THE MESON PROBLEM AND THE CURRENT STATE OF THE THEORY OF COSMIC RAYS*)

I. E. Tamm

§ 1. Mesons, or mesotrons (these terms are synonymous and equally used), are the name given to elementary particles possessing a so-called “intermediate mass,” i.e., particles heavier than electrons and at the same time lighter than protons. Apparently, not all mesons have one and the same mass and spin; it seems more probable that several different kinds of mesons exist.

At the present time the existence of charged (positive and negative) mesons with a mass close to \(200m\) (\(m\) is the mass of the electron) has been established with complete certainty. However, there are also convincing data on the existence of charged mesons with another mass**); finally, there are weighty theoretical arguments in favor of the assumption that neutral mesons exist (which are sometimes called “neutrettos”).

The question of the properties of mesons is undoubtedly one of the most important and central questions of contemporary experimental and theoretical physics. This is due not only to the natural interest aroused by each newly discovered kind of the basic “building blocks of the universe”—elementary particles—but also to a number of other reasons.

First, mesons form part of cosmic rays, making up about 70% of these rays at sea level; therefore the diverse processes that occur when cosmic rays pass through the earth’s atmosphere are, in substantial part, determined by the properties of mesons. In this connection, the question of the nature and properties of mesons is at present central for the physics of cosmic rays,

*) This article is an introduction to the collection Meson, published by Gostekhizdat and written by members of the Theoretical Department of FIAN. V. L. Ginzburg’s article following this one was also written for this collection.

**) According to the observations of A. I. Alikhanov and A. I. Alikhanyan and their collaborators, at an altitude of 3200 m a noticeable fraction of the mesons in cosmic rays has a mass of the order of \(500\)—\(1000m\).

i.e. for that domain of physics which arouses special interest because cosmic rays contain particles whose energy exceeds by several orders of magnitude the energy of all particles of other origin known to us.

Secondly, insofar as one can judge at the present time, the most important problem of modern physics—the problem of nuclear forces, i.e. the forces of cohesion between nucleons (protons and neutrons) in atomic nuclei—is most closely connected with the problem of mesons. Apparently, the relation between nuclear forces and mesons corresponds approximately to the relation between electromagnetic forces of interaction of charged particles and light quanta (photons). From the properties of photons and from the laws of their emission and absorption by charged particles one can determine the forces of electromagnetic interaction of charges; similarly, from the properties of mesons and from the laws of their emission and absorption by nucleons, it will in all probability be possible to determine the nuclear forces.

Finally, the third reason determining the special interest of the meson problem is the following. Modern quantum mechanics undoubtedly gives a correct and consistent description of an enormous range of physical phenomena, in particular the laws of motion and interaction of nonrelativistic particles (i.e. particles whose velocity is small in comparison with the velocity of light). In contrast to this, relativistic quantum theory, in particular the theory of force fields (the electromagnetic field, the meson field, or the field of nuclear forces, etc.), is in a very unsatisfactory state. This is manifested in the fact that the calculation, according to modern theory, of a whole series of physical quantities leads to infinite, i.e. physically meaningless, expressions. Some of these so-called “infinities” are connected with the fact that in relativistic theory we cannot, in an invariant way, ascribe finite dimensions to an elementary particle, but must treat it as a material point. Meanwhile, the proper energy of a point particle, for example the electric energy of a point electric charge, is infinite both in quantum and in classical theory. Besides these so-called “classical infinities,” there are also infinities of essentially quantum origin; thus, for example, the quantum fluctuations of the electromagnetic-field strength turn out to be infinitely large even in the absence of electric charges. Both classical and quantum infinities lead, in particular, to the fact that when perturbation theory is used, the higher approximations turn out to be not only not small, but even infinite, etc.

Despite these serious shortcomings of modern relativistic quantum theory, there exists a rather extensive domain of phenomena to which we have learned to apply this theory successfully. Thus, for example, the theory of the processes occurring when relativistic electrons and positrons pass through matter (their scattering, ionization of mat—

... matter, bremsstrahlung and the subsequent production by gamma quanta of electron and positron pairs, the Compton effect, etc.), is excellently confirmed by experiment.

On the contrary, the domain of applicability of the modern relativistic theory to free mesons and to the meson fields of nuclear forces is much narrower than its applicability to electrons, positrons, and the electromagnetic field. This is due to two reasons. First, the applicability of the modern theory to electromagnetic phenomena is essentially connected with the smallness of the fine-structure constant \(a=\frac{e^2}{\hbar c}\), thanks to which in most cases it proves sufficient to restrict oneself to only the first approximation of perturbation theory, in which the expansion is carried out in powers of \(a\). On the contrary, the quantity \(\frac{g^2}{\hbar c}\), corresponding in meson theory to the fine-structure constant \(a\) (\(g\) denotes the “meson” charge of the nucleon), is tens of times larger than \(a\), and therefore perturbation theory is poorly applicable (and perhaps altogether inapplicable) to meson fields. Secondly, in order to explain the substantial dependence of nuclear forces on the spin of the nucleons and the large value of the cross section for the production of mesons by fast protons in the upper layers of the atmosphere, it is usually assumed either that the spin of the mesons is equal to 1, or that the interaction of nucleons with mesons having spin 0 is analogous to the interaction of electric or magnetic dipoles (and not to the interaction of electric charges). Both these assumptions lead, however, to the result that modern quantum theory proves in essence to be wholly inapplicable to mesons*).

It is precisely this inapplicability, or poor applicability, of modern theory to mesons that is one of the reasons for the special interest in the meson problem. One may hope that the study of mesons will create the necessary experimental basis for the construction of a future relativistic theory of elementary particles, capable of eliminating from it those fundamental difficulties which, in a less acute form, we also encounter in the quantum theory of the electromagnetic field.

§ 2. At the present time the only source of mesons is cosmic rays. This source has an insignificant intensity (approximately one meson per minute falls on \(1\ \mathrm{cm}^2\) of the earth’s surface) and cannot be controlled; cosmic mesons are distributed over a very wide range of energies and are accompanied by fast particles of another nature. Therefore the study of cosmic mesons is an extremely difficult experimental problem. At the same time, mesons are extremely short-lived and spontaneously decay into one electron or positron and one neutrino (the mean lifetime of a nonrelativistic meson is \(2.15\cdot 10^{-6}\ \mathrm{sec}\)). Therefore decisive

*) See on this the article by V. L. Ginzburg, “The Theory of the Mesotron,” p. 174.

successes in the study of mesons can be expected only when it becomes possible to generate mesons under laboratory conditions, just as positrons are generated by irradiating matter with gamma quanta. After all, the mesons that form part of cosmic rays are generated in the earth’s atmosphere, since the spontaneous decay of mesons eliminates the possibility that they could reach the earth from remote regions of space.

Since the mass of mesons (at least of the kind of meson that predominates in cosmic rays at sea level) is approximately 200 times greater than the mass of the electron, the rest energy of a meson is approximately \(10^8\) eV. To generate mesons it is necessary to irradiate matter with gamma quanta, or—what in all probability will prove more effective—with protons or neutrons whose energy exceeds this limit. The rapid advances in the technology of producing ultrafast particles (cyclotron, betatron, synchrotron, etc.) make it possible to expect that in the very near future it will be possible to “manufacture mesons” under laboratory conditions*). This will bring about a genuine revolution in the state of elementary-particle physics.

§ 3. In order to clarify the special features of the present stage in the development of cosmic-ray physics, it is necessary to recall the history of this extremely rapidly evolving field of physics over the past decade. By the beginning of 1937 the state of the problem was approximately as follows.

Various geomagnetic effects had been discovered and investigated, in particular the latitude geomagnetic effect, i.e. the dependence of the intensity of cosmic rays on geomagnetic latitude. These effects are due to the deflection of charged primary cosmic particles (i.e. particles falling on the earth from outer space) by the earth’s magnetic field (practically the entire deflection of a cosmic particle occurs on that part of its trajectory which lies far beyond the limits of the earth’s atmosphere). Thus it was established that, if not all primary particles, then at any rate a substantial fraction of them are charged. From the magnitude of the geomagnetic effect it was established that the energy of the primary particles reaches tens of billions of electron volts. It was further established that the intensity of cosmic rays increases rapidly with altitude above sea level and at an altitude of 20–30 km exceeds the intensity at the earth’s surface by hundreds of times. The number of negative and positive particles in cosmic rays proved to be approximately the same.

As for the mass of the particles that make up cosmic rays, it must be borne in mind that the mass can be reliably measured only for comparatively slow particles whose kinetic energy is substantially

*) Report by M. Schein and his group of collaborators (Phys. Rev., 70, 435 (1946)) that in experiments with gamma quanta of \(10^8\) eV generated by a betatron, they succeeded in observing the production of mesons in three cases, is disputed by the experiments of F. L. Fildender and collaborators (Phys. Rev., 70, 790 (1946)).

THE MESON PROBLEM

less than their rest masses. Measurements of the mass of cosmic particles, carried out at sea level, showed that many of these particles are undoubtedly electrons and positrons, and only a very small percentage are protons.

In connection with this, the view became widespread that the charged particles of cosmic radiation throughout the entire extent of the earth’s atmosphere are, for the most part, electrons and positrons. Those rare cases in which measurements of particle mass led to values intermediate between the masses of the electron and the proton were at that time attributed to the inadequacy of the theory used for calculating the mass.

In general, many processes occurring when cosmic particles pass through the earth’s atmosphere and other media—above all the absorption of these particles and the formation of showers of cosmic rays—seemed at that time to be in sharp contradiction with theory.

As is known, not very fast charged particles, when passing through matter, lose their energy mainly through ionization and excitation of the atoms of the medium. Alongside these “ionization” losses there also exist energy losses due to bremsstrahlung. When an electron or positron flies near an atomic nucleus, under the influence of the Coulomb interaction with the nucleus it undergoes an acceleration, and any nonuniformly moving charge

\[ \left( \text{if } \frac{d^{2}v}{dt^{2}} \ne 0 \right) \]

radiates electromagnetic waves. The intensity of the radiation is proportional to the square of the acceleration, i.e. proportional to

\[ \left(\frac{Ze^{2}}{m}\right)^{2}, \]

where \(Ze\) is the charge of the atomic nucleus, and \(m\) is the mass of the particle flying near it. Such bremsstrahlung is, for example, the continuous X-ray spectrum emitted by electrons when they are decelerated in the anticathode of an X-ray tube. At not very large particle energies, the energy losses due to radiation are much smaller than the losses due to ionization. However, as the energy of the charged particle increases, the relation between these two kinds of losses is reversed, and radiation losses, increasing in proportion to the kinetic energy \(E\) of the particle being decelerated, far outstrip the ionization losses, which reach a minimum at \(E \sim mc^{2}\) and increase only slightly with further increase of the energy \(E\). The value of the particle energy \(E\) at which the losses of both kinds become equal is called the critical energy \(E_{cr}\). Since (as has just been indicated) bremsstrahlung is proportional to \(Z^{2}\), where \(Z\) is the atomic number of the atoms of the medium, whereas ionization losses are proportional to the number of electrons in the atom, i.e. proportional to \(Z\) (we neglect here factors depending logarithmically on \(Z\)), the relative role of bremsstrahlung is greater, and correspondingly the value of \(E_{cr}\) is smaller, the larger the atomic number of the atoms of the medium: for air \(E_{cr} \sim 80\ \mathrm{MeV}\), for lead \(E_{cr} \sim 7\ \mathrm{MeV}\).

It must be borne in mind that bremsstrahlung is inversely proportional to the square of the mass of the particle being slowed down, whereas the ionization losses of extremely relativistic particles (i.e., particles whose velocity \(v\) satisfies the condition \(1-\frac{v}{c}\ll 1\)) are practically independent of their mass; therefore the critical energy is proportional to the square of the mass of the particle being slowed down. The numbers just given refer to electrons and positrons. Since the properties of very fast electrons and positrons are almost identical, in what follows the term “electron” will often denote electrons of both signs of charge (i.e., both electrons proper and positrons).

The range of a particle of given energy is the mean path length of the particle in a given substance over which the particle expends all its initial kinetic energy. The theoretically calculated ranges of fast electrons and positrons turned out to be much smaller than the experimentally determined ranges of cosmic-ray particles. Thus, for example, in passing an electron through the entire thickness of the earth’s atmosphere, according to the theory it should lose an energy of the order of \(10^{13}\,\mathrm{eV}\), whereas the latitude geomagnetic effect indicates that primary cosmic-ray particles have an energy of the order of \(10^{10}\,\mathrm{eV}\), i.e. a thousand times smaller.

The second fundamental difficulty consisted in the fact that the theory was powerless to explain the mechanism of formation of cosmic-ray showers. An electron or positron of high energy, falling, say, upon a lead plate, produces in it a whole beam of secondary electrons and positrons flying approximately in the same direction as the primary particle*). Such a beam of electrons and positrons, genetically connected with one another, is called a shower. Showers can also be produced by photons; they also arise in the earth’s atmosphere. The number of particles in a shower can vary from \(2\)—\(3\) to hundreds and even thousands. Finally, in 1938 Auger established the existence, it is true of relatively very sparsely populated, so-called broad atmospheric showers, or Auger showers, whose horizontal cross section reaches tens of thousands of square meters, while the number of particles in them may be counted in millions.

Both the great penetrating power of cosmic rays and the existence of showers seemed so contrary to the theory that the conviction became widespread that Dirac’s electron theory was inapplicable to electrons and positrons of high energies; it was assumed that the limits of its applicability were close to \(137\,mc^2\) \(\left(m\right.\) is the mass of the electron, \(\left.137=\frac{1}{\alpha}=\frac{\hbar c}{e^2}\right)\).

§ 4. The year 1937 was a turning point for the physics of cosmic rays. By one of those accidental coincidences which occur

*) The greater the energy of the secondary particle, the less its direction of flight deviates from the direction of the primary particle.

THE MESON PROBLEM

Sometimes in the history of science, in the first half of that year, three papers appeared independently of one another which clarified the basic difficulties of the theory. At the very beginning of 1937, two theoretical papers were published—one by Bhabha and Heitler, the other by Carlson and Oppenheimer—which explained the mechanism of the formation of cosmic-ray showers. In May of the same year, Neddermeyer and Anderson reported their discovery in cosmic rays of a new penetrating particle—the meson.

We cannot dwell here on the comparison of the experimental data that led Neddermeyer and Anderson to their fundamental discovery; let us note only that, in the chain of their reasoning, decisive importance was attached to the fact that the penetrating power of a relativistic charged particle of a given energy must be the greater, the greater its rest mass. Indeed, bremsstrahlung, as was already indicated above, is inversely proportional to the square of the mass of the particle being decelerated. Since the mass of the meson is approximately 200 times greater than the mass of the electron, the losses of mesons to radiation are approximately \(200^{2}=4\cdot10^{4}\) times smaller than the losses of electrons of the same energy. Thus it turns out that, up to very high energies (of the order of \(3\cdot10^{11}\ \mathrm{eV}\) in lead and \(4\cdot10^{12}\ \mathrm{eV}\) in air), mesons, in passing through matter, practically do not give rise to bremsstrahlung, but expend energy only on ionization of the medium. These losses constitute only a small fraction of the radiative losses experienced by fast electrons. Thus, for example, a fast charged particle (independently of its mass), in passing through the thickness of the earth’s atmosphere, expends on ionization only about \(2\cdot10^{9}\ \mathrm{eV}\), whereas, owing to radiative losses, the minimum energy required for an electron to pass through the thickness of the atmosphere reaches \(5\cdot10^{12}\ \mathrm{eV}\). Thus, the large mass of mesons ensures their great penetrating power *). We now know that the energy of the primary cosmic rays falling on the surface of the atmosphere is transferred to the surface of the earth mainly not by poorly penetrating electrons and positrons, but by penetrating mesons. The overwhelming majority of the electrons and positrons that make up cosmic rays at sea level are produced not at the surface of the atmosphere, but in its lower layers, and they are produced by mesons that have penetrated into these layers.

It is customary to distinguish two principal components of cosmic rays—the hard, or penetrating, component and the soft component. These components are not very sharply separated; experimentalists usually regard as soft

*) In passing through matter, mesons may expend their energy not only on ionization and radiation, but also on specifically meson-nuclear processes. However, these specific losses play no significant role for mesons with energies of the order of \(10^{9}\ \mathrm{eV}\), which predominate in the lower layers of the atmosphere. We know very little about the behavior of mesons of very high energies.

those cosmic rays which are absorbed by approximately 10 cm of lead, and as hard those which pass through such a layer of lead. The so-called ionizing (i.e., consisting of charged particles) part of the hard component consists of fast mesons and protons; in the lower layers of the atmosphere there are few protons, while in the very upper layers they probably constitute the predominant part of the cosmic rays. The soft ionizing component of cosmic rays at sea level consists mainly of electrons and positrons, whose low penetrating power is due to losses by radiation. In addition, the soft ionizing component includes relatively slow mesons and protons, the number of which increases rapidly when rising from sea level to great heights.

In addition to ionizing (i.e., charged) particles, cosmic rays also include neutral (non-ionizing) particles. The penetrating non-ionizing component consists of neutrons and, probably, of neutral mesons; the soft non-ionizing component consists mainly of photons.

The low penetrating power of photons is closely connected with the mechanism of formation of showers of cosmic particles. As was first established by the works of Bhabha and Heitler and of Carlson and Oppenheimer, this mechanism is as follows. A fast electron or positron, flying near the nucleus of some atom of the medium, with high probability emits a photon of high energy (bremsstrahlung). In turn, a photon of high energy, flying near an atomic nucleus, with high probability “materializes,” i.e., produces an electron–positron pair (the photon itself, of course, disappears in the process). Each particle of such a secondary pair, just like the primary one, emits bremsstrahlung photons of high energy, which in turn form pairs, and so on. The result is an avalanche-like growing beam of electrons, positrons, and photons flying (if their energy is sufficiently large) approximately in the direction of flight of the primary particle. The energy of the primary particle is distributed among the particles of such a shower, the number of which continues to grow until the average energy of the shower particles falls so far that the ionization losses of energy of the charged shower particles begin to predominate over losses by radiation. At this stage, and at this distance from the point of origin of the shower, the number of particles \(N\) in it reaches a maximum and (provided \(E \gg E_{cr}\)) is equal to \(N = \dfrac{0.3\,E/E_{cr}}{\sqrt{\ln E/E_{cr}}}\), where \(E\) is the energy of the primary particle, and \(E_{cr}\) is the critical energy of the substance in which the shower is formed. Thereafter there occurs a gradual absorption of the shower—the multiplication of shower particles gradually ceases, and losses by ionization lower their energy to a limit below which these particles are no longer recorded by measuring instruments.

It is clear that a shower can be produced by photons, but not by electrons or positrons.

The low penetrating power of high-energy photons is due precisely to the high probability of their materialization into a pair. The path length in a given substance over which a fast electron or positron emits, on average, one high-energy photon (the so-called shower unit of length*), is approximately equal to (more precisely, one third less than) the mean path length traveled in the same substance by a high-energy photon before it is converted into a pair. The shower unit of length in lead is equal to \(0.5\ \mathrm{cm}\), and in air to about \(300\ \mathrm{m}\).

The electron-positron-photon showers which have been discussed all along naturally form part of the soft component of cosmic rays, by which they are produced. It is precisely shower formation that accounts for the low penetrating power of the soft component, in contrast to mesons, which do not give bremsstrahlung (and therefore do not form showers and, it became clear, are penetrating). At present one of the main experimental criteria for deciding whether a given charged particle (so fast that its mass cannot be estimated from the ionization of the medium caused by it) is a meson or an electron is the following sign: if this particle, passing through a layer of lead \(2\text{--}3\ \mathrm{cm}\) thick, does not produce a shower in it, then it is a meson or a proton, and not an electron.

The creation of a cascade theory of showers, the results of which agree excellently with experiment, and the discovery of a penetrating cosmic particle—the meson—removed the former doubts about the applicability of Dirac’s relativistic theory to electrons of very high energy.

§ 5. As has already been noted, the predominant part of the soft component of cosmic rays in the lower layers of the atmosphere does not come from above, but is produced in these same layers by the hard component—mesons. There are three principal ways in which the soft component is generated by mesons.

First, a fast meson knocks electrons out of the outer electron shells of the atoms of the medium lying along its path. Most electrons of this origin are slow, and only a small fraction of them are fast. If they have an energy of the order of \(1\ \mathrm{MeV}\) or higher, they are called \(\delta\)-electrons. If the energy of a \(\delta\)-electron exceeds the critical energy for the given medium, then this \(\delta\)-electron produces a shower.

*) More precisely, in one shower unit of length an electron whose energy is much greater than

\[ \frac{137mc^2}{Z^{1/3}}, \]

emits on average one photon whose energy exceeds the \(1/e = 1/2.8\) part of the electron’s energy and, in addition, photons of lower energies.

Secondly, mesons of very high energy (of the order of \(10^{11}\) eV) give appreciable bremsstrahlung, i.e. produce photons of high energy, which in turn produce showers.

In gaseous media, the formation of \(\delta\)-electrons is the principal mechanism for the generation of the soft component. But in the generation of this component in air the predominant importance belongs to a third mechanism—the decay of the meson.

It has been known for quite a long time that cosmic rays are absorbed in the atmosphere considerably more strongly than in an equivalent, by mass, layer of solid or liquid substances. According to the theory developed by Heisenberg and Euler in 1938, this anomaly is explained by the spontaneous decay of mesons, analogous to the radioactive decay of heavy nuclei. Subsequently, the decay of mesons was demonstrated by direct measurements of the mean lifetime of slow mesons (see the article by E. L. Feinberg in the collection Meson), which turned out to be equal to \(\tau_0=2.15\cdot10^{-6}\) sec.; upon decay a meson is transformed into one electron or positron (depending on the sign of the meson’s charge) and one neutrino*). If a meson moves with high velocity, then its lifetime \(\tau\), measured by an observer moving together with it, will have the same duration \(\tau_0\); however, owing to the relativistic effect of the slowing of moving clocks, the lifetime \(\tau\) of the meson, measured by a “stationary” observer, will be equal to

\[ \tau=\frac{\tau_0}{\sqrt{1-v^2/c^2}}=\frac{\tau_0 E}{\mu c^2}, \]

where \(v\) is the velocity, \(E\) the energy, and \(\mu\) the mass of the meson. The faster the meson, the longer it lives.

If the meson is not very slow (so that its velocity is comparable with the velocity of light), then it traverses comparatively thin layers of solid or liquid substances so quickly that it practically has no time to decay in them. On the contrary, the paths of mesons in the atmosphere are measured in kilometers, and the time required to traverse such distances with the velocity of light is large in comparison with \(\tau_0\); therefore a considerable fraction of mesons decay while passing through the earth’s atmosphere. The emergence, during meson decay, of electrons and positrons (so-called decay electrons) is the chief mechanism for the generation of the soft component in the atmosphere.

The anomalous absorption of cosmic rays in the atmosphere is explained, first, by the fact that the decay of the penetrating mesons converts them into a strongly absorbed soft component, and, secondly, by the fact that half of the energy of the decaying meson is transferred to the neutrino and is therefore entirely lost to observation, since neutrinos do not produce any effects accessible to experimental detection.

*) It is not excluded, although it is unlikely, that in the decay of a meson not one but several neutrinos are produced.

Since mesons decay spontaneously, they cannot arrive from cosmic spaces, but must be generated by primary cosmic rays in the upper layers of the Earth’s atmosphere. What, then, do we know about primary cosmic rays? Analysis of data on the latitude geomagnetic effect shows that about 60% of the energy of cosmic rays falling on the surface of the Earth’s atmosphere is due to primary charged particles whose kinetic energy does not exceed \(1.7 \cdot 10^{10}\ \mathrm{eV}\). It is assumed that the remaining 40% of the total energy of cosmic rays is also brought mainly by charged particles of such high energy (\(>1.7 \cdot 10^{10}\ \mathrm{eV}\)) that the latitude effect is not manifested in them. Further, analysis of data on the azimuthal geomagnetic effect (i.e., the difference in intensity of cosmic rays falling from the east and from the west at a given angle to the vertical) shows that cosmic rays reaching the lower layers of the atmosphere are produced mainly by positively charged primary particles.

The most widespread point of view at present is that the overwhelming majority of primary cosmic particles are positively charged protons*). This point of view is based on the experiments of M. Schein and his collaborators, who found an almost complete absence of fast electrons and positrons in the very upper layers of the atmosphere (at an altitude of 25–35 km). Schein’s results are apparently confirmed by recent, as yet unpublished, measurements by S. N. Vernov.

Thus, the most probable scheme for the passage of cosmic rays through the atmosphere is as follows: primary protons with an average energy of the order of \(10^{10}\ \mathrm{eV}\) generate mesons in the upper layers of the atmosphere; these mesons partly penetrate into the lower layers of the atmosphere, constituting the hard component of cosmic rays, and partly decay along the way. The soft component, consisting of electrons and photons, is tertiary and is generated by the secondary component (i.e., by mesons) both in the decay of mesons and through the formation of \(\delta\)-electrons (and to a far lesser extent through bremsstrahlung of mesons).

§ 6. This scheme, in all probability, corresponds in general outline to reality. However, the experimental study of many processes connected with the passage of cosmic rays through matter is still at its very beginning and apparently harbors so many surprises that, it seems to me, a new phase in the development of the theory of cosmic rays is now beginning.

*) The fact that in the upper layers of the atmosphere the azimuthal effect is absent can be explained by the fact that in these layers very many slow mesons are formed, which, first, themselves scatter strongly and, second, in their decay emit electrons more or less isotropically in all directions.

Indeed, the processes in cosmic rays can be divided into three classes: the first includes electromagnetic processes—ionization and excitation of atoms by charged particles, the knocking out by them of δ-electrons and the emission by them of bremsstrahlung photons under the action of the Coulomb fields of atomic nuclei and atomic electrons, the formation by photons of electron–positron pairs, the Compton effect, Rutherford scattering of charged particles on atomic nuclei, etc. The second class includes the spontaneous decay of mesons and, finally, the third class includes processes that may be called meson-nuclear, or simply nuclear, because they are determined by nuclear forces or are closely connected with them. Such nuclear processes include, first of all, the generation of mesons by protons, neutrons, and mesons themselves, as well as the disintegration of atomic nuclei by cosmic rays*).

The modern theory of electromagnetic processes raises no doubts and is well confirmed by experiment. Therefore the properties and behavior of the soft component of cosmic rays (more precisely, of the electron–photon part of this component) are known to us comparatively well. The same applies also to the electromagnetic processes (ionization, formation of δ-electrons, etc.) excited by mesons.

Nevertheless, even within this range of questions a number of uncertainties remains. First, if the spin of the meson is not equal to 0 or 1/2, but to 1, then at very high meson energies (of the order of \(10^{11}\ \mathrm{eV}\)) their bremsstrahlung and the probability of their producing δ-electrons must increase so much that the modern theory cannot be applied to these processes (see the article by V. L. Ginzburg, “Theory of the Meson”). However, the assumption that the meson has spin 1, which at one time was widely accepted, is apparently refuted by experiment.

Second, the theory of broad atmospheric showers—the so-called shower O—whose number rapidly increases with height above sea level, is in a peculiar position. Modern ideas about these showers reduce to the following. These showers are produced by primary particles of ultrahigh energies, of the order of \(10^{14}\)–\(10^{16}\ \mathrm{eV}\), which constitute an insignificant part of the primary radiation. These particles either themselves are electrons or photons, or they produce such particles in the upper layers of the atmosphere. An electron or photon of ultrahigh energy produces in the earth’s atmosphere a powerful shower, at whose maximum the number of shower particles reaches \(10^{4}\)–\(10^{6}\). This shower is an approximately vertical bundle of particles; in the very upper part of the shower its cross section grows, and then begins to decrease inversely proportionally to the density of the air; in the lower layers of the atmosphere the radius of the shower must

*) Processes of mixed character may also be indicated, for example the possible formation of meson pairs by photons.

be of the order of 100 m. Such a geometrical shape of the shower is obtained on the basis of the following considerations. The direction of flight of bremsstrahlung photons and electron–positron pairs of high energy, generated in the shower, deviates very little from the direction of flight of the particles that generate them. Only shower particles of comparatively low energies fly at a considerable angle to the axis of the shower. The range of these particles determines the width of the shower. Since the range of a particle in air is inversely proportional to its density, the width of the shower must vary in the same ratio.

The theory of Auger showers is based on these ideas; in its development an outstanding role belongs to Soviet theoreticians (L. D. Landau, I. Ya. Pomeranchuk, S. Z. Belenky, A. B. Migdal). Until very recently the agreement of this theory with experiment seemed so good that this agreement was regarded as direct confirmation of the applicability of the modern theory of electromagnetic processes up to the grandiose energies of \(10^{14}\)—\(10^{16}\) eV. Recently, however, it apparently has become clear that in the formation of Auger showers an essential role is played not only by the electromagnetic processes taken into account by the cascade theory of showers, but also by meson–nuclear processes.

This is indicated, first of all, by the connection with Auger showers of the so-called broad penetrating showers. Penetrating showers, i.e. showers of penetrating particles, in all probability mesons, differ sharply from ordinary electron–positron showers. They may be divided into two classes—narrow penetrating showers, whose radius is approximately \(\frac{1}{2}\) m and which will be discussed below, and broad penetrating showers, whose radius is not known but in any case is not less than several meters. The experimentally established correlation of these broad penetrating showers with Auger showers is apparently explained by the fact that photons or electrons of high energies can generate mesons—a process not taken into account by the modern theory of Auger showers.

To a much greater degree the incorrectness of this theory is revealed by the recent measurements of Yu. Zatsepin and others in the Pamirs. These measurements established that the radius of Auger showers at an altitude of 3860 m above sea level in any case substantially exceeds 600 m, which cannot in any way be reconciled with the theoretical value of the radius of 100 m. The reasons for this discrepancy between theory and experiment are unclear; it is possible that they are again connected with the generation of mesons, not taken into account by the theory, by photons and electrons of high energy.

Although, therefore, the properties and behavior of photons and electrons of ultrahigh energies remain unclear in a number of respects, nevertheless, as has already been said, processes of electromagnetic character in cosmic radiation are known to us comparatively well.

As for meson decay, the lifetime of mesons with a mass of the order of \(200\,m\), which undoubtedly predominate in the lower layers of the atmosphere, is known. Hypothetically, but very plausibly, these mesons decay into one electron or positron and one neutrino. This is all that is required to know about the decay. However, it is probable that in the upper layers of the atmosphere there exist mesons of another mass, about whose decay we in fact know nothing.

Our information is scarcest concerning the third class of processes—meson-nuclear processes. There is as yet no more or less reliable theory of these processes, and their experimental study is only at its very beginning.

Let us begin with the generation of mesons by primary particles. The mean energy of mesons at sea level is approximately \(2\cdot 10^{9}\,\mathrm{eV}\); in passing through the atmosphere each meson loses approximately the same amount of energy (\(\sim 2\cdot 10^{9}\,\mathrm{eV}\)) to ionization. Consequently, even if—as is commonly assumed (though for not very convincing reasons)—the predominant part of the mesons originates in the very uppermost layer of the atmosphere, whose mass is about \(1/10\) of the entire mass of the atmosphere, then the mean initial energy of the mesons reaching sea level is, at their place of origin, approximately \(4\cdot 10^{9}\,\mathrm{eV}\). Meanwhile, an analysis of the latitudinal geomagnetic effect at sea level shows that the predominant part of these mesons is generated by primary particles whose energy exceeds \(1.7\cdot 10^{10}\,\mathrm{eV}\). Thus, the mean energy of the mesons is substantially smaller than the energy of the primary particles that generate them. If one takes into account that in the upper layers of the atmosphere, in all probability, the number of slow mesons that do not reach sea level but decay en route increases sharply, it turns out that the energy of the primary particle (let us suppose that it is a proton) is distributed on the average, say, among ten secondary mesons.

A column of the earth’s atmosphere with a cross section of \(1\,\mathrm{cm}^{2}\) contains \(4.3\cdot 10^{25}\) atoms of N and O. The effective cross section for the interaction of fast protons with atomic nuclei cannot exceed the area of the geometrical cross section of these nuclei, which in the case of N and O is approximately \(4.2\cdot 10^{-25}\,\mathrm{cm}^{2}\). Therefore, over a distance equal to \(1/10\) of the earth’s atmosphere, a fast proton cannot undergo more than
\[ \frac{1}{10}\times 4.3\cdot 10^{25}\times 4.2\cdot 10^{-25}\sim 2 \]
collisions. If the proton actually generates about ten mesons over this distance, then in each act of collision with air atoms it must create, on the average, about five mesons. Such generation of many particles in a single act does not occur in electromagnetic processes.

Although, probably, not all the assumptions made above are correct,* nevertheless, in any case, from the estimates given it is evident that the probability

* It is possible that meson generation occurs intensively not in \(1/10\) of the atmosphere, but over a greater distance. It is possible that primary protons

generation of mesons in the collision of the primary cosmic particle with the atoms of the air must be very large (of the order of the geometrical cross section of these atoms).

Even if it is true that the predominant fraction of mesons is generated in the very uppermost layers of the atmosphere, nevertheless, as has become clear in the very recent years, there is no doubt that in the intermediate layers of the atmosphere there occur intensively processes of a “nuclear” character according to our classification, which are almost completely absent at sea level. The most important processes of this kind are, on the one hand, the generation of meson showers and, on the other, the disintegration of atomic nuclei.

Meson showers are observed at an altitude of 3–4 km above sea level directly in a Wilson chamber. In all probability, the so-called narrow atmospheric (i.e., originating in the atmosphere) showers, observed in large numbers at the same altitudes with the aid of Geiger counters, also consist mainly of mesons. These showers, in the discovery and study of which an outstanding role belongs to Soviet scientists (the high-altitude cosmic-ray stations on Alagez—directors A. I. Alikhanov and A. I. Alikhanyan, and in the Pamirs—directors D. V. Skobeltsyn and V. I. Veksler), differ sharply from ordinary atmospheric showers of the soft component (Auger showers) in that the radius of their horizontal cross section is approximately \(1/2\) m, whereas the radius of Auger showers is not less than several hundred meters. Theoretical calculations show that electron-photon showers cannot possibly be so narrow; the great penetrating power of the particles in narrow showers indicates that they consist of mesons; finally, as yet unpublished direct measurements of the mass of the particles making up narrow showers, with the aid of the large magnet of the Alagez high-altitude cosmic-ray station, apparently prove definitively that the mass of these particles is approximately \(200\,m\).

The narrowness of the showers can be explained only by the fact that they originate at a comparatively small height above the measuring apparatus, while the relatively large number of them shows that the processes of meson generation at an altitude of the order of 4 km occur incomparably more intensively than had been supposed only a few years ago*).

At the same altitudes of 3–4 km the number of nuclear disintegrations caused by cosmic rays also increases sharply. One of

when passing through the atomic nucleus, knock out of it several protons and neutrons, which subsequently generate mesons. In general, our information about the processes occurring in the upper layers of the atmosphere is so scanty that they do not exclude a whole range of conceivable possibilities.

*) In contrast to the broad penetrating showers mentioned above, narrow showers do not correlate with Auger showers.

One of the most convenient methods of observing these disintegrations is the study of the so-called “stars,” i.e. star-shaped traces (tracks) left in the photosensitive layer of a photographic plate by protons and \(\alpha\)-particles flying apart from the disintegrated nuclei of the atoms of this layer. A certain part of these disintegrations is undoubtedly produced by mesons. This is confirmed, in particular, by the as yet unpublished results of measurements of particle tracks in stars made by P. I. Lukirskii and Perfil’ev. These measurements make it possible to calculate the total energy and total momentum of the protons and \(\alpha\)-particles in a star; estimating, in addition, the energy and momentum of the neutrons emitted in the disintegration of the nucleus and leaving no tracks in the photographic plate, one can calculate the energy and mass of the particle causing the disintegration. According to P. I. Lukirskii, this mass, determined from measurements of stars of a certain definite type, lies within the limits between \(140\,m\) and \(200\,m\).

At the same time there is no doubt that a considerable, and possibly predominant, part of nuclear disintegrations is produced by comparatively slow protons and especially by neutrons (with energies of several hundred million electron-volts). The number of such protons and neutrons increases rapidly with altitude above sea level; their role in cosmic rays and the character and regularity of the processes produced by them in passing through matter have as yet been studied quite insufficiently.

§ 7. In our brief survey of the present state of the theory of cosmic rays we have by no means sought exhaustive completeness. We have not touched at all not only on questions that are inessential for our main theme,* but also on such important, though as yet little-studied, questions as, for example, the composition and properties of cosmic radiation at great depths below the surface of the earth, the elucidation of which should provide very substantial information about the properties of high-energy mesons and, perhaps, about neutral mesons. It seems to us, however, that our survey can give a correct idea of the principal problems now facing the physics of cosmic rays. Let us draw some conclusions.

At the present time the composition and properties of cosmic rays near sea level have been comparatively well studied and theoretically explained. The processes occurring at these altitudes belong, in our classification, mainly to electromagnetic processes and to the decay of mesons of mass \(200\,m\). Therefore the study of cosmic rays near sea level gives little information about specifically meson-nuclear processes (meson generation, disintegration of nuclei by mesons and nucleons, etc.). Thus, substantial progress in our knowledge of nuclear processes can be expected

* For example, the question of the origin of cosmic rays, about which we know essentially only that a number of the simplest assumptions concerning the origin of cosmic rays do not withstand criticism.

only on the further development and expansion of experimental work on cosmic rays at medium and high altitudes.

At the same time it must be noted that, as work in recent years has shown, it can by no means be considered that the processes in cosmic rays at medium altitudes (beginning at roughly 3 km) are, at least qualitatively, no different from processes at sea level. On the contrary, meson–nuclear processes (which include, for example, according to our classification, all processes of meson generation) play an essential role not only in the upper layers of the atmosphere, but also at medium altitudes. At these same altitudes, according to as yet unpublished data of A. I. Alikhanian, a heavy type of meson with a mass of the order of \(500—1000\,m\) also begins to play a noticeable role. The properties of these mesons are still completely unknown to us.

At the same time it must be noted that as yet there are no convincing experimental data either in favor of or against the assumption of the existence in cosmic rays of neutral mesons (neutrettos). This question is extremely important, since weighty considerations based on present-day ideas about the nature of nuclear forces speak in favor of this assumption.

The rapid development of high-altitude cosmic-ray investigations interrupted by the war, and in particular the quite well-founded hopes of carrying out the generation of mesons under laboratory conditions, mentioned at the beginning of this article, allow one to expect that in the near future an experimental basis will be created for constructing a rational theory of mesons.