.” In § 2 we saw that protons and neutrons are in fact produced in approximately equal numbers, as should be the case in “stars.”
Using (3) and taking into account that the range of protons with energy 15 MeV is equal to \(R = 200\) cm, it is easy to find approximately the number of protons formed:
\[ q_{3400}\simeq \frac{2S^{p}_{3400}}{R}\simeq 5\cdot 10^{-5}\, \frac{\text{protons}}{\text{cm}^{3}\cdot \text{min}} . \tag{13} \]
In a “star” there are on average 4 protons, and thus from (12) it follows that from “stars” with \(n \geq 3\) there are formed
\[ q'_{3400}\simeq 10^{-5}\, \frac{\text{protons}}{\text{cm}^{3}\cdot \text{min}} . \tag{14} \]
If one takes into account disintegrations with \(n < 3\), then, as is clear from what was said above, the value of \(q'\) may increase by a factor of 2–3. Moreover, in § 1 it was already pointed out that the value of the proton flux \(S^{p}\) cannot be regarded as established with an accuracy better than 100–200%. Therefore, comparing (13) with (14), one may come to the conclusion that individual protons are formed as a result of nuclear disintegrations. The same applies to neutrons. In view of the inaccuracy of the experimental data, it is hardly reasonable to make more detailed calculations.^26
The establishment of the fact that protons and neutrons with relatively small range are formed as a result of nuclear disintegrations is almost trivial. The value of the comparison made here of the data on the number of “stars” formed and on the flux of individual protons and neutrons therefore consists mainly in revealing the mutual consistency of the various experimental facts, namely the data on individual heavy particles (§§ 1, 2) and on the formation of “stars” (§ 3).
§ 4. The Generating Component
Investigation of “stars” in a Wilson chamber makes it possible to draw very important conclusions about the nature of the particles that produce nuclear disintegrations. Namely, it turns out^10 that almost all “stars” not containing particles of high energy are produced by non-ionizing particles. Indeed, of the observed 58 “stars,” in 31 “stars” there were no particles with a range greater than 0.7 cm Pb*), and of these 31 “stars” only one was produced by an ionizing particle and in several cases
*) The figure 0.7 cm appears because this was the thickness of the plates placed in the chamber.^10
the track of the particle could not be seen; of 400 unit protons observed in the chamber, only 8 were produced by an ionizing particle. “Stars” containing particles with a range greater than 0.7 cm Pb are produced approximately equally by ionizing and non-ionizing particles: 8 “stars” were produced by ionizing particles and 13 by non-ionizing particles.
There is no correlation between the “stars” and the soft, shower-producing component; in particular, the non-ionizing particles causing disintegrations, at least in the majority of cases, are not γ-rays, since they do not give showers. For the same reason, the ionizing particles producing “stars” are not electrons or positrons.
It should be noted that the absence of a connection between the formation of “stars” and the shower-producing component in Hazen’s experiments\(^{10}\) is to a certain extent at variance with the results of Heitler et al.\(^{4}\); as is seen from Fig. 3, Heitler et al. observed a transition effect in lead, which compels one to assume that some of the unit protons are produced by the shower-producing component. If we suppose that here we are dealing with a nuclear photoeffect, then the cross section for this process is \(\sigma \sim 10^{-25}\ \mathrm{cm}^{2}\) per Pb nucleus\(^{4}\). The question of the role of the soft component in the formation of “stars” remains insufficiently clear; nevertheless, the basic conclusion that in the overwhelming majority of cases the “stars” are not associated with the soft component appears to us quite reliable. The mass of the generating particle can, in principle, be determined experimentally from the following considerations\(^{36}\). If the energy of all the particles in a “star” is equal to \(E\), the momentum of these particles together with the momentum of the residual nucleus is equal to \(P\), and it is assumed that a nonrelativistic particle of mass \(m\) incident on the nucleus is absorbed by this nucleus, then
\[ m=\frac{P^{2}}{2E}. \]
As the energy \(E\) one may take the total energy liberated in the “star” (see § 3, Fig. 11); the momentum \(P\) is equal to the vector sum of the momenta of all protons, neutrons, and the residual nucleus. In determining \(P\) it is assumed that the momentum of all neutrons is equal to the momentum of all protons, and that the velocity of the residual nucleus is the same as the resultant velocity of all protons. A determination of the mass carried out in this way for a large number of “stars” led to the conclusion\(^{36}\) that this mass is of the order of the proton mass. However, the error is such that the mesotron mass cannot in any way be excluded, even if all the assumptions made above are considered justified. In reality, however, the emission of relativistic particles, not taken into account in the method of photoplates, can very greatly reduce the accuracy of the calculation. Moreover, if, for example, it were possible to establish that \(\frac{P^{2}}{2E}\sim\mu\), where \(\mu\) is the mesotron mass, then even in that case it would not be possible, without further argument, to assert that it is precisely a mesotron that strikes the nucleus. Indeed, let us suppose that a relativistic particle (an electron or a photon) whose energy is \(E_{0}=cP_{0}\), where \(P_{0}\) is the momentum, is captured by the nucleus. Then from
measured values \(E\) and \(P\) for a “star” must be equal to
\[ \frac{E}{P}=\frac{E_0}{P_0}=c; \]
at the same time, by assumption,
\[ \frac{P^2}{2E}=\mu. \]
Hence one obtains the equality
\[ \frac{E}{2c^2}=\mu, \]
which, in order of magnitude, holds for typical “stars” with \(E\sim 10^8\ \mathrm{eV}\)
\[ \left(\frac{E}{2c^2}\sim 10^{-25},\quad \mu\sim 10^{-25}\right). \]
Thus, in order to distinguish a nonrelativistic generating particle from a relativistic one, a relatively high accuracy in the determination of \(E\) and \(P\) is needed, which has not been achieved experimentally. Therefore the only conclusion that we can reliably draw here is the assertion that analysis of the relation between energy and momentum in “stars” does not contradict the assumption that the generating particles are neutrons, protons, or mesotrons.
The performance of experiments in a Wilson chamber on “stars” born in gas could, in principle, make it possible to determine the mass of the generating particles quite reliably.
The neutral particles generating the majority of “stars” may be either neutrons or as yet unknown particles, which may conventionally be called neutral mesotrons. If the generating component is neutron, then the mean energy of the neutrons is about \(100\ \mathrm{MeV}\) and may be considerably greater (see Fig. 11). From this point of view it is very probable that the ionizing particles forming “stars” with large energy release are protons. Indeed, the fluxes of neutrons and protons must be proportional to their ranges; since, furthermore, a relativistic particle loses \(2\cdot 10^9\ \mathrm{eV}\) to ionization in passing through the atmosphere \(^{45}\), it is clear that the number of protons and neutrons with energy \(\gtrsim 10^9\) must be approximately the same, which is in qualitative agreement with experiment \(^{10}\).
Charged generating particles cannot be fast mesotrons, since the increase in the number of mesotrons with altitude is considerably slower than the increase in the number of “stars” (see §§ 1 and 3). The number of slow mesotrons increases with altitude very rapidly \(^{12,52}\), and at the same time negative mesotrons are energetically captured by the nucleus \(^{47}\). Therefore it would seem that slow mesotrons may play a significant role in the formation of “stars.” However, capture of a slow mesotron will lead to an excitation energy of only \(100\ \mathrm{MeV}\); meanwhile charged particles produce predominantly “stars” with large energy release. The question of the formation of “stars” by mesotrons still requires further investigation, but nevertheless it seems to us that the role of slow charged mesotrons cannot be significant.
The assumption that the generating uncharged component consists of neutral mesotrons has no experimental basis whatsoever. Nevertheless, this hypothesis deserves discussion, for the existence of neutral mesotrons is probable on grounds connected with the theory of nuclear forces. If neutral
mesotrons exist, then they must interact with the nucleus and could cause nuclear disintegrations.
Assuming that the mass of these particles is of the order of several hundred electron masses, we see that the majority of “stars” could be produced by slow neutral mesotrons; the decay of these particles, if it takes place, can be established by the experiments discussed in § 1.
In favor of the supposition that the generating particles are neutrons speaks the already noted possibility of naturally connecting, in this case, the formation of “stars” with a large energy with fast protons. Experiments in which, for example, carbon or aluminum is placed above the Wilson chamber in one case, and paraffin or another hydrogen-containing substance in another, may help clarify the nature of the component generating the “stars.” The appearance of fast recoil protons will make it possible to determine their effectiveness for the formation of “stars”; moreover, neutrons and neutral mesotrons will knock protons out of paraffin differently, which one may hope to establish as a result of a detailed analysis of the experimental data.
It appears possible to estimate the flux of particles generating “stars,” i.e. the intensity of the “generating component.” The absorption of this component is determined by formula (11), i.e. \(\sigma \sim 1.6\cdot 10^{-25}\ \mathrm{cm}^2\). The total effective cross section for the formation of “stars” \(\sigma_{\mathrm{зв}}\) is smaller than the total cross section; equality of the cross sections takes place if the absorption is caused only by the formation of “stars”*). Further, the number of “stars” \(N_{\mathrm{зв}}\), the flux of generating particles \(S^2\), and the cross section \(\sigma_{\mathrm{зв}}\) are related by
\[ N_{\mathrm{зв}}=\sigma_{\mathrm{зв}}N_{\mathrm{в}}S^2, \tag{15} \]
where \(N_{\mathrm{в}}\) is the number of nuclei in \(\mathrm{cm}^3\) of air.
As is clear from what has been said, \(\sigma_{\mathrm{зв}}\leqslant 1.6\cdot 10^{-25}\), and according to the data of § 3
\[ N_{\mathrm{зв}}>4\cdot 10^{-3}\ \frac{\text{stars}}{\mathrm{cm}^3\,\text{day}} \]
[see (12)]. Hence at an altitude of \(3400\ \mathrm{m}\):
\[ S^2_{3400}>0.3\ \frac{\text{particles}}{\mathrm{cm}^2\,\min}. \tag{16} \]
Since the flux of particles of the hard component at this altitude is equal to
\[ S^{\mathrm{жс}}_{3400}=2\ \frac{\text{particles}}{\mathrm{cm}^2\,\min}, \]
we see that
\[ \frac{S^2_{3400}}{S^{\mathrm{жс}}_{3400}}>0.15. \tag{17} \]
The value (12) is smaller than the total number of disintegrations by several times and, moreover, \(\sigma_{\mathrm{зв}}\) may be smaller than \(\sigma \sim 1.6\cdot 10^{-25}\), since the generating component produces not only disintegrations, but also forma-
*) It is assumed here that the generating particle, along its entire path, produces only one “star,” i.e. after the disintegration it disappears or loses almost all of its energy.
also produces penetrating particles (see below). Therefore, apparently, the ratio \(\dfrac{S^2_{3400}}{S^{\mathrm{hard}}_{3400}}\) is of order unity. At the altitude where the pressure is \(0.2\) atm, the intensity of the hard component is \(\sim 7\) times greater than its intensity at an altitude of \(3400\) m\(^1\); at the same time, according to (12), the number of “stars” and \(S^2\) in this case should increase by a factor of 22.
Experiments with a Wilson chamber\({}^{10,39}\) are in agreement with the estimate given for \(\dfrac{S^2}{S^{\mathrm{hard}}}\). Thus, Hazen\({}^{10}\) observed in his photographs about 9000 hard particles and 58 “stars.” The total number of “stars,” however, is considerably larger, since the majority of them are formed in the thickness of the lead plates and do not emerge. Since the range of protons with an energy of 15 MeV is \(R=0.035\) cm Pb, while the thickness of the plates is \(0.7\) cm Pb, one may think that about 20 times more “stars” are formed than emerge\(*\). In fact, however, a factor \(\sim 50\) is closer to reality, since many particles have energy \(>15\) MeV. The total number of “stars,” equal to \(58\cdot 50\sim 3000\), should be equal to \(\sigma_{\mathrm{st},\mathrm{Pb}}N_{\mathrm{Pb}}S^2\), where \(\sigma_{\mathrm{st},\mathrm{Pb}}\) is the cross section for the formation of a star on a Pb nucleus and \(N_{\mathrm{Pb}}\) is the number of Pb nuclei in the path of the generating particle \((N_{\mathrm{Pb}}\sim 5\cdot 10^{22})\). Taking \(\sigma_{\mathrm{st},\mathrm{Pb}}=2\cdot 10^{-24}\), we obtain for \(S^2\) the value \(3\cdot 10^4\). At the same time, as already indicated, \(\sim 9000\) hard particles were observed. Further, one third of the stars contained secondary particles, and thus, at least with respect to these “stars,” the efficiency of the chamber for hard particles and for “stars” is the same (this argument belongs to V. I. Veksler). As a result we see that, in agreement with what was said above,
\[ \frac{S^2_{3000}}{S^{\mathrm{hard}}_{3000}}\sim 1. \]
A more detailed discussion of the determination of the ratio \(S^2/S^{\mathrm{hard}}\) in the experiments of Hazen\({}^{10}\) and Powell\({}^{38}\) is not advisable in view of a whole series of insufficiently definite points. Here it is important only to emphasize that the chamber method fully confirms the estimate\({}^{17}\) and shows that
\[ \frac{S^2_{3400}}{S^{\mathrm{hard}}_{3400}}\sim 1. \tag{18} \]
Thus, the component generating stars at an altitude of \(3400\) m, and especially at greater altitudes, is very intense and fully deserves the name of the third component of cosmic rays\({}^{3,13}\). If this component is proton-neutron in character, which is most probable, then the number of protons in it is approximately \(1/5\) (in Hazen’s
\(*\) In Hazen’s\({}^{10}\) experiments the lead plates were covered with thin layers of iron, so that the observed “stars” were formed in iron. We do not take this circumstance into account.
43 “stars” were produced by non-ionizing particles and 9 stars by ionizing ones). The protons in this case must have an energy \(>10^8\) MeV and, consequently, must mainly enter into the hard component, constituting an appreciable percentage of it. Further observations are needed in order to bring greater clarity to the question of the number and energy of the protons.
The “stars” and the protons associated with them are apparently responsible for Hoffmann’s ionization bursts at medium and great altitudes (see \(^{16,39,48,49}\) and § 1).
It is hard to doubt that the particles generating the “stars” are also responsible for the production of penetrating particles observed by a number of authors \(^{44,50-53}\). This point of view is supported by the fact that in the cited works the penetrating (hard) particles were produced to a greater extent by the non-ionizing component. Further, penetrating particles were observed directly in the “stars” \(^{10,44,45}\). Finally, the altitude dependence of the penetrating showers is approximately the same as the course of the particles generating the “stars.” Indeed, for penetrating showers, \(\mu\) in the law \(S=S_0 e^{-\mu z}\) is approximately equal to \(10\ \mathrm{atm}^{-1}\) \(^{53}\), whereas for “stars” \(\mu \simeq 7\ \mathrm{atm}^{-1}\). The accuracy of all the measurements is such that, of course, there is no need to speak of a discrepancy here.
The value \(\mu = 10\ \mathrm{atm}^{-1}\) is also obtained in the experiments of Alikhanov and Alikhanyan \(^{13}\) on the absorption in water of particles indirectly responsible for the difference in the readings of an ionization chamber and a counter.
As is clear from all that has been set forth, investigation of the question of the third component of cosmic rays and of the effects caused by it (“stars,” penetrating and soft particles, showers) is the most urgent problem in cosmic-ray physics.
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-
If all particles have the same range and are produced with an isotropic distribution, then their flux through an area of $1\ \text{cm}^2$ is $S = qR/2$. ↩