Electron-Nuclear Showers and the Nuclear-Cascade Process*

N. G. Birger and I. L. Rozental

In setting forth the modern point of view on the passage of cosmic rays through the atmosphere, Powell nowhere mentions the work of Soviet physicists, who were the first to systematically investigate the non-electromagnetic processes that occur when high-energy particles interact with matter. On the basis of these investigations, in 1948–1949 Soviet physicists proposed a scheme of the fundamental processes caused by cosmic radiation.^128,129 This scheme was based on the results of the study of electron-nuclear and extensive air showers.

In the present supplement we briefly set out the results of experiments that make it possible, with greater justification than on the basis of the data used by Powell, to outline the general picture. In addition, a special paragraph of the supplement is devoted to the work of Soviet authors on the study of the mechanism of $\mu$-meson decay.

I. Electron-Nuclear Showers

a) Discovery of electron-nuclear showers

The essential role of non-electromagnetic processes was discovered in experiments carried out in 1945 by G. B. Zhdanov and A. L. Lyubimov.^130 Using the arrangement shown in Fig. 43, a, the altitude dependence of showers under 10 cm of lead was measured; at the same time the altitude dependence of the penetrating component of cosmic radiation was also determined. The result obtained is presented in Fig. 43, b. From Fig. 43, b it is seen that the number of showers under lead increases with altitude considerably faster than the penetrating component. From comparison of the altitude dependences it follows that showers under lead cannot be fully explained by elec-

*) See the note on p. 15.

by the electromagnetic interaction of the $\mu$-mesons of the hard component. At the same time, control experiments showed that at sea level practically all showers under lead are $\delta$-showers and, consequently, already at an altitude of about 4 km above sea level about half of all recorded showers cannot be explained by electromagnetic processes. Such showers later received the name electron-nuclear showers.

Subsequently, the altitude dependence of showers was studied over a wide range of altitudes (up to 23 km) with the aid of various installations \[31, 132\]. It was shown that the altitude dependence of showers can be represented in the form of an exponential with exponent

\[ \mu = \frac{1}{120}\ \text{cm}^{2}/\text{g}. \]

Fig. 43. a) Arrangement for determining the change with altitude in the number of showers under 14 cm of lead.
b) Comparison of the altitude dependence of the hard component (curve I) and of showers under 14 cm of lead (curve II).

The subsequent experiments were then devoted to investigating the nature of these showers and their connection with various phenomena occurring in cosmic rays.

These investigations were carried out chiefly at the high-mountain station (3860 m) by workers of the FIAN laboratory under the direction of N. A. Dobrotin, and in the first period also by V. I. Veksler.

b) Composition of electron-nuclear showers

For understanding the processes leading to the appearance of electron-nuclear showers, the question of their composition is essential.

Already in the first experiments with counters \[29\] it was shown that electron-nuclear showers consist of both soft and penetrating particles.

In subsequent investigations with a Wilson chamber placed in a magnetic field \[33\], and also with the aid of hodoscopic installations \[34\], it was shown that the soft component of electron-nuclear showers consists of electrons and photons, and the penetrating component—of protons and mesons (as is now known, of all

in the totality of the data, the mesons forming part of electron-nuclear showers are \(\pi\)-mesons). In some cases the penetrating particles formed in electron-nuclear showers, in turn, produce secondary electron-nuclear showers in the apparatus. Such cases were observed both in a Wilson chamber containing lead and carbon plates \(^{135}\), and in a hodoscopic apparatus \(^{134}\). Thus, some of the penetrating particles are nuclear-active. The mixed composition of the showers directly indicated that electron-nuclear showers could not be the result of the electromagnetic interaction of high-energy particles with matter, but were formed through the interaction of cosmic particles with the nuclei of the atoms of matter. The photographs obtained of showers formed in thin carbon and lead plates inside a Wilson chamber \(^{135}\) also confirm the “explosive” character of the formation of electron-nuclear showers.

The penetrating showers described in Section 7 of Powell’s review are, in essence, the same electron-nuclear showers, in which, owing to the features of the apparatus used for registration, only their penetrating part has been singled out.

b) The transition density effect and the decay of particles generating electron-nuclear showers

The existence in electron-nuclear showers of secondary nuclear-active particles may be the cause of the so-called transition density effect. This effect plays, on the one hand, an important role in interpreting many results and, on the other hand, proves the existence of a nuclear-cascade process (see below).

Fig. 44. Diagram explaining the existence of the density effect.

Let us briefly consider the essence of the transition density effect. Suppose that two or more nuclear-active particles are generated in an electron-nuclear shower. In that case a difference will be observed in the absorption coefficients of the shower-generating component in air and in a dense substance, even with the same atomic number as for air. Indeed, suppose that both in air and in a dense substance the primary particle creates several secondary nuclear-active particles. If a nuclear-active particle reaches the apparatus from the air, then mainly showers formed by single nuclear-active particles will be recorded (in air the nuclear-active particles have time to move apart from one another).

If, however, a layer of dense substance is located above the apparatus, then cases may be observed of the simultaneous formation in the apparatus of two or several electron-nuclear showers (Fig. 44)

and, consequently, depending on the ratio of the probabilities of registering a double and a single shower, a definite difference will be found in the absorption coefficients in air and in a dense substance. Absorption in a dense substance may turn out to be either greater or less than absorption in air. A detailed analysis of the transition effect was carried out in the review paper on electron–nuclear showers\(^{139}\), as well as in the papers of M. I. Podgoretskii\(^{136}\) and others.

The latter finally established that the experimental data prove the existence of the transition effect and, consequently, that in electron–nuclear showers two or more nuclear-active particles are sometimes formed.

The density transition effect has an essential bearing on the interpretation of compensation experiments carried out to investigate the stability of the nuclear-active particles that produce electron–nuclear showers.

The idea of the experiments proposed as early as 1946–1947 by V. I. Veksler, L. V. Kurnosova, and A. L. Lyubimov\(^{137}\) reduces to comparing the number of showers recorded at two altitudes, with a layer of dense substance placed above the apparatus at the higher altitude, close to air in atomic number and compensating, in mass, for the column of air between the two altitudes. If unstable particles were present among the shower-producing particles, then a larger number of showers would be recorded under the dense substance at the higher altitude than at the lower altitude. This was in fact observed experimentally.

However, the presence of the density transition effect can, under certain experimental conditions, lead to the same result. An analysis of the conditions realized in analogous experiments showed that the density transition effect should only have emphasized the decay of the shower-producing particles\(^{138}\). Consequently, already in these works an indication was obtained of the decay of at least part of the shower-producing particles.

A more rigorous conclusion about decay follows from experiments\(^{139}\) carried out under conditions free (or almost free) from the influence of the transition effect, namely, when the layer of absorber above the apparatus considerably exceeds the range of the secondary nuclear-active particles (water in a lake situated at an altitude of 3860 m was used as the dense substance). The authors found that the absorption coefficient in water is

\[ \frac{1}{\mu}=170\pm10\ \mathrm{g/cm^2}, \]

whereas in air

\[ \frac{1}{\mu}=123\pm6\ \mathrm{g/cm^2}. \]

The difference found in the absorption coefficients in water and in air indicates the decay of at least part of the shower-producing particles. It is natural to suppose that the decaying nuclear-active particles are \(\pi\)-mesons.

d) Relation of electron-nuclear showers to extensive atmospheric showers

The unstable character of some of the shower-forming particles indicates the secondary origin of nuclear-active particles in the atmosphere. The same conclusion follows from the existence of a connection between electron-nuclear and extensive atmospheric showers. Thus, already in the first experiments on the study of electron-nuclear showers \(^{139}\) it was shown that in some cases showers under lead are accompanied by extensive atmospheric showers. On the other hand, the connection between electron-nuclear and extensive atmospheric showers was studied in greater detail by G. T. Zatsepin and L. I. Sarycheva \(^{140}\) with the aid of the apparatus shown in Fig. 45. In the work it was shown that the penetrating particles of extensive atmospheric showers possess a considerably greater shower-forming capacity than ordinary \(\mu\)-mesons of the hard component. An estimate of the number of nuclear-active particles in extensive showers gives a value from 0.1 to 1% of the total number of electrons in the shower.

Fig. 45. Diagram of the apparatus for studying the shower-forming capacity of penetrating particles of extensive atmospheric showers.

The secondary character of the particles that produce electron-nuclear showers is further confirmed by the fact that about half of these particles are neutral \(^{149}\).

The secondary character of nuclear-active particles, and the formation of electron-nuclear showers in dense substances with different atomic numbers \(^{135}\) (graphite, lead), show that electron-nuclear showers are also produced in air.

e) Study of electron-nuclear showers in the stratosphere

Experiments by S. N. Vernov \(^{141}\) and co-workers to determine the nature of cosmic rays in the stratosphere showed that the soft component at great altitudes consists of photons and electrons. (This conclusion was drawn both from the presence of a large transition effect of the soft component, characteristic of electrons, and from the capacity for shower formation, which proved to be of the same order as that expected for electrons and photons.) Experiments to determine the ionization produced by the soft component in the stratosphere found \(^{141}\) that the energy of the soft component excee-

reduces by at least a factor of two the energy transferred to electrons through the decay of ordinary mesons (as early as 1940, D. V. Skobel’tsyn and S. N. Vernov\(^{143}\), on the basis of K. Alekseeva’s experiments,\(^{143}\) pointed out the impossibility of explaining all the energy released by the soft component for ionization solely by the electrons of decay).

Thus, in passing through the atmosphere, the primary particles must create an electron–photon component, since special experiments by Vernov and co-workers\(^{144}\) showed that the electrons themselves are not part of the primary component.

In the stratosphere (up to altitudes of \(\sim 23\) km) the character of showers produced by primary particles in lead and aluminum was studied.\(^{145}\) It was shown that the showers consist of an electron–photon and a penetrating component. On this basis it was concluded that, in interaction with matter, primary particles of high energy create electron–nuclear showers.

Thus, the totality of the experiments carried out in the atmosphere indicated that it is precisely electron–nuclear showers that are the source of the soft component of cosmic rays.

II. EXTENSIVE ATMOSPHERIC SHOWERS

Investigations of extensive atmospheric showers carried out in recent years under the direction of Academician D. V. Skobel’tsyn and G. T. Zatsepin have shown that non-electromagnetic processes also play an essential role in the development of extensive atmospheric showers.

The principal facts that led to this conclusion are as follows.

1. The observed spatial distribution of extensive atmospheric showers is considerably broader than that expected according to cascade theory.\(^{146}\)

2. The composition of an extensive atmospheric shower includes penetrating particles, whose number is about \(2\%\) of the number of electrons in the central region of the shower; moreover, the energy carried by the penetrating particles is comparable with the total energy of the shower.\(^{147}\) The appearance of penetrating particles does not fit within the framework of the electromagnetic (cascade) theory of extensive showers.

3. A considerable part of the penetrating particles is nuclear-active, capable of producing electron–nuclear showers.\(^{149}\)

On the basis of these facts, taking into account the already known process of formation of electron–nuclear showers, G. T. Zatsepin in 1948\(^{128}\) put forward a hypothesis of a nuclear-cascade process leading, at very high energies of the primary particles, to the formation of an extensive shower in the atmosphere. The essence of this hypothesis is as follows.

Primary particles of cosmic radiation, upon entering the atmosphere, interact with air nuclei with a cross section of the order of the geometrical cross section of a nucleus, thereby producing an electron-nuclear shower consisting of mesons and nucleons of high energies and of photons or electrons (in 1948 the question of the origin of the soft component of electron-nuclear showers remained open, although on the basis of indirect considerations it seemed more probable that the primary particles were photons). Passing through the atmosphere, the nuclear-active particles give rise to secondary electron-nuclear showers until the energy of the nuclear-active particles becomes less than some “threshold” value. This energy value is apparently \(\sim 5\cdot 10^{9}—10^{10}\) eV. The electron-photon component formed in electron-nuclear showers, multiplying in ordinary cascade processes, creates a shower in the atmosphere. The hypothesis considered made it possible to explain a whole series of facts observed in the study of extensive showers which did not fit within the framework of the usual cascade theory.

At lower energies of the primary particles, the nuclear-cascade process ceases already after a small number of nuclear cascades. The \(\pi\)-mesons formed in electron-nuclear showers, decaying in flight, turn into \(\mu\)-mesons, which in this case will be observed as single particles because of the rapid attenuation of the electron-photon shower.

III. DECAY OF \(\mu\)-MESONS

Until very recently (1948) it was believed that the \(\mu\)-meson decays into an electron and one neutrino*). To test this assumption, G. B. Zhdanov and A. A. Khaidarov in 1948\(^{148}\) carried out, at an altitude of about 4 km, an investigation of the absorption of decay products in various substances by the method of delayed coincidences. The arrangement of the apparatus used is shown in Fig. 46. In this work, stopped mesons are registered by counter group \(I\), and the decay electrons are registered by groups \(II\) and \(III\), connected into delayed branches

Fig. 46. Apparatus of G. Zhdanov and A. Khaidarov for studying the spectrum of decay electrons.

*) It should be noted that the first indications that the scheme of decay of the \(\mu\)-meson into an electron and one neutrino is incorrect were obtained by C. Alexeyev\(^{142}\) as early as 1940.

schemes. The mesons were stopped in filter \(d\); the absorption curve of the decay electrons was investigated by varying the thickness of filter \(D\). The experimentally obtained dependence of the number of delayed coincidences on the thickness of the lead filter \(D\) (curve 1) or the thickness of the graphite filter (curve 2) is presented in Fig. 47. The difference between the curves shows that the particles produced in the decay also undergo ionization losses and, consequently, are electrons, and not mesons of small mass (of the order of several \(m_e\)).

The absorption curves obtained in this way make it possible to decide the question of the correctness of the scheme of decay of the \(\mu\)-meson into two particles (an electron and one neutral particle). For this purpose a calculated absorption curve in graphite for electrons with energy 50 MeV was plotted (Fig. 47, curve 3). Such a curve would have had to be obtained if the scheme of decay of the \(\mu\)-meson into an electron and a neutrino had proved correct.

Fig. 47. Absorption curves of decay electrons in filter \(D\): 1 — experimental absorption curve in graphite; 2 — absorption curve in lead; 3 — calculation of absorption in graphite under the assumption that all decay electrons have energy 25 MeV; 4 — calculation of absorption in graphite under the assumption that all decay electrons have energy 50 MeV.

As is seen from Fig. 47, it is impossible to reconcile the experimental curve (2) with the assumption of the decay of the \(\mu\)-meson into two particles. However, the form of the spectrum obtained is easily explained by the assumption of the decay of the \(\mu\)-meson into three particles (an electron and two neutral ones).

The authors analyze two decay schemes:

\[ \mu \to e + 2\nu, \]

\[ \mu \to e + \nu + \mu^0 \]

(\(\nu\) is a neutrino, \(\mu^0\) is a neutral meson), and come to the conclusion that both decay schemes can occur if one assumes that the mass of the neutral meson \(m_{\mu^0} < 70 m_e\). The first of the above schemes appears more natural, since it does not require the existence of new hypothetical particles besides the neutrino.

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