MESONS*)

C. F. Powell

1. INTRODUCTION

The reviews devoted to mesons that appeared earlier in the present series were written by Heitler[^1] and by T. H. Johnson[^2]. The reviews contained the basic data corresponding to our knowledge of these particles up to the end of 1939. Since then, especially during the last four years, this field of knowledge has been developing rapidly. Although some details are still not known to us, at the present time the basic properties—at least of the most widespread types of mesons—may be regarded as established. Their connection with cosmic rays is now also understood.

In order to give an idea of the discoveries of the last ten years, I shall begin with a brief historical survey of the principal lines along which our knowledge has developed; then I shall consider in more detail the basic properties of $\pi$- and $\mu$-mesons, as well as the evidence for the existence of mesons of other types, and, in conclusion, I shall outline the modern point of view on the principal processes connected with the formation of mesons as a result of the passage of cosmic rays through the atmosphere.

Of great importance in broadening our knowledge of mesons was the development of a new method for recording charged particles by means of photographic emulsion.**) In addition to the well-known properties of this method—such as simplicity and convenience of use, and the “integrating” property of the emulsion due to its continuous sensitivity and the possibility of direct and detailed study of the nuclear processes occurring in the emulsion—the plates have the further advantage that they make it possible to study in

*) C. F. Powell, Mesons, Reports Progress in Physics, vol. XIII, p. 350, 1950; translated by N. G. Birger and I. L. Rozental.
In view of the fact that Powell’s article “Mesons” does not take into account the work of Soviet scientists, which is of great importance for the development of the field under consideration, the editors considered it necessary to supplement it with an article by N. G. Birger and I. L. Rozental, “Electron–Nuclear Showers and the Nuclear-Cascade Process,” placed below. In order to facilitate use, the numbering of figures and literature references in both articles has been made continuous. (Ed.)

**) This method was first proposed by the Soviet physicists L. Mysovskii and P. Chizhov[^118]. (Translator’s note.)

over time, various types of transformations. In particular, particles with a very short lifetime, such as, for example, $\pi$-mesons, which usually decay in air “in flight,” are stopped in dense substances in a time thousands of times shorter than the time of motion before stopping in a gas. Thus it proves possible to study the spontaneous decay of particles or their interaction with nuclei upon stopping in an emulsion, i.e. phenomena which are very difficult or altogether impossible to observe by other methods.

A considerable part of this survey naturally consists of a discussion of results obtained by the new method, which has played such an important role. An interesting feature is that $\pi$-mesons were discovered immediately after the development of the experimental methods necessary for their observation.

2. HISTORICAL SURVEY

2 (1). “Heavy quanta” of Yukawa*)

For the first time the hypothesis of the existence of heavy particles with a mass intermediate between the masses of the proton and the electron was put forward in 1935 by Yukawa$^{3}$. Already several years before this it had been known that the forces between nucleons in the nucleus, i.e. protons and neutrons, are not of electromagnetic origin. The observed degree of stability of nuclei can be explained only if one assumes that special forces of a new type act between nucleons—nuclear forces.

Furthermore, as a result of precise measurements of nuclear masses it was shown that the energy required to tear a nucleon out of a nucleus—the binding energy of the nucleon—changes little in passing from the light to the heavy elements of the periodic table. It follows from this that nuclear forces are short-range and vary with the distance between two nucleons more rapidly than forces inversely proportional to the square of the distance. Proceeding from these facts and relying on a formal analogy described in detail in earlier surveys, Yukawa came to the conclusion that there must exist “quanta” of the nuclear field, analogous to the photons of the electromagnetic field. These “quanta” must have a finite rest mass $\cong 150\,m_e$, where $m_e$ is the rest mass of the electron, and decay with a lifetime $\sim 10^{-7}$ sec., emitting an electron. Just as the electromagnetic field of an electron may be regarded in the quantum theory of radiation$^{4}$ as the emission of photons, and the forces between two electrons as the mutual emission and absorption of photons, so too the forces of nuclear binding between nucleons are connected, according to

) See also the survey on meson theory by V. L. Ginzburg. Collection Meson, Gostekhizdat, 1948. (Translator’s note.*)

theory of Yukawa, with virtual exchange between neutrons and protons in the nucleus by charged quanta*).

The hypothetical “heavy quanta” in this respect differ essentially from photons. First, a finite value of the rest mass is a necessary consequence of the short-range character of nuclear forces. Secondly, since, as is supposed, exchange of “quanta” between neutrons and protons in the nucleus is accompanied by exchange of charge (a neutron becomes a proton and conversely), the supposition was put forward that, at least in some cases, the “quanta” possess a positive or negative electric charge.

Thirdly, to explain the $\beta$-activity of radioactive substances, the supposition of the instability of the particles was introduced. Processes of nuclear disintegration were ascribed to the spontaneous decay of charged “quanta” into an electron and a neutrino.

To explain the existence of a force between identical nucleons (between two neutrons or two protons), in addition to charged quanta it was necessary to postulate the existence of neutral particles of an analogous type$^{5}$. It is known that the magnitude of these forces is of the same order as between a proton and a neutron, and if they are of the same origin, then among the particles participating in the exchange there must also be neutral ones. Therefore, in what follows it will be convenient to denote the hypothetical quanta, both charged and neutral, as Yukawa particles.

One cannot expect the effective emission of these particles by unexcited nuclei, since energetically such a process is impossible. However, one may think that in nuclear collisions of particles with high energy (for example, in cosmic rays) such a restriction does not apply.

2 (2). Discovery of $\mu$-Mesons

A remarkable confirmation of the correctness of Yukawa’s calculations, it seemed, was obtained in the experiments of Anderson and Neddermeyer$^{6}$ in 1936–1938, as well as by other investigators who studied the nature of particles in cosmic radiation. As is known, cosmic radiation can be phenomenologically divided into two components with different absorption coefficients in matter. The “soft” component, rapidly absorbed in lead, causes the well-known phenomena of “cascade showers,” usually studied by means of a Wilson chamber or counters$^{7**}$. As is known, this component consists of photons and electrons.

) The idea of explaining nuclear forces by the exchange of charged and neutral particles was first put forward in 1934 by D. Ivanenko and I. Tamm$^{119}$. (Translator’s note.*)

) As is known, cascade showers were discovered in 1929 by D. V. Skobeltsyn$^{120}$ (Translator’s note.)

Anderson\(^{6}\) showed that among the particles of the “hard,” or penetrating, component there are particles with a mass of about \(200m_e\), capable, unlike electrons, of passing through many centimeters of lead without losing a significant fraction of their energy in the well-known process of bremsstrahlung. These particles are now customarily called \(\mu\)-mesons\(^{9}\); later measurements of their mass gave the value \((215 \pm 5)m_e\).

The assumption that \(\mu\)-mesons can be identified with Yukawa’s particles was confirmed by experiments which established that these particles decay, having a lifetime \(\sim 1.5 \cdot 10^{-6}\) sec.—a value exceeding that predicted by Yukawa by about a factor of ten. It also proved possible to modify certain original features of the theory for calculating the magnetic moments of protons and neutrons and certain properties of the energy states of light nuclei, for example the ground and first excited states of the deuteron. Such remarkable success made it possible to hope that the basic features of Yukawa’s theory were correct, that \(\mu\)-mesons were in fact identical with Yukawa’s particles, and that, consequently, it would be possible to provide a theoretical foundation for the processes of nuclear collisions and the characteristics of atomic nuclei. Such a hope was also expressed in earlier reviews. However, serious theoretical difficulties immediately began to arise.

2 (3). Decay and capture of \(\mu\)-mesons

The first determinations of the lifetime of \(\mu\)-mesons were based on the fact that the attenuation of the intensity of the flux of these particles in the atmosphere depends not only on the mass \((\mathrm{g}/\mathrm{cm}^2)\) of matter traversed, but also on the path length in it. For one and the same amount (by mass) of air traversed, the decrease in intensity is the greater, the lower the density of the air. Such an effect can be explained if one assumes that the removal of mesons from the flux due to collisions with atoms is accompanied by spontaneous decay of the particles, the role of the latter process being the greater, the longer the flight time\(^{10}\).

Decisive confirmation that \(\mu\)-mesons do indeed undergo spontaneous decay with the emission of a charged particle of small rest mass, presumably an electron, was obtained in the experiments of Williams and Roberts\(^{11}\). With the aid of a Wilson chamber placed in a magnetic field, they obtained two photographs of penetrating particles that had stopped in the gas of the chamber after passing through a lead plate. From the ends of the tracks of these particles there emerged fast particles with a specific ionization close to minimal for particles with elementary charge, and with a momentum, determined from the curvature of the track, equal to \(70 \pm 35 \dfrac{Mev}{c}\).

The observed specific ionization of the decay particles shows that they were emitted with a velocity close to the speed of light \(c\). Consequently, their kinetic energy \(E\) is approximately equal to \(pc\) (\(p\) is the momentum of the particle), i.e. the particle energy is \(\simeq 50\) MeV. The result indicated that, in the decay, owing to the law of conservation of momentum, a neutral particle with a small rest mass— a neutrino—must also be emitted; since an energy \(\simeq 100\) MeV is divided equally between the two decay products, the energy of the decay electrons should have been constant and approximately equal to 50 MeV. We shall see in the following paragraphs that this conclusion proved to be incorrect.

A more direct and precise determination of the lifetime of \(\mu\)-mesons was carried out by Rasetti\(^{12}\), and then by Rossi\(^{13}\) and others\(^{14}\), by the method of delayed coincidences. The principle of the method is as follows (Fig. 1): with the aid of suitably arranged groups of counters, \(\mu\)-mesons of cosmic rays are selected which have passed through a thick layer of lead and have stopped in the following layer of absorber. The time between the moment of stopping of the \(\mu\)-meson and the discharge in a special group of counters registering charged particles emitted in the decay is measured. The distribution of the observed delay times proved to be close to the exponential law characteristic of radioactive decay. The mean lifetime obtained by this method in later work proved to be \(2.15 \cdot 10^{-6}\) sec.

Fig. 1. Diagram of the apparatus for determining the lifetime of \(\mu^+\)- and \(\mu^-\)-mesons. Both halves of the iron block are magnetized so that the magnetic field strength in them is directed perpendicular to the plane of the drawing, but in the two halves it has opposite directions. Such a device serves to concentrate particles of one sign. Particles are selected which produce discharges in the counters \(C_A\), \(C_B\), \(C_C\), but not in the counters \(A\). The time elapsed from the stopping of these particles in the block to the discharge of the counters \(D\) is measured. The distribution of these times makes it possible to determine the half-life period (see, for example, Figs. 17 and 18). By changing the direction of the magnetic field, one can select particles of the other sign (after Rossi).

Thus, the results of most experiments served as confirmation of Yukawa’s hypothesis. However, it was difficult to understand why, in experiments with a Wilson chamber, cases of interaction of \(\mu\)-mesons with the nuclei of matter were rarely observed. Further difficulties appeared when experiments were undertaken to study the properties of positive and negative \(\mu\)-mesons.

Tomanaga and Araki \(^{15*)}\) proposed that when a positive meson is stopped in matter, the meson remains free until the moment of decay because of the existence of Coulomb repulsive forces between like charges. Negative mesons, however, reach the nucleus. It may be expected that if the spin of \(\mu\)-mesons is equal to the spin of electrons, then the mesons will pass into the state of lowest energy. This transition is accompanied by the emission of an Auger electron.

Since the mass of the meson is much greater than the mass of the electron, mesons in the ground state are two hundred times closer to the nucleus than an electron in the corresponding “\(K\)-orbit”; in this state the particles must spend a considerable time near the nucleus. The results obtained by Rasetti and Rossi agree with this picture. In their setups only about half of the stopped mesons decayed.

To confirm the existence of a nuclear interaction of \(\mu\)-mesons before they have time to decay when stopped in a dense substance, Conversi and others \(^{16}\) carried out special experiments by the method of delayed coincidences. Positive and negative mesons were separated in these experiments by the method of magnetic deflection. As expected, positive mesons, stopping in iron, decayed with the same lifetime as mesons not separated according to the sign of charge, whereas the negative mesons disappeared without giving decay electrons. The results obtained did not agree with the data of Auger and others, according to which almost all negative mesons stopped in aluminum undergo decay. Although these experiments were considered erroneous, the experiments of Conversi and others \(^{16}\) were nevertheless also carried out for the case in which \(\mu\)-mesons are stopped in a substance with a small atomic number. Graphite was chosen as such a substance. In this case a surprising result was obtained, namely: it was shown that at least a large part of the \(\mu\)-mesons decay with the emission of electrons.

The time required for a \(\mu\)-meson, slowed down to “thermal” velocity, to pass into the ground state was estimated. Although it evidently depends on the substance in which the meson moves, it is usually assumed that this time is less than \(10^{-12}\) sec. \(^{17}\). Therefore it was expected that particles stopped in a dense substance reach the nucleus in a time small compared with their lifetime. If, moreover, \(\mu\)-mesons are identical with “heavy quanta” of the nuclear field, then they must interact with the nucleus in such a way that for them the probability of spontaneous decay should be very small. True, there were no data for solving the ques-

*) An estimate of the probability of meson capture by a nucleus was also made by A. Migdal and I. Pomeranchuk \(^{12}\). (Transl. note.)

questions about the results of such an interaction. It could be assumed that the disappearance of a particle and the associated release of energy corresponding to its rest mass leads either to the emission of photons, or to the splitting of the nucleus, or to some other as yet unknown processes.

The results of the experiments of Conversi and others proved incompatible with the assumption that $\mu$-mesons are identical with Yukawa’s particles. It was shown that in carbon $\mu$-mesons can remain in the $K$-orbit without interacting with the nucleus for a time of the order of $2\cdot 10^{-6}$ sec. Hence it was concluded that the interaction of $\mu$-mesons with the nucleus is several orders of magnitude weaker than the interaction expected for the “heavy quanta” of the nuclear field. Attempts were made$^{18}$ to explain the difficulties that had arisen by the assumption that the time spent by the $\mu$-meson in stopping and in reaching the $K$-orbit is greater than had been obtained from the initial estimates. Nevertheless, although doubts were expressed about the accuracy of the values obtained, it remained evident that they were several orders of magnitude smaller than the lifetime of the particles. Thus this fundamental difficulty could not be eliminated.

Even before the full significance of the data obtained became clear, Sakata and Inoue$^{19}$ expressed the view that the data obtained in cosmic rays indicate the existence of mesons of two types; and Møller,$^{20}$ on the basis of general theoretical considerations, came to the conclusion that there exist several types of particles with intermediate masses genetically related to one another. Somewhat later, Marshak and Bethe,$^{21}$ starting from the contradiction between the large value of the cross section for the formation of mesons in nucleon–nucleon interactions and the small interaction between penetrating particles and nuclei, proposed that, as a result of interaction with the nuclei of air in the atmosphere, heavy mesons are formed which spontaneously decay, with a lifetime $\cong 10^{-8}$ sec, into mesons constituting the penetrating component.

2 (4). Discovery of $\pi$-mesons

The creation, several years ago, of more sensitive photographic plates made it possible to study mesons by this new method. Thus Perkins$^{22}$ and Occhialini and Powell$^{33}$ showed that in plates exposed to cosmic rays at high mountains it is possible to detect stopped mesons. The mass of these mesons could be determined by the method of grain counting and by observing the deviations along the track caused by Coulomb scattering. It turned out that the mass of the mesons is $\cong 200$–$300\,m_e$. It therefore seemed established that at least some of them are identical with the $\mu$-mesons of the penetrating component of cosmic rays.

investigation. The new plates, although they were better than the old ones, were still not sensitive enough to register electrons moving with relativistic velocity, and consequently it was not possible to observe the fast decay particles formed at the end of the mesons’ range. In 10% of the cases it was found that mesons stopped in the emulsion cause nuclear disintegrations with the emission of slow protons, $\alpha$-particles, etc. (see microphotographs II and III at the end of the issue). At that time it was believed that such disintegrations were due to the capture of $\mu^{-}$-mesons by nuclei of silver or bromine—processes which in heavier substances lead to the disappearance of negative $\mu$-mesons before they have time to decay into an electron and a neutrino. Later, however, it was shown that the mesons producing nuclear disintegrations are not $\mu$-mesons. Soon after the discovery of nuclear disintegrations caused by charged mesons in Bristol, it was found that about 10% of the stopped mesons emit secondary mesons. It was then established that the secondary particles have an approximately constant range. It was natural, therefore, to suppose that the secondary particles are emitted with a constant velocity, and that the small scatter in their ranges is connected with fluctuations of ionization losses; this indicates that the observed process corresponds to a spontaneous decay of particles. Thus there must exist two types of mesons. The kinetic energy of the secondary particles is obtained at the expense of part of the energy released in the disappearance of the rest mass of the primary, heavier meson. The validity of this hypothesis was indeed subsequently proved, and it was also shown that the secondary mesons are identical with the $\mu$-mesons of the penetrating component of cosmic rays. The heavier particles were called $\pi$-mesons, and the spontaneous transition, by analogy with $\beta$-decay, received the name $\mu$-decay.

In addition to individual meson tracks, nuclear disintegrations in which slow mesons were emitted were also recorded on plates exposed to cosmic rays. A considerable fraction of such mesons produce disintegration at the end of their range. It was therefore concluded that these are negative partners of $\pi$-mesons, possessing positive charge and therefore incapable, at low velocities, of interacting with nuclei. It was further assumed that negative and positive $\pi$-mesons are the primary product of high-energy nuclear interactions occurring in the atmosphere. Having a short lifetime, $\pi$-mesons then decay in flight with the formation of negative and positive $\mu$-mesons of the penetrating component of cosmic radiation.^9 Further experiments showed that this view of the formation of particles and of their role in cosmic radiation is correct. At the same time, to an approximately

the same conclusions, but proceeding from other considerations, were reached by Marshak and Bethe.

In the three years following the discovery of the $\pi$-mesons, great progress was made in the study of the properties of these particles. The second section of the review is devoted to this question. The observations were facilitated by the discovery$^{23}$ of the artificial production of $\pi$-mesons in collisions of fast $\alpha$-particles and protons with matter. This made it possible to carry out experiments in the laboratory, under controlled conditions.

The new data also serve to confirm earlier reports from a number of laboratories on the existence of particles with mass of about $1000m_e$, which we shall call $\tau$-mesons. The question of the existence of these particles is of serious significance for the development of meson theory and the theory of nuclear forces, and at present the study of their nature and properties is one of the fundamental problems of nuclear physics.

2 (5). Terminology Used in the Review

In connection with the difficulties of determining the mass and charge of mesons observed in emulsion in the first experiments, a phenomenological classification of them was proposed according to the secondary processes occurring at the end of the range.

A $\pi$-meson was the name given to a particle emitting, at the end of its range, a secondary meson with a range of about $600\mu$. Later experiments confirmed the initial assumption that these were positive particles, and we shall call them, accordingly, $\pi^+$- and $\mu^+$-mesons. Mesons which, upon stopping in the emulsion, produce registered nuclear disintegrations were denoted as $\sigma$-mesons. It is now known that these are entirely, or almost entirely, $\pi^-$-mesons captured by nuclei. A nuclear disintegration with tracks of charged particles emitted from a single center we shall usually call a “star”; the individual tracks making up the star, “rays.”

The majority of mesons observed in the most sensitive of the plates used earlier and not giving visible products of decay were denoted as $\rho$-mesons. It is now known that in electron-sensitive plates,$^{36}$ which register particles with elementary charge moving with relativistic velocity, 65% of the $\rho$-mesons decay with the emission of a fast electron. This part of the $\rho$-mesons consists of $\mu^+$-mesons formed in the decay of $\pi^+$-mesons outside the emulsion, and of $\mu^-$-mesons (formed in the decay of $\pi^-$-mesons in flight) captured by nuclei of the light elements entering into the composition of the emulsion (carbon, oxygen, and nitrogen). It is also possible that a small fraction of the $\rho$-mesons is due to $\pi^+$-mesons that have undergone direct $\beta$-decay.

Among the 35% of \(\rho\)-mesons not associated with electron tracks, the majority are \(\mu^-\)-mesons captured by silver and bromine atoms. These particles interact with the nucleus before they have time to undergo decay, but as a result of the nuclear transformation no charged particles are emitted. In addition, a small fraction of the \(\rho\)-mesons is due to \(\pi^-\)-mesons captured by the nucleus without the formation of a visible disintegration. This may occur if, as a result of the nuclear transformation, only neutral particles are produced, as, for example, in the case when a \(\pi^-\)-meson interacts with hydrogen.

In describing the properties of the various types of mesons, wherever possible we shall use the designations: \(\pi^+\)- and \(\pi^-\)-mesons, or particles; \(\mu^+\)- and \(\mu^-\)-mesons, or particles; we shall call \(\rho\)-mesons and \(\sigma\)-mesons particles whose nature has not been precisely established.

3. MASS AND CHARACTER OF THE DECAY OF \(\pi\)-MESONS

3 (1). Decay of \(\pi^+\)-mesons

A positive \(\pi\)-meson coming to rest in a dense substance decays spontaneously with the emission of a lighter \(\mu\)-meson (see microphotograph 1). Figure 2 gives the distribution of the ranges of 90 \(\mu\)-mesons formed in the decay of \(\pi^+\)-mesons that had come to rest in Ilford C2 photographic emulsion. The mean range is \(612\,\mu\).

Fig. 2. Distribution of range values in Ilford C2 emulsion for 90 \(\mu^+\)-particles formed in the decay of \(\pi^+\)-particles that had stopped in the emulsion. The observed distribution agrees with that expected for particles of constant velocity because of fluctuations in range, and proves that \(\pi^+\)-particles usually have a very small velocity at the moment of decay. The mean value of the range is \(612\,\mu\); the corresponding value of the kinetic energy is

\[ E_\mu = 4.15\ \text{MeV}. \]

As was noted above, the observed distribution agrees with the assumption that the velocities of the emitted \(\mu\)-mesons are contained within a narrow interval of values and that, consequently, upon emission of the \(\mu\)-meson the law of conservation of momentum will be ensured by the emission of one neutral particle. The question arises as to the nature of this neutral particle. The following possibilities exist: either it is a photon, or a neutrino, or a neutral particle with a large rest mass, i.e., a “neutretto.”

The observed value of the mean range of the \(\mu\)-meson in the emulsion makes it possible to determine the momentum and energy of the particle, if its mass is known. A charged particle, passing through matter, loses the same ...

energy as a result of interactions of various types with atoms lying near its trajectory: a) due to bremsstrahlung, i.e., the formation of photons in inelastic collisions with electrons, b) due to inelastic collisions with nuclei, in which the latter either split or pass into an excited state, c) due to ionization losses caused by elastic collisions with electrons, and d) in the formation of electron pairs in the field of the nucleus. In the region of comparatively small particle velocities, the energy losses due to ionization are predominant, while the energy losses in other processes may be neglected.

The magnitude of the energy loss due to ionization per unit length of track depends on the charge of the particle \(Ze\) and its velocity \(v\), but does not depend on its mass. For particles with elementary charge we may therefore write

\[ \frac{dE}{dR}=f(v). \tag{1} \]

Hence the ranges \(R_{M,v}\) and \(R_{m,v}\) of two particles, each of which has velocity \(v\) and, respectively, masses \(M\) and \(m\), are proportional to their masses, i.e.,

\[ \frac{R_{M,v}}{R_{m,v}}=\frac{M}{m}. \tag{2} \]

Fig. 3. Dependence between \(\ln R\) (range in microns) and \(\ln E\) (energy in MeV) for protons in Ilford C2 emulsion (Lattes, Fowler, Cuer, Barkas, Bishop, Bradner \(^{32}\)). The straight line corresponds to the equality

\[ E(\text{MeV})=0.251 [R(\mu)]^{0.591}. \]

Suppose that the dependence of the mean range of a proton on the value of its initial energy is known. From the well-known Bragg curve for \(\alpha\)-particles it follows that the specific ionization of a particle increases rapidly with decreasing velocity and, consequently, the dependence between range and energy is not linear. For protons it was found that this dependence can, with a high degree of accuracy, be represented by the equation

\[ E=kR^n, \tag{3} \]

where \(k\) and \(n\) are constants which must be determined for the types of emulsion used (Fig. 3).

From equality (2) it follows that for a particle whose mass is equal to \(\mathfrak{M}\) proton masses, the relation between energy and range can be written in the following form:

\[ E=k\mathfrak{M}^{1-n}R^n. \tag{4} \]

The range–energy relation for particles with an assumed mass \(m\) can be calculated from the corresponding curve for the proton, and, consequently, the energy and momentum of the \(\mu\)-meson can be determined for the assumed value of its mass \(m_\mu\). Taking \(m_\mu\) to be \(215\,m_e\) (where \(m_e\) is the electron mass), we find that the energy of the emitted \(\mu\)-mesons is \(4.2\) MeV.

Let \(m_\pi\) be the mass of the \(\pi\)-particle, \(E_\mu\) and \(p_\mu\) the kinetic energy and momentum of the \(\mu\)-meson formed in the decay, and \(E_\nu\), \(p_\nu\), and \(m_\nu\) the corresponding values for the neutral particle ensuring fulfillment of the law of conservation of momentum. Then from the conservation laws it follows that

\[ m_\pi c^2 = m_\mu c^2 + m_\nu c^2 + E_\mu + E_\nu, \tag{5} \]

\[ p_\mu = p_\nu . \tag{6} \]

For assumed values of \(m_\nu\), \(p_\nu\), one can calculate \(E_\nu\), and then, from equation (5), \(m_\pi\). Thus it can be shown that if \(m_\nu = 0\), then

\[ \frac{m_\pi}{m_\nu} = 1.32. \]

The ratio of the masses of the two types of mesons will be equal to this value if the neutral particle is a photon or a neutrino. On the other hand, if the mass of the neutral particle is equal to \(200\,m_e\), then the value

\[ \frac{m_\pi}{m_\nu} \]

should be equal to \(2.1\).

Valuable information about the neutral particle can thus be obtained from an accurate determination of the masses of the \(\pi\)- and \(\mu\)-mesons.

3 (2). Mass of the \(\pi\)-Meson

The problem of determining the mass of \(\pi\)- and \(\mu\)-mesons is connected with the difficulty that here knowledge of a single parameter is insufficient—for example, the curvature of the track of a particle in a magnetic field of known strength—since any one of the parameters depends both on the ratio of the charge of the particle to its mass, \(\frac{e}{\mu}\), and on its velocity \(v\). Therefore, as in the classical experiments with the electron, two independent measurements are necessary, which determine both \(\frac{e}{\mu}\) and \(v\). The value of \(\frac{e}{\mu}\) determines the mass \(\mu\), if one assumes that the charge of the particle is equal to the charge of the electron—an assumption which in most cases is correct and the grounds for which are given in Section 4 (1). To determine \(\frac{e}{\mu}\) and \(v\), a number of methods have been developed; the most important of them may be divided into five classes.

Method A. Residual range and grain density. The first method used to determine the mass of \(\pi\)-mesons\(^{9}\) was based on observations of: a) the grain density in the tracks of individual particles in the emulsion of photographic plates, and b) the residual range of these same particles. The grain density in a track (i.e., the number of developed grains per unit length) is proportional to the energy loss of the particle. This quantity depends essentially only on the velocity and charge of the particle. Therefore, for particles with electronic charge the observed grain density determines the value of the velocity.

The simplest way of applying this method is to measure the mean velocity from the observed grain density in a limited region of the track and to compare this result with the residual range. Equality (4) for particles moving with nonrelativistic velocity may be written in the following form:

\[ E = k\mathfrak{M}^{1-n} R^n = C\mathfrak{M}v^2, \tag{7} \]

whence it follows that

\[ \mathfrak{M} = k_1 v^{-\frac{2}{n}}. \tag{8} \]

The determination of the required dependence between velocity and grain density can be made by measuring the tracks of long-range protons. The velocity of such a particle for a given value of the residual range is known from the range–energy relation (see equality (3)). The grain density in a limited region of the track can thus be determined together with the corresponding value of the velocity. Although measurements were also carried out by this method, its application in the earlier experiments was limited by the small length of tracks suitable for measurement. Determination of the grain density in a region where the particle velocity may be regarded as approximately constant leads to large statistical errors because of the relatively small number of grains. To avoid these errors it is necessary to determine the total number of grains along the whole track, taking into account the change in the particle velocity.

We have seen that the energy losses for particles with elementary charge per unit path depend only on the velocity, \(dE/dR = f(v)\). Further, the number of grains per unit path depends only on the magnitude of the energy loss and, consequently, one may write \(dN/dR = \varphi(v)\). Let us consider two particles with masses \(M\) and \(m\) and charge \(e\), moving in the emulsion with velocity \(v\). The grain density of both tracks will then be the same. However, for a given change of velocity the heavier particle will travel a path \(M/m\) times greater than the lighter particle, and this result does not depend on the value of the velocity. Consequently, the total numbers of grains along the tracks of both particles

\((N\) and \(n)\) are related as their masses: \(\dfrac{N}{n}=\dfrac{M}{m}\). Since the initial velocities of both particles are equal, then \(\dfrac{R}{r}=\dfrac{M}{m}\), and we may write

\[ \frac{N}{n}=\frac{M}{m}=\frac{R}{r}=\mathfrak{M}. \]

Suppose that the relation between \(n\) and \(r\) is determined for a particle of known mass \(m\). Then for a particle with mass \(M\)

\[ N=\mathfrak{M}F\!\left(\frac{R}{\mathfrak{M}}\right), \]

i.e., the relation between the total number of grains along the track and the range for a particle with

Fig. 4. a) Dependence of \(\ln N\) on \(\ln R\), where \(N\) is the number of grains in the track of a particle with residual range \(R\), for artificial \(\pi^+\)-mesons and protons\({}^{27}\).

b) Dependence of the grain density \(\dfrac{dN}{dR}\) on the range \(R\) for \(\pi\)- and \(\mu\)-mesons of cosmic rays (Brown and Fowler). The mean value \(\dfrac{m_{\pi}}{m_{\mu}}=1.35\pm0.05\) was determined from five \(\pi\)- and five \(\mu\)-meson tracks.

a given mass. Consequently, the observed dependence between \(N\) and \(R\) determines the particle mass.

In applying this method, one usually represents \(\ln N\) as a function of \(\ln R\) for the two types of particles whose masses are being compared. On such a graph, points lying on a line drawn at an angle of \(45^\circ\) to the axes correspond to particles with constant velocity. Thus, the range \(r\) of a proton may be written: \(r=\Phi(v)\). Consequently,

\[ \frac{R}{\mathfrak{M}}=\Phi(v);\quad \text{but}\quad N=\mathfrak{M}F\!\left(\frac{R}{\mathfrak{M}}\right), \]

so that \(N=\mathfrak{M}\Psi(v)\).

and \(\dfrac{R}{N}=\xi(v)\), where \(\Phi(v)\), \(\Psi(v)\), and \(\xi(v)\) are related functions. For the straight line \(\ln N=\ln R\),

\[ \xi(v)=\frac{R}{N}=\mathrm{const}. \]

The intersection of such a straight line with two curves representing the results of measurements for two types of particles determines the ratio of their masses. If the values of the ranges at the points of intersection are \(R\) and \(r\), then \(\mathfrak{M}=\dfrac{M}{m}=\dfrac{R}{r}\) (Fig. 4,a).

In earlier works in which this method was used, it was necessary to confine oneself to observing tracks of \(\pi\)- and \(\mu\)-mesons that were associated with one another. Two associated tracks of such a pair are necessarily formed simultaneously. It is not known, however, what their relation in time is to other particles forming tracks in the emulsion, for example to single protons; consequently it is impossible to estimate the effect of disappearance of the latent image (regression). In experiments with cosmic radiation at mountain altitude the exposure usually lasts several weeks. As a result of regression in the photographic plates that were used at that time (1947), the grain density of tracks of particles with the same specific ionization is different, depending on the moment at which the particle passed through the plate. From observation of the tracks of \(\pi\)- and \(\mu\)-mesons of one and the same pair one can draw a conclusion about the ratio of their masses, \(\dfrac{m_\pi}{m_\mu}\), but one cannot obtain absolute values of the meson masses by comparison with proton tracks.

The second difficulty was connected with the circumstance that, in the comparatively thin emulsion used at that time, it was possible to find very few long tracks providing favorable conditions for measurements. At present it is known that the previously obtained value for \(\dfrac{m_\pi}{m_\mu}=1.65\pm0.15\) is too high. This method is now used in experiments carried out under more advantageous experimental conditions, namely with a thicker emulsion and with shorter exposures. A characteristic example of results obtained in experiments with artificial \(\pi\)-mesons\({}^{27}\) is given in Fig. 4,a. Fig. 4,b shows the results of processing observations of \(\pi\)- and \(\mu\)-mesons of cosmic rays (Brown and Fowler). The conditions realized in these experiments were especially favorable, since the duration of the exposures was small. The results included in Table I are in good agreement with those obtained in other experiments and show that the present method, when used under favorable conditions, can give reliable data in the hands of an experienced observer.

Table I

Results of measurements of the masses of $\pi$- and $\mu$-mesons

Authors	Method	Particle type	Mass in $m_\pi$	Mass in $m_\mu$	$\dfrac{m_\pi}{m_\mu}$
Lattes et al. $^{9}$	(A) ph. pl.*	$\pi^+;\ \mu^+$	—	—	$1.65 \pm 0.15$; cosmic-ray mesons
Goldschmidt et al. $^{28}$	(B) ph. pl.	$\pi^+;\ \pi^-;\ \mu^+;\ \mu^-$	$272 \pm 12$ $290 \pm 80$	$202 \pm 8$ —	Cosmic-ray mesons
Lattimore	(B) ph. pl.	$\pi^-$	—	—	Cosmic-ray mesons
Brown et al.	(A) ph. pl.	$\pi^+;\ \pi^-$	$290 \pm 20$	—	Cosmic-ray mesons
Barbour $^{29}$	(B) ph. pl.	$\pi^+;\ \pi^-;\ \mu$	$270 \pm 23$	$220 \pm 26$	Cosmic-ray mesons
Franzinetti $^{30}$	(B) ph. pl.	$\pi^+;\ \mu^+$	$281 \pm 7$	$217 \pm 4$	Cosmic-ray mesons
Camerini et al. $^{31}$	(G) ph. pl.	$\pi^+;\ \pi^-$	$283 \pm 7$	—	Cosmic-ray mesons
Fretter et al.	(B) W. ch.*	$\mu^+;\ \mu^-$	—	$215 \pm 2$	Artificial mesons
Gardner et al.	(B) ph. pl.	$\pi^-$	$313 \pm 16$	—	Artificial mesons
Bowker $^{27}$	(A) ph. pl.	$\pi^-$	$264 \pm 24$	—	Artificial mesons
Barkas et al. $^{33}$	(A) ph. pl.	$\pi^-;\ \mu^-$	$305$	$202$	Artificial mesons
Same	(B) ph. pl.	$\pi^-$	$280 \pm 6$	—	Artificial mesons
» »	(B) ph. pl.	$\pi^+;\ \mu^+$	$278 \pm 8$	—	Artificial mesons
» »	(D) ph. pl.	$\pi^+$	$276 \pm 6$	—	Artificial mesons

*) W. ch. and ph. pl. denote, respectively, experiments with a Wilson chamber and with photographic plates.

3 (3). Method B. Scattering and residual range

When passing through matter, a charged particle often undergoes small deflections as a result of Coulomb scattering. Such scattering was first considered by Williams $^{33}$. At present this problem has acquired great importance, since it is directly related to the determination of particle energies by the photographic-plate method. Observation of the mean angle of deflection per unit length of track $\bar{\alpha}$ gives the value of the quantity $p\beta$ for the particle, where $p$ is the momentum of the particle, $\beta=\dfrac{u}{c}$ is the velocity of the particle, and $c$ is the velocity of light.

The simplest way of applying this method consists in determining $\bar{\alpha}$, and consequently also $p\beta$, from observation of a bounded region of the track in its initial portion for particles,

which then comes to rest in the emulsion. The range–energy relation, expressed by equation (4), can be used to compute the relation between the range and the velocity, and consequently also between the range and the quantity \(p\beta\) for a particle of given mass. The mass of the particle can then be calculated from the experimental data. At present it appears possible to use this method in the case of \(\pi\)-mesons of comparatively high energies stopping in the emulsion (Camerini and others, unpublished). However, in earlier work, as also in method A, the tracks suitable for measurement had a small length—less than \(1\) mm. It was therefore necessary to measure the scattering over the entire length of the track and to take into account the change in the particle velocity. By this method Goldschmidt and others \(^{28}\) obtained values of the masses of \(\pi\)- and \(\mu\)-mesons which are in good agreement with later and more accurate measurements (see Table I).

Although this method is less accurate than others, it provides considerable experimental possibilities under conditions in which more refined methods cannot be used (see, for example, \(^{34}\)).

3 (4). Method B. Momentum and residual range

a) Experiments of Barkas and others.

The most accurate method developed for determining the mass of mesons consists in measuring the momentum of the particle from its deflection in a magnetic field and the residual range in a specified substance. For particles with elementary charge moving in an emulsion, equation (3) can be transformed and written in the form

\[ E = k_2 m^{1-n} R^n, \]

where \(m\) is the mass of the particle.

Further, if \(\rho\) is the radius of curvature of the particle trajectory in a magnetic field of strength \(H\), then one may write

\[ E = e^2 (H\rho)^2 / 2m, \]

where the quantities are measured in the corresponding system of units. Then

\[ m = \left\{\frac{e^2 (H\rho)^2}{2 k_2 R^n}\right\}^{\frac{1}{2-n}} . \tag{9} \]

This method was applied in the apparatus shown in Fig. 5 by Barkas and others \(^{32}\) for determining the mass of \(\pi\)-mesons produced in the Berkeley synchrocyclotron. Bombardment of a target by fast protons or \(\alpha\)-particles leads to the formation of \(\pi^+\)- and \(\pi^-\)-mesons emitted in all directions.

Only those particles are recorded by the photographic plates which are emitted from the thin target in a direction making

[Diagram labels: “Trajectory of \(\pi^+\)-particles”; “Primary particles”; “Target”; “Photographic plates”; “Target”; “Trajectory of \(\pi^-\)-particles”]

Fig. 5. a) Apparatus for determining the mass of \(\pi^+\)-mesons produced in the 384-inch synchrocyclotron at Berkeley. The apparatus is placed inside the vacuum chamber of the cyclotron; fast protons or \(\alpha\)-particles bombard the target and produce \(\pi^+\)- and \(\pi^-\)-mesons, which are emitted in all directions. A channel in the metal screen prevents particles from reaching the photographic plate if they are emitted in a direction making, with the direction of motion of the bombarding particle, an angle exceeding \(14^\circ\). The use of a thin target eliminates the uncertainty in determining the point of formation of the particle and the radius of curvature of the trajectory in the magnetic field. b) Apparatus for determining the mass of \(\pi^-\)-mesons.

with the direction of motion of the bombarding particles an angle smaller than \(14^\circ\). Knowing the point of entry and the direction of the initial segment of the track of a given particle, one can determine its trajectory and, consequently, the corresponding value of \(H\rho\). This value of \(H\rho\) and the values

of the observed range, substituted into formula (9), make it possible to calculate the mass of the particle. It is necessary, in addition, to introduce corrections for the inhomogeneity of the synchrotron magnetic field. In Fig. 6 a histogram is given of the results obtained by Barkas et al. The mean value obtained for the mass of the π-meson after the introduction of the corresponding corrections is equal to \(280.5 \pm 6\,m_e\).

An analogous determination of the mass of positive π-mesons, carried out by Barkas with the apparatus shown in Fig. 5, a, led to a mass value equal to \(278 \pm 8\,m_e\). In this case it proved possible to observe μ\(^+\)-mesons formed in the decay of π\(^+\)-mesons stopped in the target. The value obtained in this way for the mass of the μ\(^+\)-meson is \(212 \pm 6\,m_e\) (see Fig. 6).

Fig. 6. Distribution of mass values: a) \(\pi^-\) and b) \(\pi^+\)- and \(\mu^+\)-mesons, determined by Barkas and others by method B.

b) Experiments of Francinetti, Barbour, and Goldschmidt-Clermont. Experiments analogous to those described above for determining the mass of cosmic π-mesons were carried out by Francinetti (1949), Barbour (1949), and Goldschmidt-Clermont (1950). The apparatus used by Francinetti is shown in Fig. 7. The method consists in observing the tracks of individual particles in two photographic plates placed with their emulsions facing one another in a magnetic field of intensity 30,000 gauss. The thickness of the emulsion of each plate was 3 mm. Only particles entering the gap at a small angle to the surface of the emulsion and stopping in one of them were considered. It was possible to reconstruct the track of a particle that had passed through both plates and to determine the change in the direction of motion caused by the magnetic field and, consequently, the corresponding value of \(H\rho\). The distribution of the mass values of π- and μ-mesons obtained by Francinetti is given in Fig. 8, and the mean values—in Table I.

Labels in the figure: Plates; magnet pole; magnet yoke.

Fig. 7. Setup used by Franchetti to determine the mass of cosmic-ray particles in experiments on magnetic deflection. Method B.

Labels in the graphs: number of particles; \(+\) positive particles; \(-\) negative particles; mass in \(m_e\).

Fig. 8. Distribution of mass values of positive and negative particles in cosmic rays at an altitude of 3400 m. The results show that particles with mass \(\sim 1000m_e\) constitute, in number, no more than \(5\%\) of the number of \(\pi\)- and \(\mu\)-mesons. The black squares refer to \(\pi^+\)- and \(\pi^-\)-mesons identified by secondary effects observed at the end of their range.

c) Experiments with a Wilson chamber. Experiments with photographic plates are essentially analogous to experiments carried out for many years with a Wilson chamber placed in a magnetic field. In such experiments the curvature of the track is measured directly from the photograph, while the range of the particle is determined by the number of lead plates—

Fig. 9. Apparatus of a) Freter and b) Brode for determining the mass of cosmic-ray particles. In Freter’s apparatus two Wilson chambers \(A\) and \(B\) simultaneously photograph, at discharges controlled by counters \(C_1\) and \(C_2\). The upper chamber is placed in a magnetic field of \(\sim 5000\) gauss and serves to measure the momentum of particles stopped in the lead plates in the lower chamber. In Brode’s apparatus the momentum is measured by means of two Wilson chambers \(D\) and \(E\), separated by a region \(H\), in which a constant magnet creates a magnetic field. The change in the direction of motion of the particle in the magnetic field, determined from the track in both chambers, gives the value of its momentum. The particle is stopped in one of the lead plates in the third Wilson chamber.

through which the particle passes successively. A modern form of such an apparatus, used by Brode and Freter, is shown in Fig. 9 (see Section 9).

A disadvantage of this method is the low accuracy in determining the particle range, caused both by the finite thickness of the plates in which it is stopped and by the fact that certain secondary effects arising at the end of the range cannot be observed. Nevertheless, this method was successfully applied to determine the mass of \(\mu\)-mesons and, in particular, has yielded the most accurate information presently available on the mass of \(\mu\)-mesons.

Fig. 10. Distribution of the values of \(\bar{\alpha}\) (scattering parameter) and \(g\) (grain density) for particles formed in stars \({}^{36}\). Method I.

3 (5). Method G. Grain density and scattering

In the case of a charged particle moving with a velocity less than \(0.8c\), simultaneous measurement of the specific ionization and of the momentum makes it possible to determine its mass. Experiments based on this principle were carried out with a Wilson chamber. The specific ionization, giving the magnitude of the velocity of a particle of known charge, was determined by the method of counting drops, and the momentum—from the observed curvature of the particle track caused by the magnetic field.

The accuracy of such measurements is limited by fluctuations in the number of drops. It can be shown that in experiments with a chamber (and especially in experiments with a controlled Wilson chamber) it is difficult to establish exactly the same degree of supersaturation at each expansion, so that the number of drops for particles with equal specific ionization will depend on uncontrolled fluctuations. Despite this difficulty, this method is of great importance. It makes it possible to distinguish \(\mu\)-mesons of the penetrating component of cosmic radiation from electrons and protons.

This method was applied by a number of authors in experiments with \(\tau\)-mesons, described in Section 9.

An analogous method has recently been applied by Camerini and others\(^{35}\) and by Fowler\(^{36}\) with photographic plates. The theory of the method was independently considered by Goldschmidt-Clermont\(^{37}\). The velocity of the particle is determined by the method of counting grains, and \(p\beta\)—from observation of scattering. If one disregards the difficulty connected with the regression effect, which is insignificant when using a modern electron-sensitive emulsion and short exposure times, then the determination of the grain density in the track depends only on the uniformity of development and on the sensitivity of the emulsion.

This method is therefore better than the method of counting drops in a Wilson chamber. The measurement of the quantity \(p\beta\) from observation of scattering can be made with no less accuracy than that usually attained in determining momentum from observation of the curvature of tracks in a Wilson chamber placed in a magnetic field. A characteristic result obtained by this method is given in Fig. 10, on which, for individual tracks, the corresponding values of the mean angle of deflection per unit track length \(\bar{\alpha}\) and the number of grains per unit path \(g\) are plotted. All results refer to particles with large ranges, and therefore the change of \(\bar{\alpha}\) and \(g\) along the whole track may be neglected. The curves denoted in the figure by the letters \(\pi\), \(P\), \(D\), \(T\) refer to the calculated dependence of \(g\) on \(\bar{\alpha}\) for \(\pi\)-mesons, protons, deuterons, and tritons.

A clear clustering of the experimental points around the calculated curves for \(\pi\)-mesons and protons is plainly visible. The abscissa is the distance from the curve \(P\) to some experimental point plotted ...

that on this figure is proportional to the ratio of the mass of the corresponding particle to the proton mass. The characteristic mass distribution obtained by this method for particles emitted in disintegrations produced by cosmic protons and high-energy $\alpha$-particles is shown in Fig. 11. The data presented show that in such disintegrations fast $\pi$-mesons are usually produced, and they make it possible to calculate the mass of these particles. The results thus obtained are included in Table I.

Fig. 11. Distribution of the values (determined by method Г) of the masses of particles emitted in stars$^{31}$.

A substantial feature of this method for determining the masses of charged particles is the possibility of applying it to tracks of particles with large ranges that do not end in the emulsion. Thus, it is applicable under conditions in which other methods are not applicable.

3 (6). Method Д. Ratio of the ranges and momenta of protons and $\pi$-mesons

One of the most important sources of errors in the experiments of Barkas and others (see method В), which gave the most accurate of all values of the mass of $\pi$-mesons obtained at the present time, is the lack of knowledge of the exact form of the range–energy dependence for protons. To avoid this difficulty, Bishop and others$^{38}$ applied a method that does not depend on the absolute value of the magnetic field and on exact knowledge of the range–energy dependence.

We have seen that for particles with one and the same velocity and with masses respectively equal to $M$ and $m$, the relation
$\frac{M}{m}=\frac{R}{r}$ holds. Further, since the velocities of the particles are the same, their

are proportional to the rest masses and, consequently,

\[ \frac{M}{m}=\frac{R}{r}=\frac{(H\rho)_M}{(H\rho)_m}. \]

This result does not depend on the form of the range–energy relationship. The method therefore consists in determining the ratios of the values \(H\rho\) for protons and \(\pi\)-mesons for which the same ratio of ranges is observed. This is done with the aid of the apparatus shown schematically in Fig. 12.

Fig. 12. Apparatus\({}^{38}\) for determining the mass of \(\pi^+\)-mesons by the D. method. The two targets \(T_p\) and \(T_\pi\) serve as sources of protons and \(\pi\)-mesons. The radii \(\rho_p\) and \(\rho_\pi\) are related approximately as the masses:

\[ \frac{\rho_p}{\rho_\pi}=\frac{m_p}{m_\pi}. \]

The apparatus, placed in the vacuum chamber of a synchrocyclotron, has two targets \(T_p\) and \(T_\pi\) (Fig. 12), which are sources of protons and \(\pi\)-mesons and are positioned with respect to the photographic plates so that the ratio of the energies of the two types of registered particles is approximately equal to the ratio of their masses. In passing through the plate, a rapid change in the velocity of the \(\pi\)-mesons is observed and a considerably smaller change for the protons. The experiment consists in determining the values of the ratios \(\dfrac{R_p}{R_\pi}\) and \(\dfrac{(H\rho)_p}{(H\rho)_\pi}\) for small successive segments of path in the plate.

A typical set of data is shown in Fig. 13. The point of intersection of the best straight line drawn through the experimental points with the straight line

\[ \frac{R_p}{R_\pi}=\frac{(H\rho)_p}{(H\rho)_\pi} \]

determines the mass ratio \(\dfrac{m_p}{m_\pi}\). The value of \(m_\pi\),

obtained by this method is equal to \((276 \pm 6)m_e\), and the authors point to the possibility of obtaining more accurate results if the details of the experiment are improved.

The values given in Table 1 show that the difference in the masses of cosmic and artificially produced \(\pi\)-mesons lies within the errors of the experiments. This is good con-

Fig. 13. Dependence of \(\dfrac{\overline{R}_p}{R_\pi}\) for tracks of individual mesons on \(\dfrac{\rho_p}{\rho_\pi}\). The intersection of the best straight line drawn through the experimental points with the straight line

\[ \frac{\overline{R}_p}{R_\pi}=\frac{\rho_p}{\rho_\pi} \]

determines \(\dfrac{m_p}{m_\pi}\) independently of the range–energy relation. Method E.

firmation of the identity of both types of particles. It should be noted that the difference in the masses of \(\pi^+\)- and \(\pi^-\)-mesons is very small.

3(7). The nature of the neutral particles emitted in \(\mu\)-decay

Application of the laws of conservation of energy and momentum leads to the conclusion that the neutral particles which ensure the balance of energy and momentum during the decay of \(\mu\)-mesons must have a small or zero rest mass. It may therefore be supposed that these are either photons or neutrinos. Recent experiments

O’Ceallaigh’s experiments\({}^{39}\) are evidence that the first possibility can be regarded as excluded, and therefore the neutral particle may naturally be considered as a neutrino, i.e., as a certain form of neutral radiation with small or zero rest mass.

Let us set forth the idea of O’Ceallaigh’s experiments. Suppose that the decay process is accompanied by the emission of a photon in a direction opposite to the direction of motion of the \(\mu\)-meson. The direction of motion of the photon and its energy (\(\simeq 30\) MeV) are known.

Therefore, if one examines electron-sensitive plates in which the decay of \(\mu\)-mesons is recorded, electron pairs formed by the “recoil” photons should be observed. Photons with an energy of about \(30\) MeV form pairs\({}^{40}\) in photographic plates with an opening angle \(\simeq 3^\circ\); the bisector of this angle determines the direction of motion of the primary photon. Under favorable conditions, the electron energy, and hence also the photon energy, can be determined from Coulomb scattering. From these indications it is easy to establish whether the observed pairs are connected with the decay of nearby \(\pi\)-mesons that have stopped in the emulsion, or are due to \(\gamma\)-radiation not connected with \(\pi\)-mesons. O’Ceallaigh carefully examined the emulsion in the neighborhood of \(\pi\)-mesons that had stopped in photographic plates exposed to cosmic rays, and found no pairs over a total path length of recoil neutral particles of \(38\) cm. For photons with energy \(\simeq 30\) MeV the value of the radiation unit in emulsion is \(6.5\) cm. If the decay process led to the emission of photons, then under the conditions of the experiment six electron pairs would have been observed. The probability of observing not a single pair is \(< 0.005\). Hence one may conclude that the momentum balance is ensured by neutral radiation of another type, namely by some form of neutrino.

It is well known that in the \(\beta\)-decay of radioactive nuclei an “disappearance” of energy is observed, due, according to Fermi and Pauli, to the emission of a neutral particle with small rest mass—a neutrino. Experiments on the \(\beta\)-decay of certain light nuclei have shown that, if such neutral particles exist, then their rest mass is less than \(0.1\,m_e\). It had long been clear that important data on the existence of the neutrino could be obtained if it were shown that the law of conservation of momentum, just like the law of conservation of energy, requires the assumption of emission of a neutral particle. In a whole series of experiments, recoil nuclei in \(\beta\)-decay were therefore measured; the results obtained indicate the existence of the neutrino.

In the case of \(\pi\)-meson decay, the secondary charged particles—the \(\mu\)-mesons—have a rest mass small in comparison with atomic nuclei, while the neutral “recoil” particles have a large energy. It is therefore possible to determine accurately the momentum and energy of the \(\mu\)-meson. Since at present the possibility is excluded that the neutral

particle ensuring momentum balance is a photon, the observed values of the masses of the π- and μ-mesons and the characteristics of μ-decay provide important additional data on other forms of neutral radiation—on the existence of the neutrino.

4. PROPERTIES OF π-MESONS

4 (1). Charge of π-mesons

Microphotographs of cases of successive decay of π-particles, leading to the scheme π→μ→e, are given at the end of the issue (microphotograph 1).

If charge is conserved in the decay, i.e., if there are no particles with a charge smaller than the electron charge that have escaped observation in the emulsion, then the magnitude of the charge of all three particles must be the same. If the last particle formed as a result of the decay is in fact an electron (the grounds for such a conclusion are discussed in Section 5 (5)), then the charge of π- and μ-mesons is equal to the elementary charge.

Bradner noted that the closeness of the values of the π-meson masses obtained by different methods is an indication that the charge of π-mesons is apparently equal to the electron charge. In particular, he showed that the observed scatter in the mass values, when measured by methods A and B (see Table I), indicates that the magnitude of the charge of π-mesons differs from the electron charge by no more than 3% ^41.

4 (2). Lifetime of π-mesons

The most accurate measurements of the lifetime of π-mesons were made at Berkeley by the method shown schematically in Fig. 14. Positive and negative π-mesons are produced by bombardment with α-particles. Negative π-mesons emitted from the target in a definite direction within a narrow interval of momentum values are deflected in a channel cut in a thick metal block and are recorded by means of one of two photographic plates (Fig. 14). If the particles do not undergo spontaneous decay, then the relative number per unit area recorded in the two plates will be determined by the well-known “effect” of focusing associated with the helical trajectory of particles in a magnetic field, and will be approximately proportional to the path length; i.e., for the given experimental arrangement the number of particles recorded in the two plates will be in the ratio 3:1. However, in the case of decay of the particles in flight, the number of particles reaching the plates decreases, and this effect will be the more noticeable the longer the path. Thus, a deviation from the simplest ratio, observed in the case of stable particles, should be observed ^43. The method described above

applicable only in the case where the lifetime is of the same order as the period \(T\) of motion of the particle in the magnetic field. For particles of mass \(275\,m_e\), moving at right angles to a magnetic field of magnitude 15,000 gauss, \(T \simeq 10^{-8}\) sec.—a value close to the lifetime of \(\pi\)-mesons. The latest measurements by this method have shown that the lifetime \(\tau_\pi\) lies in the interval \((1.4—0.9)\cdot 10^{-8}\) sec. (see \(^{43}\)).

The lifetime of \(\pi\)-mesons contained in cosmic rays was determined by Camerini and others \(^{44}\), who used a method

Fig. 14. Richardson’s apparatus \(^{43}\) for determining the lifetime of \(\pi\)-mesons artificially produced in a synchrocyclotron. In the absence of decay, the number of particles per unit area of each plate (neglecting autophasing) is inversely proportional to the path length to the corresponding plate. The trajectory of the bombarding beam of \(\alpha\)-particles is not shown.

based on the following considerations: at mountain altitudes (\(\simeq 3400\) m), the bombardment of atoms by fast nucleons moving in the cosmic-radiation flux leads to the formation of high-energy \(\pi\)-mesons. Some of these particles are emitted in the reverse direction, so that in addition to the main flux of \(\pi\)-mesons moving from above downward, which forms the penetrating component, there is a weak flux of mesons moving upward from the surface of the Earth. At the point of their formation in the surface layer of the Earth, the mesons consist, at least predominantly, of \(\pi\)-particles. With increasing time of flight, the initial flux of \(\pi\)-mesons is spontaneously transformed into a flux of \(\mu\)-mesons. The photographic plates were therefore exposed at a distance of 2 m from the surface of the Earth. Identification of the particles of the reverse flux was carried out from the direction of their motion at the point where the tracks of particles, which then stopped in the plate, entered the emulsion. Further, mesons of different types could be separated according to the secondary processes occurring at

the end of their range. Thus it was possible to determine the rate of transformation of \(\pi\)-mesons into \(\mu\)-mesons by observing the ratio between mesons of the two types in plates placed at various heights above the Earth. The value of the lifetime determined in this way is \(0.6\cdot 10^{-8}\) sec, which agrees with the result obtained by more accurate methods using artificial particles.

The short lifetime of \(\pi\)-mesons explains their absence in experiments with the Wilson chamber and counters. In the following paragraphs it will be shown that the majority of \(\pi\)-mesons of cosmic radiation, produced in nuclear disintegrations, have kinetic energy greater than \(100\) MeV. When moving in the atmosphere, the magnitude of ionization losses is so small that only an insignificant fraction of \(\pi\)-mesons will be stopped before transformation into a \(\mu\)-meson occurs. Hence it follows that there is a very small probability of observing the spontaneous decay of \(\pi\)-mesons in the gas of a Wilson chamber.

4 (3). Disintegrations produced by \(\pi\)-mesons

The old data on nuclear disintegrations produced by mesons stopped in photographic plates were formerly interpreted as the result of capture of \(\mu\)-mesons by nuclei of silver or bromine. At present it has been established that the majority, and possibly all, of the disintegrations are in fact caused by \(\pi\)-mesons. The proof of this statement is based on the following facts: mesons observed in photographic plates exposed at high altitudes are \(\mu\)- and \(\pi\)-mesons, present in a ratio that depends on the total amount of matter in the immediate vicinity of the plates. This is connected with the fact that the overwhelming number of mesons observed in the atmosphere are \(\mu\)-particles formed in the decay of \(\pi\)-mesons (for more detail on this see below). Most \(\pi\)-particles—the primary products of nuclear explosions—are produced with energies less than \(10^9\) eV, and, owing to their short lifetime, usually travel before decay a path in flight of less than \(50\) m. When exposed at an altitude of about \(3000\) m, the downward-directed flux of \(\mu^+\)- and \(\mu^-\)-mesons, the greater part of which moves in a direction making an angle of less than \(40^\circ\) with the vertical, can be separated according to the direction of the tracks at the point of their entrance into the emulsion, in which the particles stop. On the other hand, most \(\pi\)-mesons are formed near the plates. The direction of their motion depends on the arrangement of the nearest dense materials and usually has an angular distribution close to isotropic. Furthermore, in plates exposed in free space in the atmosphere, the number of \(\pi\)-mesons is no more than \(10\%\) of the number of \(\mu\)-mesons; however, their number can be increased by the presen—

MESONS

by the action (during exposure) of lead blocks around the plates.

In a series of experiments carried out over a large range of altitudes with different amounts of material of high atomic number, it was found that the number of $\pi^+$-mesons recorded in $1 \text{ cm}^2$ of emulsion is approximately equal to the number of mesons producing nuclear disintegrations [$\sigma$-mesons], and that no appreciable change is observed in the ratio of the two types of mesons over a sufficiently wide range of experimental conditions. These experiments can be readily explained if it is assumed that $\pi^+$- and $\pi^-$-mesons are produced in approximately equal numbers in collisions of cosmic particles with nuclei of material of high atomic number, and that only $\pi^-$-mesons, when captured by nuclei, produce disintegrations with the emission of protons and other charged particles.

On the other hand, if an appreciable fraction of $\mu$-mesons also produces disintegrations, then the number of $\sigma$-mesons should correspondingly increase, and the ratio $\dfrac{N_\sigma}{N_\pi}$ should change with a change in the experimental conditions, in particular when the material around the plates is changed.

The absence of such an effect is good confirmation that there are very few, and perhaps no, $\mu$-mesons producing disintegrations with the emission of protons and $\alpha$-particles. Experiments at Berkeley with artificially produced negative $\pi$-mesons strongly confirm this point of view. Although in these experiments $\mu^-$-mesons are sometimes recorded, the place of their generation usually remains unknown, since it is possible that only $\pi$-mesons are produced directly in nucleon–nucleon collisions, while $\mu$-mesons appear only as a result of the decay of heavier particles. Therefore identification of $\mu^-$-mesons is difficult. On the other hand, $\pi^-$-mesons can be reliably identified. One can find the relative frequency with which $\pi$-mesons stopped in the emulsion produce disintegrations with the emission of various numbers of protons, $\alpha$-particles, etc.

Such a distribution, obtained by Adelman and others^45, is given in Fig. 15, b. The corresponding distribution for cosmic mesons is given in Fig. 15, a. Both distributions in Fig. 15 agree within the statistical errors of the experiments. This result can be explained by assuming either that only $\pi^-$-mesons cause disintegrations, or that the disintegrations caused by $\mu^-$-mesons are of the same type as those produced by $\pi^-$-mesons. Confirmation of the first assumption was obtained in work^28 on determining the mass of $\sigma$-mesons by the scattering method. The mean values obtained for the mass, $m_\pi = 272 \pm 12$ and $m_\pi = 290 \pm 80$, are consistent with the assumptions that $\sigma$-mesons are negative $\pi$-mesons.

Recent experiments by Franzinetti, in which the mass of mesons entering into the composition of cosmic rays was determined by the method of magnetic deflection, showed that the fraction of \(\mu^-\)-mesons stopping in the emulsion and producing nuclear disintegrations with the emission of heavy charged particles with a range greater than \(5\mu\) of emulsion is less than 5%. Although such evidence is not definitive, it is nevertheless clear that only a small fraction of \(\mu^-\)-mesons causes disintegrations visible in photographic plates.

Fig. 15. Distribution according to the number of “rays” for disintegrations produced by \(\pi\)-mesons in a photoemulsion: a) for cosmic particles, b) for artificial particles, c) and d) the same data, referred respectively to heavy and light elements in the emulsion.

The data are also consistent with the assumption that \(\mu^-\)-mesons do not, in general, produce disintegrations. Therefore, in any case, the overwhelming fraction of \(\sigma\)-mesons can be identified with \(\pi\)-mesons. Experiments at Berkeley also show that about 27% of \(\pi^-\)-mesons do not give registered disintegrations. In these special cases one may suppose that nuclear capture occurs prior to disintegration, but that fast neutrons escape, eluding observation, and that if they are accompanied by charged particles, the latter have a very short range. Further, from the experiments of Panofsky and others\({}^{46}\) it is known that in the interaction of \(\pi^-\)-mesons with hydrogen, the most widespread element in the emulsion, no visible stars are formed [see also Section 8 (6)].

Experiments with artificially produced \(\pi^-\)-particles showed that when \(\pi^-\)-mesons stop in photographic plates, the latter never decay (or decay only very rarely) with the emission of \(\mu^-\)-mesons, although this is the process in which the majority of \(\mu^-\)-mesons in the atmosphere are generated. We can therefore

one may say that, in contrast to \(\mu^-\)-mesons, \(\pi^-\)-mesons usually interact with nuclei and produce disintegrations before they have time to decay, and this is despite the fact that their lifetime is about one hundredth of the lifetime of \(\mu\)-mesons.

It is natural to suppose that the process of atomic capture of \(\pi^-\)-mesons is analogous to this process for \(\mu^-\)-mesons. The result obtained above therefore means that \(\pi^-\)-mesons interact with nucleons considerably more strongly than \(\mu^-\)-mesons do, and that, having entered the state with the lowest energy, \(\pi\)-mesons interact with a light nucleus, for example with a carbon nucleus, in a time small in comparison with \(10^{-8}\) sec.

4 (4). Capture of \(\pi^-\)-mesons by the nuclei of certain elements

The process of nuclear capture of \(\pi\)-mesons was studied by Heidmann and Leprince-Ringuet \(^{48}\) and by Perkins \(^{22}\). These authors assumed that an interaction takes place between the \(\pi^-\)-meson and a pair of nucleons. In studying the disappearance of artificial \(\pi^-\)-mesons stopped in a “multilayer system” consisting of successive layers of pure gelatin and normal photographic emulsion, Menon and others \(^{49}\) showed that it is possible to indicate characteristic differences between disintegrations formed in light substances (carbon, nitrogen, and oxygen) and disintegrations formed in heavy substances (silver and bromine). Typical nuclear disintegrations of light and heavy nuclei, separated by this method, are shown in microphotographs II and III.

In studying the disintegrations of light nuclei by \(\pi^-\)-mesons it is difficult to establish with which particular nucleus the interaction occurred. The disintegration is usually accompanied by the emission of neutrons, for which neither their energy nor their direction of motion can be determined. In comparatively rare cases, when in addition to charged particles only one neutron is emitted, it proves possible to find the momentum of the neutral particle by applying the law of conservation of momenta, and thus to study the complete distribution of energy among the emitted nucleons. A characteristic example of a reaction of this type is:

\[ {}^{12}_{6}\mathrm{C}+\pi \to {}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He}+{}^{3}_{1}\mathrm{H}+{}^{1}_{0}n \]

(Menon and others \(^{49}\)).

Such investigations are of great importance for broadening our knowledge of the processes of nuclear capture of \(\pi^-\)-mesons. Some authors believe that in the primary process of capture of \(\pi^-\)-mesons the energy released in the disappearance of the rest mass is usually transferred to a considerable number of nucleons, for example

group of $\alpha$-particles. This may lead to the emission of one or several fast nucleons and to the formation of an excited nucleus, which then “evaporates.” A detailed discussion of this question is given in Refs. 45, 49, 50.

4 (5). Spin of $\pi^-$ Mesons

Wentzel$^{51}$ put forward the suggestion that $\pi^-$ mesons formed in the interaction of a stream of fast nucleons with matter should be polarized, i.e., there should be some directionality of the particle spin relative to the direction of motion of the primary nucleon. Further, it is possible that when the particles are stopped in dense matter, the Coulomb forces, which play a role in atomic collisions and cause the particles to lose kinetic energy, will not significantly disturb the initial polarization. Such polarization, if it exists, will manifest itself in the appearance of a preferred direction of emission of $\mu$-mesons formed in the spontaneous decay of stopped $\pi$-mesons, relative to the direction of motion of the primary nucleons. At mountain altitude (3400 m), the flux of cosmic rays contains many protons and neutrons, most of which travel from top to bottom in a direction making an angle with the vertical of less than $40^\circ$. When passing through photographic plates, these particles cause nuclear disintegrations, some of which are accompanied by the emission of $\pi^+$ mesons, which then stop in the emulsion. One can study the direction of motion of the $\mu^+$ mesons emitted by the $\pi^+$ mesons. A typical result is shown in Fig. 16. It is easy to see that the particles are emitted in all directions and that the deviations from an isotropic distribution are small.

Fig. 16. Distribution of the emission directions of $\mu^+$ mesons relative to the vertical, produced by stopped $\pi^+$ mesons of cosmic radiation.

In the experiments described above we observed the decay of $\pi$ mesons emitted in nuclear disintegrations over a wide range of kinetic energies. In many cases the particle may be one of many mesons created in a single nuclear event (penetrating shower—see Section 7 (2)). In this case the absence of visible anisotropy is not indicative, and from these experiments no conclusion can be drawn about the spin of the $\pi$ meson. Similar conclusions have been drawn from recent experiments$^{52}$ with artificial $\pi^+$ mesons.

Convincing data confirming the usual point of view that π-mesons have zero or unit spin were obtained in Panofsky’s and others’ experiments\(^{46}\) on the capture of π-mesons by protons and on the character of the decay of the neutral mesons thereby formed (see Section 8 (2)).

4 (6). β-decay of π-mesons

The properties of π-mesons described in the preceding sections are analogous to those that were ascribed to Yukawa particles. The exception is the character of the decay, namely μ-decay instead of β-decay. At Berkeley experiments were set up to decide whether the spontaneous decay of π-mesons always leads to the emission of μ-mesons, or whether in some cases β-decay also occurs. The fraction of stopped π\(^+\)-mesons, identified by the values of their masses, which remained in the emulsion and emitted a μ-meson, was determined by means of the apparatus shown in Fig. 5,b.

The experimental data show that at least 95% of π\(^+\)-mesons undergo μ-decay and no more than 5% undergo direct β-decay. If, therefore, we assume that two types of π-meson decay exist, then one can estimate the upper limit of the decay constant leading to the emission of electrons, and the corresponding upper limit of the lifetime. Thus one can obtain the following result:

\[ \tau_{\pi}(\beta) > 20 \cdot 10^{-8} = 2 \cdot 10^{-7}\ \text{sec}. \]

This value is very close to that which was adopted by Yukawa for the lifetime of his heavy quanta with respect to β-decay.

5. PROPERTIES OF μ-MESONS

5 (1). Mass of μ-mesons

The most accurate values of the mass of μ-mesons were obtained from measurements of the curvature of particle tracks in a Wilson chamber placed in a magnetic field, and of the corresponding value of the residual range in lead plates—the method of B\(^{53–55}\). Schemes of installations using this method are presented in Fig. 9, and the results are summarized in Table I. The mass of particles was also determined by the method of grain counting and observation of scattering for tracks obtained in photographic plates\(^{28}\); however, these results are less reliable than the data obtained in the best experiments with the Wilson chamber. At the present time there are also measurements using the deflection in a magnetic field of particles recorded in photographic plates (see method B, Section 3 (4)). Investigation by this method of μ\(^+\)-mesons formed in the decay of artificially produced π\(^+\)-mesons is very promising (see Table I and Fig. 6).

5 (2). Decay of \(\mu\)-mesons*)

First of all, it is necessary to mention the work of Williams and Roberts\(^{11}\), which showed that \(\mu\)-mesons sometimes decay with the emission of a charged particle with energy \(\simeq 50\) MeV and a small value of the rest mass, which supported the point of view that mesons transform into electrons and neutral particles with small or zero rest mass (neutrinos or photons). At the present time there are facts, discussed in the following paragraph, proving that the charged particles are electrons. Although the fact that they really are electrons has not been established definitively, it is desirable to consider what such an assertion leads to.

For several years after the work\(^{11}\) no successful experiments on meson decay with a Wilson chamber were carried out. In 1947 Anderson\(^{115}\) obtained two photographs of decay electrons with energy \(\simeq 25\) MeV. Later other experimenters\(^{56–60}\), using various methods, obtained data showing that the energy of the decay electrons is not constant. Steinberger\(^{59}\) determined the energy spectrum of the electrons by measuring ranges in dense matter. Anderson and others\(^{60}\) determined the momenta of the electrons from the curvature of tracks in a Wilson chamber placed in a magnetic field at sea level. Finally, with the development of the method of electron-sensitive plates, it also became possible to record tracks of decay electrons and, in favorable cases, to determine their energy by the scattering method. In this way Brown and others\(^{34}\) showed that the energy of the 10 decay electrons observed by them was distributed in the interval from 10 to 50 MeV.

At the present time it has been established that the energy of the electrons emitted in the decay of \(\mu\)-mesons does not have a constant value, but is distributed over a certain interval; the maximum value of the energy of the decay electrons is of the order of 55 MeV. A simple application of the laws of conservation of energy and momentum to the decay of \(\mu\)-mesons into an electron and some neutral radiation makes it possible to calculate the maximum energy transferred to the electron. The value 55 MeV given above corresponds to the maximum energy of the electron if one assumes that the mass of the \(\mu\)-meson is equal to \(215\,m_e\), and that the neutral particles, i.e. the particles ensuring the balance of momenta, have zero rest mass. The best measurements of the form of the energy spectrum were carried out by Anderson and others\(^{60}\). The result obtained by them is shown in Fig. 17, a.

*) The author does not mention the important work of G. B. Zhdanov devoted to clarifying the character of the decay of \(\mu\)-mesons and discussed in detail in the supplement. (Translator’s note.)

The results show that the maximum of the distribution lies near 35–40 MeV and that there is a finite probability of emission of particles with the maximum possible energy. These results agree with Steinberger’s data.

Repeated measurements of the energy spectrum were carried out by Davis and others1, who used the scattering method for tracks of decay particles observed in photographic plates. The results obtained are shown in Fig. 17, b.

A distinctive feature of this method is that a monoenergetic group of particles gives an asymmetric peak in the curve of the energy distribution, with a “tail” extending into the region of high energies. The presence of a small number of particles with energy greater than the maximum allowed (see Fig. 17, b) is therefore not unexpected. The authors found that the mean value of the meson mass is equal to \(204 \pm 19\,m_e\). Thus, the majority of these particles are \(\mu\)-mesons, and not heavier particles with an analogous mode of decay. However, O’Ceallaigh noted that some of the cases may be due to the direct \(\beta\)-decay of \(\pi^+\)-mesons.

Fig. 17. a) Energy distribution of electrons produced in the decay of \(\mu^-\)-mesons. Measurements by Anderson et al. b) Energy distribution of electrons produced in the decay of \(\mu^-\)-mesons. Measurements by Davis et al. The dotted curve corresponds to the distribution expected for a monoenergetic group of electrons with energy 40 MeV.

In four cases, the energy of electrons emitted by \(\mu\)-mesons, which in turn were produced in emulsions in the decay of \(\pi\)-mesons, could be determined. The values obtained fall in the energy interval from 10 to 50 MeV and constitute additional evidence for the view that such \(\mu\)-mesons are identical with the mesons of the penetrating component of cosmic radiation

Examples of successive $\pi$-, $\mu$-, and $e$-decay are shown in microphotograph I.

Rossi$^{62}$ pointed out that, in studying the decay products of free $\mu$-mesons, one must confine oneself to positive particles, since negative particles may enter a Bohr orbit of an atom. Evidence for the existence of atomic capture of mesons was obtained in the experiments of Conversi et al.$^{63}$ These authors studied the energy distribution of slow electrons in the interval from 10 to 50 keV, produced in the decay of mesons that had stopped in photographic plates irradiated by cosmic rays. The authors showed that the energy distribution of these electrons can be explained by the Auger effect accompanying the atomic capture of $\mu^-$-mesons by silver and bromine nuclei, consisting in the emission of an atomic electron when the meson passes to a state of lower energy near the nucleus (see also$^{64}$). However, when captured by light nuclei, negative $\mu$-mesons undergo decay. Although atomic capture of $\mu$-mesons must also occur in light elements, the decay electrons lose only an insignificant fraction of their energy (not more than 1000 eV) in overcoming the Coulomb attraction of the nucleus. It is therefore reasonable to assume that the distortion of the energy-distribution curve for decay electrons is small; one may consider that we do not make serious errors in using results obtained by the photographic-plate method, although they also include cases belonging to the decay of negative $\mu$-mesons.

Since the energy of the decay electrons is not constant, it must be assumed that at least two neutral particles are produced in the decay. Both distributions shown in Fig. 17 exhibit a maximum in the distribution at about 40 MeV and give an average value of the decay-electron energy of the order of 35 MeV. This value is approximately equal to one third of the total energy released in the disappearance of the rest mass of the $\mu$-meson. Such a result indicates that, in the decay, two neutral particles of small rest mass are formed, the average energy of each of them being equal to one third of the total energy.

The form of the energy spectrum of the charged and neutral particles emitted in the decay is of great importance for determining the character of the forces between them. The expected distribution for various types of forces was calculated by Tiomno, Wheeler, and Rau$^{65}$. Some of these types, namely the vector and pseudoscalar variants, are in satisfactory agreement with the observed distribution. It is essential in the future to increase the accuracy and statistical weight of the measurements so that a more precise comparison of theory with experiment becomes possible (see also Michel$^{66}$).

5 (3). The Nature of the Decay Products

It is usually assumed that the charged particles emitted in the decay of $\mu$-mesons are electrons. To confirm this, Hincks and Pontecorvo67 investigated the nature of the passage of the particles through matter and the magnitude of the energy losses by the particles due to bremsstrahlung. Bremsstrahlung is the less probable the greater the rest mass of the particle. Measurements of the magnitude of the energy losses of the particles, in comparison with the losses for electrons in the same energy interval, make it possible to draw a conclusion about the value of the rest mass.

The experiments showed that the particles—the decay products—must have a rest mass less than $2m_e$.

Further confirmation of this point of view was obtained recently by Camerini and Fowler (unpublished), who observed in a photographic plate the collision of a decay particle with an electron. The energy of the primary particle, as well as the energy of the secondary particles after the collision, could be determined by the scattering method. Analysis of the case obtained showed that the mass of the decay particle is equal to $(3 \pm 2)m_e$ or $(1.2 \pm 0.5)m_e$, depending on which of the secondary particles is regarded as the recoil electron.

We have already seen that the energy spectrum of the charged particles emitted in the decay of $\mu$-mesons indicates the formation of at least two neutral particles. There is evidence that this neutral radiation is not photons. Thus Hincks and Pontecorvo67 investigated coincidences in counters caused by decay electrons and by conversion electrons from a photon possibly accompanying the decay. It was found that the appearance of photons, if they are emitted at all in the decay, occurs considerably more rarely than that of charged particles.

An analogous result was obtained by Sard et al.68.

On the basis of this result, and also of the experimental fact that the maximum energy of the decay electrons is equal to 55 MeV, it is usually assumed that the neutral radiation consists of particles with small or zero rest mass, of the neutrino type. Therefore the decay of $\mu$-mesons is usually described by the equation $\mu \to e + \nu + \nu$, where $\nu$ denotes a neutrino. Such a decay scheme for the $\mu$-meson and the decay scheme for the $\pi$-meson, usually represented by the equation $\pi \to \mu + \nu$, agree with the assumption that the spin of the $\mu$-meson is $1/2$, and that of the $\pi$-meson is 0 or 169, 70. It remains still unestablished whether all three neutral particles participating in such decay schemes belong to one and the same type, and whether they are identical with the neutrino emitted in nuclear $\beta$-decay.

5 (4). Lifetime of \(\mu\)-mesons

Figure 18 shows the latest arrangement of the apparatus used by Valley and Rossi\(^{71}\) to determine the lifetime of \(\mu\)-mesons in cosmic rays. Delayed coincidences of counters arranged according to a scheme analogous to that shown in Fig. 1 are used simultaneously with a Wilson chamber placed in a magnetic field. The sign of the charge of the mesons stopped in the last absorber is determined from their deflection in the magnetic field. The best value for the mean lifetime obtained by this method is \(2.15 \cdot 10^{-6}\) sec.

Fig. 18. Apparatus for determining the lifetime of \(\mu\)-mesons\(^{71}\). The sign of the charge of the passing particles is determined from the sign of their deflection in the Wilson chamber located in a magnetic field.

Recently a preliminary report\(^{72}\) has appeared on the determination of the lifetime of \(\mu^+\)-mesons produced artificially. When bombarded by energetic protons or \(\gamma\)-quanta, \(\pi^+\)- and \(\pi^-\)-mesons are produced (see section 6 (4)); these can be stopped in an absorber placed nearby. The \(\pi^+\)-mesons then decay with the emission of \(\mu^+\)-mesons, which in turn give electrons. The interval of time from the formation of the \(\pi^+\)-mesons to the stopping of the produced \(\mu^+\)-mesons is of the order of \(10^{-8}\) sec.—a time small in comparison with the lifetime of the \(\mu\)-mesons. Therefore one can use the production, by means of a synchrocyclotron, of short proton pulses, and then detect the decay electrons by means of scintillation counters. The pulse leads to the formation of a large number of \(\pi\)-mesons; in this case it is possible to find the distribution of delayed times

... in the emission of electrons in the decay of \(\mu\)-mesons. By this method one can obtain data with great statistical weight and determine a more accurate value of the lifetime of \(\mu\)-mesons.

A characteristic example of the observed distribution of delay times obtained by this method is shown in Fig. 19 (see also the work of Steinberger et al.\(^{73}\)).

5 (5). Nuclear interaction of \(\mu^{-}\)-mesons

In the preceding paragraphs the great importance of studying the properties of \(\mu^{-}\)-mesons stopping in elements with different atomic numbers for the development of our knowledge of mesons has already been noted. In a substance with a small atomic number the process of spontaneous decay predominates, and the lifetime determined by the delayed-coincidence method is equal to \(2.15\cdot 10^{-6}\) sec, whereas in heavy elements no delayed coincidences are observed. This effect was attributed to nuclear capture, and there are now weighty data showing that this explanation is correct. Thus, for example, decay electrons from \(\mu^{-}\)-mesons stopped in silver bromide were not observed.

During the first experiments, however, the alternative possibility had not been excluded that the absence of delayed coincidences was connected with an acceleration of the meson decay process in the strong field of the nucleus\(^{74}\). In this case \(\mu^{-}\)-mesons would emit electrons with a delay time less than \(\simeq 2\) \(\mu\)sec. Such electrons would be regarded as coincident in time with the meson, i.e., as emitted without appreciable delay when counters with ordinary resolving power are used. The assumption of accelerated decay was excluded by the direct experiments of Ticho and Stein\(^{75}\) and of Valle and Rossi\(^{71}\) on the study of the behavior of \(\mu\)-mesons stopping in substances with intermediate atomic number. These experiments were based on the following considerations.

If the disappearance of \(\mu^{-}\)-mesons in a substance with a large atomic number is due to nuclear capture, then a change in the character of the process with changing \(Z\) should be observed; thus, for iron \((Z=26)\) capture should predominate, while for graphite it should play

Fig. 19. Data on the delay of the decay times of artificially produced \(\mu^{+}\)-mesons\(^{72}\).

...a small role in comparison with spontaneous decay. Therefore it was assumed that, in a substance with an intermediate value of the atomic number, the two competing processes should play approximately the same role. As a result, one should observe, first, a decrease in the mean lifetime of the particles in comparison with that observed in light elements, and, second, a decrease in the fraction of mesons producing electrons, owing to the loss of some of the particles in nuclear capture. On the other hand, if the effect is connected with an acceleration of the decay process, then the lifetime will change in the same way as under the alternative hypothesis, while the fraction of observed mesons that yield decay electrons will be the same as in light elements.

A characteristic result showing the change in the number of electrons as a function of delay time for mesons stopped in sodium fluoride (a) and aluminum (b) is given in Fig. 20. It is clear from the figure that the lifetime in heavy elements is approximately equal to half the lifetime of positive mesons and that the number of electrons emitted per unit time at zero delay time also decreases.

Table II gives a summary of the values of the lifetimes of $\mu^-$-mesons stopped in substances with different atomic numbers.

Table II

Mean lifetime (in $\mu$sec) of $\mu$-particles stopped in solids with different atomic numbers

Substance	$Z$	Lifetime $\tau^-$	$\dfrac{\tau^-}{\tau^+}$	$f$	Author
O	8	$1.89 \pm 0.15$	$0.87 \pm 0.08$	$0.83 \pm 0.04$	Ticho
NaF	9,11	$1.23 \pm 0.12$	$0.57 \pm 0.06$	$0.60 \pm 0.065$	Ticho and Shein
Mg	12	$0.96 \pm 0.06$	$0.45 \pm 0.01$	$0.52 \pm 0.04$	Ticho
Mg	12	$1.1 \pm 0.2$	—	—	Vallee
Al	13	$0.75 \pm 0.07$	$0.95 \pm 0.04$	$0.40 \pm 0.04$	Ticho
Al	13	$0.70 \pm 0.06$	$0.35 \pm 0.035$	$0.47 \pm 0.05$	Vallee
S	16	$0.54 \pm 0.12$	$0.25 \pm 0.03$	$0.27 \pm 0.03$	Ticho

In addition to the values of the lifetime \(\tau^{-}\), the table gives the ratio \(\dfrac{\tau^{-}}{\tau^{+}}\) of this value to the corresponding value \(\tau^{+}\) for positive particles, as well as the fraction \(f\) of negative mesons decaying with the emission of electrons. Then \(1-f\) denotes the fraction of negative mesons that have interacted with the nucleus.

This result establishes the fact that \(\mu^{-}\)-mesons stopping in a solid substance disappear mainly in two

Fig. 20. Decay of \(\mu^{-}\)-mesons in NaF and in Al.

competing processes, and the number of mesons that disappear during the time \(\delta t\) can be written in the form

\[ dN=-(k_a+k_0)N\delta t, \]

where \(N\) is the number of particles, and \(k_a\) and \(k_0\) are the “decay constants” corresponding to nuclear absorption and spontaneous decay. Then

\[ f=\frac{k_0}{k_a+k_0}=\frac{\tau_a}{\tau_f}, \]

where \(\tau_a\) is the apparent decay time determined by both competing processes, and \(\tau_f\) is the lifetime of free particles.

Wheeler^76 showed on theoretical grounds that \(k_a \sim Z^4\), where \(Z\) is the atomic number of the absorbing substance. Although the experimental results are in satisfactory agreement with this assumption, the statistical accuracy of the measurements is nevertheless insufficient for a detailed verification of this relation.

It remains, further, to consider the nature of the transformations occurring in the capture of \(\mu^-\)-mesons by heavy nuclei. At present there is evidence that the capture process is never accompanied (or is accompanied only very rarely) by the emission of charged particles. In a number of papers, tracks of \(\mu^-\)-mesons stopping in thin plates of heavy elements in a Wilson chamber were recorded^64–67. In not a single case were particles observed that could be unambiguously identified as protons. Furthermore, data obtained in experiments with photographic plates show that stopped \(\mu^-\)-mesons producing stars either are absent altogether or are very few^44,30. From this one may conclude that capture of a \(\mu\)-meson leads to the emission of neutral radiation.

Experiments by Piccioni^78 with counters prove that the nuclear absorption of \(\mu^-\)-mesons is not accompanied by the emission of photons. On the other hand, Sard and others^63 have shown that this process leads to the formation of neutrons. These authors found that in the nuclear absorption of each \(\mu\)-meson approximately one neutron is produced. The simplest explanation of this result is the assumption that, in the process of nuclear capture, the meson interacts with one of the protons with the formation of a neutron and a neutrino according to the equation

\[ P + \mu^- \to n + \nu . \]

From general theoretical considerations it follows that in such a process the greater part of the energy is transferred to the lighter of the two particles, so that the recoil energy of the neutron must be small. From this it may be concluded that even in those cases when the neutron collides with other nucleons, the excitation energy of the nucleus is usually insufficient for the “evaporation” of charged nucleons and the formation of the observed nuclear disintegrations^65,64. A more detailed discussion of this question is given by Rossi^63.

6. FORMATION OF ARTIFICIAL MESONS

The formation of artificial mesons was first studied by Gardner and Lattes^25 with the aid of a beam of fast \(\alpha\)-particles produced in the 384-inch synchrocyclotron at Berkeley. During the past two years substantial progress has been made in the study of the properties of artificial mesons, now also produced by fast protons and high-energy \(\gamma\)-rays. These experiments provide—

Thus, on the one hand, favorable conditions were obtained for determining the mass and lifetime of \(\pi\)-mesons by means of the methods described above; on the other hand, the experiments indicated yielded information on the production of mesons near threshold by particles of relatively low energies. At such energies only a small fraction of nuclear disintegrations is accompanied by the emission of mesons. Before turning to a discussion of the corresponding results obtained in cosmic rays, it is convenient to consider the data obtained in these experiments.

6(1). The excitation curve for meson production

Jones and White\(^{79}\) used the apparatus, shown schematically in Fig. 5, \(a\), to determine the excitation curve and the energy spectrum of \(\pi^-\)-mesons produced by \(\alpha\)-particles.

The relative probability of formation of \(\pi\)-particles as a function of the energy of the primary \(\alpha\)-particles was determined by measuring the distance of the recording apparatus from the center of the cyclotron vacuum chamber. Usually the energy of particles accelerated in a cyclotron varies approximately in proportion to the square of the orbit radius; therefore, by placing the target in a suitable way, particles of a given energy can be obtained. For each value of the energy of the \(\alpha\)-particle, the number of mesons with kinetic energy lying in the interval from 2 to 10 MeV, emitted from the target at an angle of \(45^\circ\) relative to the direction of motion of the primary particles, was determined. The number of tracks in the photographic plate per unit area per unit time was recorded. The results obtained are presented in Fig. 21 (curve \(b\)).

Fig. 21. Dependence of the yield of \(\pi^-\)-mesons as a function of the energy of the primary particle; curve \(a\) — protons; curve \(b\) — \(\alpha\)-particles.

The results of analogous experiments in the case of meson production by fast protons\(^{79}\) are also shown in Fig. 21 (curve \(a\)).

Peterson \(^{80}\) measured the effective cross section for the formation of mesons with energies from 2 to \(5\) MeV by \(390\)-MeV \(\alpha\)-particles. The author found that the magnitude of the cross section for a carbon nucleus is approximately equal to \(3.0\cdot 10^{-32}\ \mathrm{cm}^2\) per unit solid angle and \(1\) MeV.

6 (2). Energy spectrum of mesons

Jones and White also determined the energy spectrum of \(\pi^-\)-particles produced by \(390\)-MeV \(\alpha\)-particles by means of an apparatus similar to that shown in Fig. 5, \(a\); the difference consisted in the possibility of simultaneous registration of mesons over a wider

Fig. 22. Apparatus used to study the production of mesons by a beam of \(345\)-MeV protons.

interval \(H\rho\). The energy spectrum of mesons emitted at angles less than \(30^\circ\) relative to the direction of motion of the \(\alpha\)-particles was determined. Preliminary results on the study of the energy spectrum of mesons produced by \(345\)-MeV protons were obtained in work \(^{52}\). The apparatus used in this work is shown schematically in Fig. 22. In these experiments the energy of the mesons was determined from the thickness of the absorber traversed by the particle before stopping in the photographic emulsion. The results of the observations (Fig. 23) show that the distribution is very similar in shape to the energy spectrum of \(\pi\)-particles produced by high-energy cosmic-ray protons (see Section 7 (3)). The results presented do not take into account nuclear collisions of \(\pi\)-particles in the absorber (see Section 7 (5)).

In work \(^{81}\), positive and negative \(\pi\)-mesons produced when carbon and hydrocarbon were irradiated with high-energy protons and emitted in the direction of the primary beam were studied. Using targets containing the same number of carbon atoms, it is possible to determine the effect due to the pri-

coexistence of hydrogen atoms. It was found that the energy distribution of $\pi$-mesons formed in the interaction of 345-$M_{\text{эв}}$ protons with protons and emitted in the direction of the incident beam has a sharply pronounced maximum at an energy of about 70 $M_{\text{эв}}$. This value is close to the maximum possible for $\pi$-mesons in accordance with the conservation laws. The authors draw attention to the desirability of a more detailed study of the energy spectrum of mesons emitted in different directions when a target is irradiated by $\alpha$-particles of specified energy.

In Section 5(4), measurements are described for determining the lifetime of $\mu^+$-particles formed in the decay of artificial $\pi^+$-particles; an advantage of the indicated method is the presence of a short proton “pulse” created in the synchrocyclotron. An analogous technique cannot be used in the case of $\gamma$-rays obtained in an electron synchrotron, because the duration of the “pulse” is too great. However, in this case crystal counters can be used for the successive determination of the following processes: a) stopping of $\pi^+$-particles, b) emission of $\mu^+$-particles, if the delay exceeds $3\cdot 10^{-8}$ sec., and c) emission of delayed electrons. Preliminary measurements by means of this very promising method$^{82}$ gave the following values for the mean lifetime of $\pi^+$-particles$^{23}$:

Fig. 23. Energy spectrum of artificial mesons formed by protons.

\[ \tau_{\pi+}=(1.65\pm0.33)\cdot 10^{-8}\ \text{sec.} \]

and for the decay of $\mu^+$-mesons:

\[ \tau_{\mu+}=2.16\cdot 10^{-6}\ \text{sec.} \]

6(3). Ratio of the Number of Positive $\pi$-Mesons to the Number of Negative Ones

Direct observations of the formation of $\pi$-mesons in photographic emulsion under the action of cosmic rays showed that, in the case of the emission of particles of low energies, there is a large excess of negative particles relative to positive ones. This effect can be explained by the influence of the Coulomb field of the nucleus, in which

particles were formed. Even if the energy spectra of both types of particles at the place of their birth have the same character, then in the region of small energies the Coulomb field of the nucleus, accelerating positive particles and slowing negative ones, has a substantial influence on the observed spectrum. This effect, which depends on the charge of the nucleus, was studied by Barkas, who bombarded targets consisting of elements with different atomic numbers with 390-MeV α-particles. The dependence of the ratio of the number of positive π-mesons to the number of negative ones on the atomic number is presented in Fig. 24.

For mesons of higher energies \((E > 50\ \text{MeV})\) the effect connected with the Coulomb field should be small; however, in the case of bombardment of targets by protons a difference should nevertheless be observed in the number of positive and negative particles formed. Indeed, suppose that the nucleus consists of \(N\) neutrons and \(Z\) protons.

Fig. 24. Ratio of the number of positive mesons to negative ones
\[ \frac{N(\pi^+)}{N(\pi^-)} \]
in the energy interval from 2 to 5 MeV; the mesons were formed in collisions of 390-MeV α-particles with nuclei having different atomic numbers\({}^{82}\).

If the incident proton interacts with a nuclear proton, then one of the colliding particles is transformed into a neutron; in this process a positive meson is formed:

\[ \mathrm{p} + \mathrm{p} \to \mathrm{p} + \mathrm{n} + \pi^+ . \]

On the other hand, if the primary proton interacts with a neutron, then, in accordance with two equations, there are two possibilities for the formation of charged mesons:

\[ \mathrm{p} + \mathrm{n} \to \mathrm{n} + \mathrm{n} + \pi^+, \]

\[ \mathrm{p} + \mathrm{n} \to \mathrm{p} + \mathrm{p} + \pi^- . \]

If both types of reactions are equally probable, then the ratio of the number of positive mesons formed to negative ones is equal to

\[ \frac{2Z + N}{N}. \]

If the nucleus has atomic weight \(A\) and charge \(Z\), then one may write:

\[ \frac{N(\pi^+)}{N(\pi^-)}=\frac{A+Z}{A-Z}. \tag{10} \]

The experiments of Bradner and Jones\({}^{47}\) show that the ratio of the num-

of positive mesons to negative ones for energies from 50 to 70 MeV is approximately equal to 5 instead of 3 in accordance with formula (10). In these experiments the mesons were produced by irradiating graphite with 345-MeV protons.

6 (4). Experiments with γ-rays

Analogous experiments on the study of artificial mesons were carried out with the aid of γ-rays produced in a 335-MeV electron synchrotron[^83]. The results obtained with the apparatus shown schematically in Fig. 25 show that the distribution of π-particles over angles is isotropic. The energy distribution of the mesons produced in graphite is very similar, in the interval up to 150 MeV, to the distribution that was obtained under irradiation by fast protons, and has a maximum at 35 MeV. It was found that the effective cross section for meson production is equal to \(5\cdot 10^{-28}\ \mathrm{cm}^2\) per steradian per one graphite nucleus.

Labels in the figure: γ-rays; photographic plates; graphite target.

Fig. 25. Diagram of an apparatus for studying the production of mesons by high-energy γ-rays[^83]. The energy distribution of \(\pi^+\)- and \(\pi^-\)-mesons was determined from the total thickness of absorber through which the mesons had to pass before stopping in the photographic emulsion[^82].

In the case of meson production by photons the number of negative particles is considerably larger than the number of positive ones:

\[ \frac{N(\pi^-)}{N(\pi^+)}=1.7\pm 0.2. \]

These results are of great importance for the theory of the meson. As was pointed out by Brueckner[^84], the experimental curves of the distributions of mesons over angles and energies agree well with the pseudoscalar version of the theory of nuclear forces*). On the contrary, from the sca-

) More complete calculations of the effective cross sections for the production of mesons by γ-quanta and of the angular distribution of mesons were made by A. M. Baldin and V. V. Mikhailov[^122]. See also UFN 44, 200 (1951). (Translator’s note.*)

it follows from the pion variant, in contradiction with experiment, that the angular distribution has little anisotropy. It should also be noted that comparison of the results of observations with theoretical predictions makes it possible to exclude the possibility that the mesons have spin 1.

6 (5). Formation of mesons by neutrons of high energies

Beams of high-energy neutrons were obtained as a result of charge exchange in collisions of fast protons with the nucleons of nuclei. When a target was bombarded with a beam of 340-MeV protons obtained in a synchrocyclotron, neutrons were produced with an energy approximately equal to 270 MeV; they could emerge through the corresponding channels in the shielding materials surrounding the accelerator. Fissions produced when neutrons passed through photographic plates were recorded. Approximately in 10,000 recorded “stars” in one an event was observed of the formation of a short-range meson; this phenomenon is often observed in photographic plates exposed to cosmic rays^116.

7. FORMATION OF π-MESONS BY COSMIC RAYS

7 (1). Emission, in nuclear explosions, of π-particles of relatively small energies

Soon after the discovery of π-mesons, nuclear explosions were observed in photographic plates, accompanied by the emission of e-mesons, i.e., particles which we must at the present time identify as π^−-mesons^9. A microphotograph of one of the many hundreds of cases now observed is given at the end of the issue (microphotograph IV).

Considerably rarer are analogous cases of emission of π^+-mesons which have stopped in the emulsion; up to the present only a few examples have been published^85,86.

In the case shown in microphotograph V, a π^+-particle is emitted in a nuclear disintegration. After stopping, this particle decays, emitting a μ^+-meson, which also stops, producing an electron in its decay.

It may be considered that the inequality between the observed number of “emitted” π^+- and π^−-particles of small velocities is a consequence of the influence of the Coulomb field in which the particle was formed. In the early experiments, the emitted mesons were identified, in the event of their stopping in the emulsion, only by the secondary effects caused by them. The probability that a particle stops in the emulsion decreases rapidly as the velocity of emission increases. All positive particles, as a result of the action of Coulomb repulsive forces, ...

are captured by the nucleus and thereby acquire an energy equal, at the very least, to several Mev. On the other hand, the negative particles must pass through the Coulomb barrier and therefore may be emitted with small velocities. An effect of this type is emphasized by the rapid increase of the particle range with increasing initial velocity; as a result, the probability of the formation of events analogous to that shown in microphotograph V is very small.

Up to now there has not been a single observation of the formation of a slow μ-particle in a nuclear interaction; however, the experiments of Piccioni\(^{78}\) and Fowler\(^{36}\) cited in the next paragraph indicate that at least the major part of those born in showers of penetrating particles are π-particles. The features discussed above of the production and nuclear capture of π-particles are consistent with the assumption of their strong interaction with nucleons. Therefore π-mesons have a much closer analogy with Yukawa particles than do μ-mesons, which, as we saw above, interact only weakly with nucleons. Although, apparently, π-particles are emitted as the primary products of interactions between nucleons, cosmic-ray experiments still cannot exclude the possibility that π-mesons are the decay product of very short-lived “primary” particles of larger mass and that, consequently, chains of π-, μ-, e-processes are the last stages of a longer sequence of spontaneous transformations. Such a possibility is difficult to exclude if one assumes that the lifetime of such postulated particles is less than \(10^{-14}\) sec.; in this case the path traveled by the particle before decay is less than a few microns. Even with the aid of the photographic method, which for this purpose has appreciably wider limits of applicability than other methods, it is impossible to detect the decay of particles with so short a lifetime.

Although a final judgment cannot yet be expressed, the observation of the formation of π-particles in Berkeley makes it possible to assert that π-mesons in any case can be created directly in nuclear collisions. The proof of this assertion is based on the following considerations. The initial observations of the artificial production of π-mesons were carried out with the aid of a beam of α-particles with an energy \(\simeq 360\) Mev. At first sight it is natural to suppose that such an α-particle is equivalent to four nucleons, each of which has an energy of about 90 Mev. From the laws of conservation of momentum and energy it follows that, in the collision of such a nucleon with a proton or neutron, no more than 45 Mev can be lost in the formation of a new particle with a finite rest mass. Thus, one might expect that, in the collision of 360-Mev

$\alpha$-particles with nuclei do not form particles with a rest mass greater than \(90\,m_e\). Experiment shows, however, that \(\pi\)-particles are formed when targets are bombarded by \(\alpha\)-particles of even lower energies; the threshold for such processes lies near \(300\) MeV (see Fig. 21).

The apparent contradiction is removed if one takes into account the relative motion of the nucleons composing the \(\alpha\)-particle and the target nucleus. If one makes a reasonable estimate of the magnitude of this internal motion and assumes that meson formation occurs preferentially when the relative velocities of the interacting particles have the greatest permissible value, then the observed threshold for meson formation agrees satisfactorily with the fact that the particles produced have a mass of \(300\,m_e\). On the other hand, in this way it is difficult to explain the formation of particles of considerably larger masses, particles which could be the “ancestors” of \(\pi\)-mesons. This result strongly supports the supposition of the direct formation of the \(\pi\)-particle in a nuclear interaction.

Fig. 26. Installations \(^{87,88}\) for observing showers of penetrating particles.

7. (2). Formation of “showers” of penetrating particles

It has been known for a comparatively long time \(^{87,88}\) that “showers” of penetrating particles are formed in air by cosmic-ray particles.* Typical installations intended for the study of penetrating showers are shown in Fig. 26. Simultaneous discharges are registered in several Geiger counters arranged in a massive lead block in such a way that these coincidences could not be caused by cascade “showers” of electrons or photons.

The origin of such penetrating showers was investigated by Fretter and others with Wilson chambers. Charged particles were observed which were capable of penetrating through several centimeters of lead. These particles sometimes interact with the nuclei of one of the lead blocks; in such an interaction groups of particles arise which pass through the lead plates without producing

* This remark by the author is incorrect; in the cited works only the following alternative proposition was proved: either there are airborne penetrating showers, or penetrating showers are formed in the filter surrounding the counter. Proof of the existence of airborne penetrating showers was given in a paper by Soviet authors \(^{123}\). (Translator’s note.)

cascading showers and, consequently, having a non-electronic nature. It is usually considered that such cases correspond to the interaction of fast nucleons with nuclei, leading to the formation of many mesons. Such processes are envisaged in the theories of meson production of Heisenberg, Heitler and Janossy, Oppenheimer, and others.

Until very recently three important features of this phenomenon remained unexplained. First, the nature of the shower particles had not been established, although it was supposed that the showers consist of protons and mesons. It was believed that the protons acquire large energy in collisions with the primary particle, while the mesons are formed in nucleon–nucleon collisions in the course of the passage of the primary particle through the nucleus. Second, it had not been clarified whether the appearance of many mesons in a nuclear interaction is the consequence of a single collision of a nucleon with a nucleon, or the consequence of successive multiple collisions of the primary particle with the nucleons of the nucleus, with only one meson usually arising in each such collision.

The first of these alternative theories of the origin of showers of penetrating particles (the so-called theory of “multiple production”) was put forward by Heisenberg^89 and by Oppenheimer and others.^90 In this theory it was assumed that, in collisions between two nucleons, a large part of the energy is lost in the form of radiation of heavy “quanta”; the upper limit of their number is determined only by the requirements following from the law of conservation of energy and momentum.

On the other hand, Heitler and Janossy,^91 while not considering the possibility of multiple birth to be entirely excluded, assume that the predominant process is multiple formation. In this case it is assumed that, in each of the successive collisions of the primary particle with the nucleons of the nucleus, only one meson is formed.

A third feature of penetrating showers is that they are often accompanied by soft radiation—electrons and photons—which, “multiplying” in passing through lead plates, form characteristic cascading showers. Until very recently it was unclear whether the soft radiation arises together with the penetrating particles in nuclear collisions or whether it has a secondary origin.

Possibilities for investigating the indicated problems appeared in connection with observations of analogous phenomena by means of an “electron-sensitive” photographic emulsion.^92 Characteristic microphotographs of cases of this type are given at the end of the issue (microphotographs VI, VII, and VIII).

There are two important features of the new observations: 1) the path of the shower particles can be traced from the point of their forma-

… 2) one may also observe secondary processes accompanying the production of shower particles: subsequent “evaporations” of nuclei and the emission of protons and $\alpha$-particles of relatively low energies.

7 (3). The nature of shower particles

The first definite indications of the nature of shower particles were obtained in experiments carried out by Piccioni$^{78}$. The author used an apparatus schematically shown in Fig. 27. Three rows of counters were separated by lead blocks $A$, $B$, and $C$, the third row being surrounded by additional blocks of graphite or sulfur $D$ and $E$. The method was based on differences in the behavior, in light and heavy elements, of stopped $\mu^-$- and $\pi^-$-particles. Whereas stopped $\pi^-$-particles interact with nuclei both of sulfur and of graphite, $\mu^-$-particles are absorbed only by nuclei of heavy elements; in graphite they decay with emission of an electron (see Section 5 (5)). Piccioni observed single charged particles that had passed through rows of counters (1) and (2), but had stopped in blocks $D$ or $E$; delayed coincidences due to discharges in the counters of group (3) were then recorded. The author found that the ratio of the number of such events per unit time in graphite to the number of events in sulfur was

\[ \frac{N_C}{N_S}=1.8. \]

Fig. 27. Piccioni’s apparatus for the identification of “shower” particles.

This result is consistent with our ideas about the behavior of $\mu$-mesons; electrons are produced in graphite when both positive and negative mesons stop, whereas in sulfur they are produced only when positive ones stop. The result obtained differs somewhat from 2, owing to the well-known excess of positive particles among the $\mu$-mesons of the penetrating component.

In contrast to the effect produced by single penetrating particles, nuclear explosions arising in lead block $A$ and accompanied by the emission of shower particles produce discharges in two or more counters of group $A$. It was further found that a coincidence of discharges in two counters of group $A$

with the discharge of one or more counters of group \(B\) is a consequence of the formation of local showers. In these cases the number of delayed coincidences proved unchanged when the graphite blocks \(D\) and \(E\) were replaced by gray ones. This fact agrees with the supposition that all mesons produced in local showers are \(\pi\)-particles. Indeed, if this supposition is correct, then both in light and in heavy elements only positive particles should transform into \(\mu\)-particles, while the latter should decay with the emission of positrons. Conversely, the result obtained contradicts the supposition that a significant fraction of the mesons produced in local showers are \(\mu\)-particles.

Although Piccioni’s experiments prove that \(\pi\)-mesons are formed in nuclear explosions, nevertheless from these experiments one cannot draw conclusions either about their relative number in the penetrating component of local showers or about their energy distribution. Most particles of penetrating showers have relativistic velocities, and it is well known that this usually leads to considerable difficulties in determining the rest mass. However, certain conclusions can be drawn from simultaneous observation of the curvature of the particle trajectory in a controlled Wilson chamber located in a magnetic field (from the curvature one can judge the particle momentum) and of its specific ionization, determined by the “drop-counting” method. These experiments are difficult to carry out with sufficient accuracy (see section 3 (5)), and they have recently been supplemented by investigations carried out with the aid of photographic plates. The momentum of particles observed in a photoemulsion was determined from the deviation of the trajectory from a straight line due to multiple Coulomb scattering \(^{35,37,93}\). The limits of applicability of the latter method were considerably expanded thanks to the use of a very simple and rapid method for measuring scattering (Fowler \(^{36}\)). A typical result obtained by Fowler is shown in Fig. 10. In this figure the ordinate gives the logarithm of the grain density, and the abscissa gives the scattering parameter \(\bar{\alpha}\), which is the mean deviation per unit length. Measurements of particle masses were carried out only in those cases when the track length in the emulsion exceeded 3 mm. In the measurements, no account was taken of the relation of the particles to the “stars” with which they were associated. Therefore some tracks belonged to primary particles producing nuclear explosions, but such cases occurred rarely compared with the frequency of detection of tracks of secondary particles. It follows from Fig. 10 that a significant fraction of the particles for which the grain density along the track is close to minimal have a mass smaller than the proton mass. Further, the mean value of the meson mass with specific ionization exceeding the minimum, calculated from the arrangement of the experimental

points relative to the corresponding proton curve was found to be equal to \((283 \pm 7)m_e\) (see Fig. 11). Therefore these particles can be identified as \(\pi\)-mesons. The study showed that if \(\mu\)-mesons and electrons with energies below 150 MeV are emitted in nuclear explosions, their fraction in this energy interval amounts to less than 2% of the number of \(\pi\)-mesons. These observations strongly support the view that nucleons and \(\pi\)-mesons constitute the overwhelming fraction of the particles directly produced in nuclear reactions.

It has long been known \(^{94}\) that the greater part of the electrons of the soft component at sea level have energies below 200 MeV*). Therefore the results of these experiments indicate that in most cases electrons are not a direct consequence of nuclear interaction, but are of secondary origin. These experiments do not exclude the possibility that \(\gamma\)-rays are produced in nuclear interaction. However, as we shall see in the next paragraph, the soft component accompanying penetrating showers can also be produced in another way, namely by the decay into photons of neutral mesons produced in nuclear interaction together with showers of charged \(\pi\)-mesons.

Fig. 28. Distribution by energy of mesons entering the composition of showers observed at an altitude of 21 km.

7 (4). Energy spectrum of mesons entering the composition of showers

The method described in the preceding section was applied to finding the energy spectrum of mesons produced in disintegrations caused by high-energy cosmic-ray particles. The results obtained by Camerini and others are shown in Fig. 28. These results may be compared with the energy distribution of mesons of the penetrating component of cosmic rays.

Sands \(^{95}\), using the results of a study of intense slow \(\mu\)-mesons at various depths in the atmosphere and the energy distribution of particles at sea level, calculated the energy spectrum of the particles at the point of their production. If it is assumed,

* As was shown by S. Z. Belen’kii \(^{124}\), in reality the principal part of the electrons of the soft component at sea level should have an energy below 70 MeV. (Translator’s note.)

that \(\mu\)-mesons are the product of the decay of moving \(\pi\)-mesons, then from Sands’s data one can obtain the energy spectrum of the \(\pi\)-mesons at the point of their production. The curve calculated in this way is in good agreement with the distribution shown in Fig. 28. This result confirms the following point of view: the \(\mu\)-mesons of the penetrating component are the product of the decay of moving \(\pi\)-mesons formed in collisions of nucleons with the nuclei of atoms in the air.

In favorable cases it is possible to measure the energy of the primary particles that produce nuclear stars in photographic emulsion. A statistical study of a large number of cases makes it possible to determine the energy of the primary particles that produce nuclear disintegrations in which \(n_s\) fast “shower” particles are emitted. One can then compare the mean energy \(\bar E_p\) of the primary particle producing a shower with the number of shower particles \(n_s\), with the total energy transferred to mesons \(n_s \bar E_s\), and with the energy carried away by the nucleons and \(\alpha\)-particles of the “star.” A preliminary result of investigations of this kind, carried out by Camerini and others, is shown in Fig. 29. From these data the following conclusions may be drawn: a) the mean energy of a meson depends little on the number of particles \(n_s\); as the energy of the primary particle increases, the number of mesons increases (with approximately the same kinetic energy); b) the fraction of the energy remaining with the primary particle is very small. It may be supposed that the missing fraction of the energy is spent on the formation of unrecorded neutral mesons (see Section 8).

Fig. 29. Energy balance of stars with different numbers of particles: \(\bar E_p\)—mean energy of the primary proton; \(n_s\bar E_s\)—mean value of the total energy of shower particles, and \(\bar E(N_h)\)—mean energy of the star. It is easy to see that some fraction of the energy is missing; it is assumed that this energy was spent on the formation of neutral mesons.

7 (5). Nuclear interaction of shower particles

To determine the nature of shower particles, the frequency with which they undergo nuclear collisions while passing through matter is of great importance. \(\mu\)-mesons can penetrate through a considerable thickness of earth because they interact only rarely with nuclei. Therefore, from the assumption that

Since the particles emitted in “showers” are $\mu$-mesons, it follows that their mean free path between successive interactions with nuclei is considerably greater than the mean free path between successive passages through nuclei. If one assumes that a particle interacts with a nucleus every time it passes through it, then the effective cross section for the interaction is approximately equal to the geometrical cross section of the nucleus:

\[ \sigma = A^{2/3}\cdot 6.8\cdot 10^{-26}\ \text{cm}^2 . \]

On the other hand, if $\pi$-particles are produced directly in showers, then the effective cross section for nuclear interaction should not differ greatly from the geometrical one. At present it is known that about 80% of shower particles are $\pi$-mesons. Thus, observation of the mean free path makes it possible to judge the magnitude of the interaction of $\pi$-mesons with nuclei. Microphotographs VI and VII present examples of secondary nuclear interactions of “shower” particles observed in photographic emulsion. A large number of experiments have been devoted to determining the mean free path of shower particles; these, however, have yielded different results. The method of observation is very similar to that which was used to study the formation of shower particles in nuclear explosions occurring inside a Wilson chamber in lead plates. Shower particles pass successively through the lead plates inside the chamber; the fraction of particles that have interacted with the nuclei of the plates is then estimated. The results obtained by various experimenters using this method are included in Table III. For comparison of the results of different experiments in which different filters were used, the table includes the ratio of the observed “mean free path” (m.f.p.) to the value of the path calculated from the assumption that the effective cross section for nuclear interaction is equal to the geometrical one.

Observations with photographic plates[^31] lead to a value of the mean free path considerably smaller than the value obtained with a Wilson chamber. These experiments indicate that the mean path length for protons and $\pi$-mesons is close to the geometrical value. The authors who used photographic plates found that $\pi$-mesons usually produce small “stars,” and suggested that the interpretation of experiments with a Wilson chamber is complicated by the fact that particles emitted as a result of secondary interaction are stopped inside the lead plates in which they are produced. In such a case the secondary interaction will not be noticed; this circumstance leads to an overestimation of the mean free path between collisions.

Thus, although the final value of the effective cross section for the interaction of $\pi$-mesons with nuclei is not yet known, the available data nevertheless indicate that the probability of interaction of $\pi$-mesons with a nucleus through which they pass is very high.

Table III

Author	Method	Result	Observed s.s.p. geometric value	Energy interval (mesons)
Piccioni \(^{78}\)	Counters at mountain altitude	\(1200\ \mathrm{g\,cm^{-2}}\) Fe	14.0	\(> 400\ \mathrm{MeV}\)
Fretter \(^{53}\)	Wilson chamber with lead plates at mountain altitude	\(750\ \mathrm{g\,cm^{-2}}\) Pb (without corrections)	4.7	\(> 150\ \mathrm{MeV}\) \(n_s > 2\)
Lovati, Mura, Salvini, Tagliaferri \(^{96}\)	Wilson chamber with lead plates at mountain altitude	\(300 \pm 100\ \mathrm{g\,cm^{-2}}\) Pb (with corrections)	1.9	\(> 150\ \mathrm{MeV}\) \(n_s > 2\)
Brown and McKay \(^{97}\)	Wilson chamber with lead plates at mountain altitude	\(316 \pm 70\ \mathrm{g\,cm^{-2}}\) Pb (with corrections)	2.0	\(> 150\ \mathrm{MeV}\)
Butler, Rosser and Barker \(^{98}\)	Wilson chamber with lead plates at sea level	\(400\ \mathrm{g\,cm^{-2}}\) Pb (without corrections) \(200\ \mathrm{g\,cm^{-2}}\) Pb (with corrections)	2.5 1.4	Mean energy of the shower \(\sim 7000\ \mathrm{MeV}\)
Harding and Perkins \(^{99}\)	Photographic plates exposed under ice	\(120\ \mathrm{g\,cm^{-2}}\) ice	2.0	\(> 100\ \mathrm{MeV}\)
Camerini, Fowler, Lock and Muirhead \(^{21}\)	Electron-sensitive plates exposed at great altitudes	\(100\ \mathrm{g\,cm^{-2}}\) emulsion	1.1	\(> 150\ \mathrm{MeV}\)

The final solution of this question is of great importance for the detailed investigation of the processes leading to the formation of showers. In the case of meson formation when nucleons pass through heavy nuclei, the secondary interaction of mesons with nucleons of the same nucleus may play an important role.

7 (6). Multiplicity of meson production

The problem of the multiplicity of meson production has already been mentioned earlier. Discussion of this problem at the international conference in Como in September 1949 led to the conclusion that the decisive experiment consists in observing the production of many mesons in the interaction of a high-energy proton or neutron with the nucleus of a hydrogen atom.

Let us suppose that there has occurred an interaction of a fast proton with a proton at rest. In a collision in which no mesons are produced, the track of the recoil proton will appear. If charged mesons are produced, then from the law of conservation of charge it follows that the number of secondary particles must be even. This conclusion is not altered even in the presence of charge exchange, leading to the transformation of one or both primary protons into neutrons. A different result is obtained in the collision of a fast neutron with a proton; in this case the total number of secondary particles is odd, and the primary particle does not produce a visible track. One may expect that the study of cases of this type by means of photographic emulsion will amount to the registration of “stars” in which all or almost all tracks have a grain density equal to the minimum value. Therefore such cases escape observation with ordinary scanning methods and can be noticed only at very high magnification. Following the results of the discussion in Como, several investigators directed their attention to the search for such cases, and a certain number of examples corresponding to a multiple process have already been found.

In a private conversation Prof. Heisenberg told me that he and his collaborators had discovered a star produced by a fast particle, with six diverging tracks. Five of these tracks have the minimum grain density, while the sixth track belongs to a slow \(\pi^{-}\)-particle. These features agree with the assumption that such an event corresponds to a collision of a proton with a proton, in which four \(\pi\)-mesons were produced. A similar event is shown in microphotograph IV; in addition to the slow \(\pi\)-particle, which produced a secondary disintegration, five fast particles and one strongly ionizing particle were produced. In another event observed in Bristol, the star had eight tracks (one corresponded to the primary and seven to secondary particles), all the tracks having minimum ionization. Such an event cannot be completely identified, since the number of tracks of secondary particles is odd. However, it is reasonable

it may be supposed that the ninth track, associated with the “star,” was not noticed because of the unfavorable direction of motion of the particle. It is known that it is difficult to detect a track going at a large angle to the surface of the emulsion.

It is necessary to note that the observed interactions of high-energy $\alpha$-particles with nuclei are difficult to explain by the influence of multiple processes alone. Bradt and others\({}^{100}\) observed such a collision in a photographic emulsion exposed by means of balloon sondes at an altitude of $\simeq 27$ km, when an $\alpha$-particle caused a nuclear explosion accompanied by the production of a narrow jet containing 23 particles; it may be assumed that most of them were $\pi$-mesons. A similar case, in which an $\alpha$-particle created 35 fast particles, is shown in microphotograph VIII. In this case only three strongly ionizing particles were emitted. In the following section it is proved that the formation of charged mesons is accompanied by the production of a considerable number of neutral mesons. It seems improbable that a purely multiple process could lead to the formation of about 40 mesons in successive collisions with the nucleons of the nucleus, as a result of which only three protons were emitted. Furthermore, some preliminary data indicate that high-energy $\alpha$-particles with considerable probability produce effects similar to that shown in microphotograph VIII; however, the emission of a relatively small number of charged nucleons is not quite usual. Thus, at the present time there are a number of indications of multiple production of $\pi$-mesons in an individual nucleon—nucleon collision. However, the relative contribution of multiple or plural processes to the formation of showers, and the detailed picture of the processes occurring inside the nucleus, remain unclear. To solve this problem, determining the mean free path of a $\pi$-particle between two collisions is insufficient, since from this one can find only an upper limit for the radius of the forces acting between the $\pi$-particle and an individual nucleon.

7 (7). Formation of showers under large thicknesses of earth

George\({}^{117}\) has recently shown that nuclear explosions occur under considerable thicknesses of earth, accompanied by the emission of relativistic particles. At a depth of 30 m below the earth, electron-sensitive plates were prepared; then at this same depth they were exposed and developed. In this way, phenomena that might have been a consequence of the emulsion’s stay at sea level were excluded.

The plates prepared in this way recorded $10^{-2}$ nuclear disintegrations in $1\ \mathrm{cm}^3$ of emulsion per day; about $1/5$ of the disintegrations were accompanied by the emission of shower particles. Approximately

in a quarter of the cases it was possible to distinguish the track of the primary particle from the secondary ones. The nature of the shower particles remained undetermined; however, the type of shower proved very similar to that observed at high altitudes; it is therefore reasonable to suppose that the shower particles are \(\pi\)-mesons.

It is difficult to suppose that these disintegrations were produced by protons and \(\pi\)-mesons of high energy, which would have traversed \(30\ \mathrm{m}\) of earth without being absorbed as a result of nuclear interaction. On the other hand, the flux of \(\mu\)-mesons at such depths has considerable intensity. Further, recent experiments at Berkeley have shown that \(\gamma\)-rays, in interaction with nuclei, produce mesons. It is therefore reasonable to suppose that the “showers” arise as a result of the electromagnetic interaction of \(\mu\)-mesons with nuclei. From the found value of the flux of these particles and the number of recorded showers it can be shown that the effective cross section for such a process is, in order of magnitude, equal to \(10^{-23}\ \mathrm{cm}^2\). Many stars observed at this depth, but not accompanied by “showers,” could have been caused by secondary \(\pi\)-mesons and fast nucleons\({}^{101}\).

Fig. 30. Momentum balance in the decay of a neutral meson into two quanta.

8. NEUTRAL MESONS

8 (1). Decay of a neutral meson into photons

In the first section of the present work it was pointed out that, if the main features of Yukawa’s theory are correct, then, owing to the approximate equality of the forces between nucleons with like and unlike charges, it is necessary to assume the existence of both neutral and charged mesons. Recent investigations\({}^{102}\) have given serious indications in favor of the formation, in nuclear interactions of high energy, of neutral particles with a mass of about \(300\,m_e\); these neutral particles have a lifetime of less than \(10^{-11}\) sec. and decay into two photons. Before proceeding to a detailed examination of the experimental facts, it is useful to consider the main characteristics of the radiation that should be expected in such a decay of a particle.

If a neutral meson, moving with a given velocity, decays into two photons, then the energy of a photon depends on the direction of its motion relative to the line of motion of the meson. The problem is analogous to the problem of the radiation of a moving source; the wavelengths and the intensity distribution are determined by the well-known Doppler principle.

Let \(m_0\) be the rest mass of the particle, \(\beta c\) its velocity, and \(m\beta c\) its momentum, where

\[ m=\frac{m_0}{\sqrt{1-\beta^2}}. \]

Next suppose that the energies of the two photons are equal to \(h\nu_1\) and \(h\nu_2\), and that the corresponding angles between the directions of motion of the photons and the direction of motion of the neutral meson are \(\Theta\) and \(\Phi\).

The vector sum of the momenta of the two photons, \(\dfrac{h\nu_1}{c}\) and \(\dfrac{h\nu_2}{c}\), (Fig. 30) is equal to the meson momentum \(m\beta c\) \((AB+BC=AC)\). From the law of conservation of energy it follows that:

\[ h\nu_1+h\nu_2=\frac{m_0c^2}{\sqrt{1-\beta^2}}=Bm_0c^2=\mathrm{const}. \]

Thus, \(AB+BC=\mathrm{const}\), and the locus of the points \(B\) is an ellipse. It is easy to show that the energy of a photon emitted at an angle \(\Theta\) is determined by the relation

\[ h\nu=\frac{m_0c^2}{2B(1-\beta\cos\Theta)}. \]

The curves shown in Fig. 31,b represent calculated energy distributions for various angles of emission and various values of the energy of neutral mesons \(Bm_0c^2\); the meson rest energy was taken to be equal to \(140\) Mev.

Emission of photons forward and backward relative to the direction of motion of the neutral meson corresponds to the maximum and minimum values of the \(\gamma\)-ray energy, determined by the relations

\[ h\nu_{\max}=B\frac{m_0c^2}{2}(1+\beta);\qquad h\nu_{\min}=B\frac{m_0c^2}{2}(1-\beta). \]

Thus, even for small values of the kinetic energy, the spectral distribution of the emitted radiation has a considerable width. The calculated form of the spectrum for various values of \(B\) is shown in Fig. 31,a; each curve corresponds to a monoenergetic group of neutral mesons.

It can also be shown that the intensity of radiation emitted at an angle \(\Theta\) (the number of photons per unit solid angle) is determined by the relation

\[ I(\Theta)=\frac{k}{B^3(1-\beta\cos\Theta)^2}, \]

where

\[ k=\mathrm{const}. \]

The curves representing the intensity distribution possess a strong asymmetry for values of \(B\) greater than 2; these curves show the predominance of photons emitted at small angles to the direction of motion of the neutral mesons.

Fig. 31. Characteristics of the radiation produced in the decay of a neutral meson: a) energy spectrum of photons produced by a monoenergetic beam of neutral mesons; b) photon energy as a function of the emission angle. The curves are given for different values of \(B\), where \(B m_0 c^2\) is the total energy of a particle with rest mass \(m_0\).

§ (2). Experimental proof of the existence of neutral mesons

In the experiments of Bjorklund and others,^102 fast protons formed in the synchrocyclotron collided with matter. During operation of the generator, owing to various nuclear processes, there is an intense background flux of radiation; therefore the generator is

Fig. 32. Arrangement of the apparatus for observations of γ-radiation produced in the collision of 340-MeV protons with matter.

Fig. 33. Apparatus for determining the intensity of γ-rays and the energy of photons.^102

surrounded by a thick layer of absorbing material. In the absorber there are channels arranged in such a way that part of the radiation arising in the immediate vicinity of the target can pass through them to the outside (Fig. 32). The emerging γ-rays enter the apparatus shown in Fig. 33. This apparatus consists of four counters, connected in a coincidence circuit and placed in a magnetic field.

When a high-energy photon strikes a thin lead “radiator,” there is a considerable probability of the formation of a positron–electron pair. The two particles are deflected by a magnetic field in opposite directions; each of them may cross one of two pairs of counters. Thus, a positron–electron pair with energies lying within definite intervals may produce simultaneous discharges in all four counters (fourfold coincidences). With the aid of these coincidences one can measure the intensity of the high-energy γ-rays that have passed through the channels.

By placing metal plates of appropriate thickness between the counters of each pair, one can estimate the energies of the electron–positron pairs. An increase in the electron energy requires an increase in the thickness of the absorber necessary for a specified reduction in the coincidence rate. Measuring the dependence of the intensity on the absorber thickness makes it possible to determine the photon energy.

Measures were taken to observe the γ-radiation formed when a target was bombarded by high-energy protons in two directions. In one case, photons emitted in a direction close to the direction of motion of the primary proton were studied; in the other, those emitted in a direction close to the opposite one.

The results obtained may be summarized as follows: a) in studying the dependence of the intensity of γ-rays emitted in a specified direction on the energy of the protons bombarding the target, it was found that the formation of photons becomes possible beginning at some definite “threshold.” This “threshold” has almost the same value as for the formation of charged mesons. The radiation intensity increases rapidly as the proton energy rises above the “threshold”; b) the energy of the γ-radiation observed in a specified direction has a definite spectral distribution with a clearly noticeable maximum (Fig. 34). For photons emitted in the direction of motion of the protons, the mean quantum energy is considerably greater than for photons emitted in the opposite direction. Furthermore, the greatest intensity is observed for the radiation emitted forward. These and other features of the experiments can be simply interpreted if one assumes that the γ-radiation is formed in the decay of neutral mesons produced together with charged mesons in a high-energy nuclear collision. It was proposed that the neutral meson is very unstable and has a lifetime of less than \(10^{-11}\) sec. The assumption of so short a lifetime is necessary, since it can be shown that the observed γ-rays are formed inside a target of thickness 3 mm; hence it follows that the decay of the meson during its passage over this distance must be highly probable.

The observed photon energies and radiation intensities agree with the assumption that neutral mesons

are emitted isotropically in the center-of-mass system of the colliding nucleons.

The conclusions drawn by the authors from the experiments described above have been convincingly confirmed by two recent results obtained at Berkeley by Steinberger et al.^73 These authors showed that high-energy photons arising when a target is bombarded by protons of considerable energy are produced in pairs. The dependence of the photon energy on the angle between the direction

Fig. 34. Characteristics of the radiation produced when carbon is bombarded with 340-MeV protons. The spectral distribution is shown for two directions of photon emission relative to the line of motion of the generating particles.

of motion of the photons and of the primary particles agrees with the assumption that the γ-radiation originates in the decay of neutral mesons.

Panofsky and others^46 studied the capture of π-mesons by compressed hydrogen. It was found that the capture process leads to the formation of neutrons and neutral mesons; the latter are detected by observing the γ-rays arising in the decay. Much less frequently, the mesons form a neutron and one photon.

Both reactions may be written in the following form:

\[ \begin{aligned} \text{a)}\quad &\pi^- + \mathrm{H}^1 \to n^0 + \pi^0,\qquad \pi^0 \to 2h\nu \quad [h\nu \simeq 70\ \text{MeV}],\\ \text{b)}\quad &\pi^- + \mathrm{H}^1 \to n^0 + h\nu \quad [h\nu \simeq 140\ \text{MeV}], \end{aligned} \]

where \(\pi^0\) denotes a neutral meson. Knowing the values of the masses of the three particles participating in reaction (a), one may assert that the mass

$\pi^0$-particle is less than the mass of the charged meson. Furthermore, the experiment makes it possible to estimate the degree of inhomogeneity of the energy of the $\gamma$-rays formed in reaction (a). We have seen that the degree of inhomogeneity is very sensitive to the kinetic energy of the recoiling neutral meson, and observations show that the recoil velocity is small. Consequently, the mass of the $\pi^0$-particle is only slightly less than the mass of the charged meson; preliminary results show that

\[ m_{\pi^+}-m_{\pi^0}\simeq 4m_e,\quad \text{therefore,}\quad m_{\pi^0}\simeq 270\,m_e. \]

§ (3). Formation of neutral mesons by cosmic-ray particles

It was reported earlier (section 7 (6)) on the formation of a narrow “stem” of shower particles, arising when a high-energy $\alpha$-particle collided with a nucleus[^100]. This case was observed in the emulsion of one of the plates belonging to an entire assembly of plates, which made it possible to observe the successive passage of the “stem” through a number of plates. The authors found that, at a distance of several centimeters from the point where the nuclear explosion occurred, pairs of electrons are formed. The electrons possess high energy and move in a direction making a small angle with the shower axis. We have called the observed pairs of particles electrons, although their nature has not been definitively established. However, it is reasonable to suppose that they are indeed pairs of electrons formed by $\gamma$-rays. At a distance of one radiation unit the authors observed nine such pairs; from this it may be concluded that 56 shower particles were accompanied by approximately 35 photons.

We have seen from Fowler’s experiments[^36] that at least 80% of the charged particles of penetrating showers are mesons and that electrons are either entirely absent or very few in number. Furthermore, the assumption of the direct formation of $\gamma$-rays in a high-energy nuclear interaction encounters serious theoretical difficulties. On the other hand, the observations of Bradt and others are explained without difficulty if it is assumed that the $\gamma$-rays forming the observed pairs are due to the spontaneous decay of neutral mesons; in this case the number of neutral mesons is comparable with the number of charged $\pi$-mesons. A detailed analysis of the features of this case leads to the conclusion that the mean lifetime of neutral mesons is less than $3\cdot 10^{-13}$ sec.

§ (4). Mass and energy of neutral mesons formed in penetrating showers

Recently Carlson, Hooper, and King[^103] described a method by means of which, in principle, one can obtain independent proof of the existence of neutral mesons and determine their lifetime. These authors determined the energy spectrum

γ-rays in the atmosphere at an altitude of 21 km by measuring the energies of individual electron pairs formed in the emulsion. Assuming that this radiation arises in the decay of neutral mesons formed in a nuclear interaction, and that its spectrum is not substantially distorted by the presence of photons of bremsstrahlung radiation, one can determine: a) the mass of the neutral meson and b) the energy spectrum of the particles near the point of their formation. The method is based on the following considerations. In Fig. 31, a is shown the calculated distribution of the energies of photons formed in the decay of monoenergetic groups of neutral mesons, for various values of the total energy \(B m_0 c^2\). For an inhomogeneous

Fig. 35. Spectrum of γ-rays in air at an altitude of 21 km \(^{103}\).

beam of mesons in the distribution of photons by energy there is a maximum at the energy \(\dfrac{1}{2} m_0 c^2\). Let now \(E_1\) and \(E_2\) be two values of the energy corresponding to one and the same arbitrarily chosen value of the radiation intensity. In that case it can be shown that, independently of the chosen value of the intensity,

\[ (E_1 \cdot E_2)^{\frac{1}{2}} = \frac{m_0 c^2}{2}. \]

From the assumption that the γ-radiation is formed in the decay of neutral mesons, it follows that the photon spectrum must have features reflecting the relation established above.

In Fig. 35 is shown the energy distribution of photons at an altitude of 21 km. Five pairs of energy values were chosen for

of different intensity values; the values of the quantities \((E_1 \cdot E_2)^{1/2}\) corresponding to these intensities are shown in the figure by circles. A remarkable agreement between the various values was found. The “mean” value of the mass of the neutral meson determined by this method turned out to be

\[ m_{\pi^0}=(295\pm 20)m_e. \]

Relying on the value of the mass of the neutral meson thus determined, one can use the obtained spectrum of \(\gamma\)-rays to find the energy distribution of neutral mesons at the point of their formation. The spectrum obtained in this way is shown in Fig. 36. In the same figure there is the corresponding curve for charged mesons formed in showers observed on the same photographic plates. From Fig. 36 it is seen that there is no substantial difference between the shapes of the two distributions. This indicates that neutral and charged mesons are formed in processes of a similar type.

Fig. 36. Energy distribution of charged (circles) and neutral (crosses) \(\pi\)-mesons in the atmosphere at an altitude of 21 km. The intensity is plotted in arbitrary units.

These observations are convincing proof that, in explosive disintegrations produced by high-energy protons and \(\alpha\)-particles, charged \(\pi\)-particles are accompanied by neutral mesons of the same type as those produced artificially. A very essential condition for the successful application of the method of Carlson, Hooper, and King is observation at such great altitudes that the spectrum of \(\gamma\)-radiation is not substantially altered by the formation of cascade showers.

8 (b). Lifetime and frequency of formation of neutral mesons

The proof of the existence of neutral mesons presented in the preceding paragraph, although sufficiently convincing, nevertheless had an indirect character. Therefore it seems very important to obtain independent proof

of the existence of neutral mesons. For this purpose, and also to measure the lifetime of the particles, Carlson and others observed electron pairs formed by $\gamma$-rays arising in nuclear explosions in emulsions near stars.

Let us suppose that a homogeneous beam of mesons with rest mass $m_0$ moves with such a velocity that the energy of each particle is equal to $Bm_0c^2$. We have seen that for values $B>2$ the $\gamma$-radiation essentially preserves the direction of motion of the neutral meson. However, owing to the features of the decay of neutral mesons, the line of motion of the photons usually deviates from the line of motion of the particle generating the shower. Further, in the case of photons with energies in the intervals considered by us, the electrons formed in conversion constitute a very narrow pair with an opening angle $\sim 0.1^\circ$. Thus these pairs indicate the line of motion of the $\gamma$-rays with an error of the same order of magnitude, i.e., about $0.1^\circ$. Consequently, the backward projection of the mean line of the pair, generally speaking, does not pass through the center of the star associated with it, but at a distance $r$ from it (Fig. 37). A simple analysis makes it possible to find the expected distribution of the values of the quantity $r$ for a given value of the energy of the neutral mesons and, consequently, to calculate the mean lifetime. A remarkable feature of this method is the independence of the distribution of the quantities $r$ from the energy for $B>2$. Consequently, the calculated distribution of the values of $r$ depends little on the distribution of the mesons in energy, if all neutral particles have an energy greater than $100\ \mathrm{MeV}$. This fact may be explained as follows: although the direction of the emitted $\gamma$-radiation tends, with increasing $B$, to approach the direction of motion of the meson, in this case there is a relativistic increase of the time scale, which neutralizes the first tendency.

Fig. 37. Principle of the method for determining the lifetime of neutral mesons.

The observed distribution of the values of $r$ is shown in Fig. 38; from this figure it follows that, if $\gamma$-rays are formed in the decay of neutral mesons, then their mean lifetime must be less than $5 \cdot 10^{-14}\ \mathrm{sec}$; more precisely, the lifetime of neutral mesons is approximately equal to $2.5 \cdot 10^{-14}\ \mathrm{sec}$; this result does not depend substantially on experimental errors.

Further investigations show that the interval of values of $r$ does indeed correspond to a finite lifetime,

having this order of magnitude; the results of these experiments may be regarded as independent evidence for the existence of neutral mesons.

Carlson and others, from the frequency of formation of electron pairs near stars, concluded that the ratio of the number of neutral mesons to the number of charged mesons emitted in nuclear explosions is

Fig. 38. Determination of the lifetime of neutral mesons. The value \(r\)—the perpendicular drawn from the “star” to the bisector of the angle between the lines of motion of the electrons of the pair. The concentration of events for which \(r < 40 \mu\) is due to “associated” pairs. Such events prove that \(\gamma\)-rays are formed in nuclear explosions and make it possible to determine the intensity of such \(\gamma\)-rays.

\[ \frac{N(\pi^0)}{N(\pi^+)} = 0.45 \pm 0.1. \]

This result is in good agreement with theoretical predictions.

8(6). Spin and other properties of \(\pi^0\)-particles

Above (Section 8(2)) the experiments of Panovsky and others\({}^{46}\) on the capture of \(\pi^-\)-particles by hydrogen with the emission of \(\gamma\)-rays were briefly described. The decay scheme of the neutral meson into two particles, which is a direct consequence of the capture process, is not consistent with the assumption that \(\pi^0\)-particles have spin 1. It is therefore natural to suppose that, like charged particles, neutral mesons have spin 0. Furthermore, the characteristics of the capture process, as a result of which a neutron and a \(\pi^0\)-particle of small kinetic energy are emitted, indicate equality of the numbers of negative and neutral \(\pi\)-mesons.

An interesting and distinctive feature of analogous experiments in which hydrogen gas was replaced by hydrogen compounds was the absence of photons. It was expected that if \(\pi^-\)-particles stop in such a compound (for example, in lithium hydride), then many of them are captured by lithium, producing nuclear disintegration. However, capture of some fraction of the mesons by hydrogen should have led to the emission of \(\gamma\)-radiation. The authors suggested that the absence of radiation is explained by migration

neutral complex consisting of a proton and a $\pi^-$-particle in the crystal lattice. Such migration continues until the $\pi^-$-particle enters the state of lowest energy in the proton–meson system. As a result of such diffusion the complex collides with a neighboring heavy atom. In such a collision there is a high probability that the $\pi^-$-particle will be captured by the proton of one of the heavy atoms, and then by the entire nucleus. The assumption of the existence of such a neutral complex between a proton and a negative meson was put forward by Frank^104 *) to explain $\pi$-$\mu$ cases by processes different from the decay of a $\pi$-particle.

9. EVIDENCE FOR THE EXISTENCE OF MESONS OF OTHER TYPES

During the last five years physicists working in various laboratories have presented data indicating the existence of particles with a mass intermediate between the masses of $\pi$-mesons and protons. Although we encounter several types of particles, all these particles are conveniently called $\tau$-mesons. Sometimes the evidence is based on individual cases observed in Wilson chambers or photographic plates; until very recently an unsatisfactory feature of all the observations was the absence of correspondence between any pair of the described cases. Therefore the question of the existence of $\tau$-mesons remained open. However, several recently observed cases have confirmed the results of earlier work. It may therefore be asserted that there are serious indications in favor of the existence of particles with a mass of the order of $1000\,m_e$.

9(1). Evidence for the existence of $\tau$-mesons

a) The first observation of $\tau$-mesons was made by Leprince-Ringuet and Lhéritier^105, who obtained, in a controlled Wilson chamber placed in a magnetic field, a photograph of the collision of a fast cosmic-ray particle with an electron. From an analysis of the photograph the authors concluded that the mass of the moving particle, which had a positive charge, was of the order of $1000\,m_e$.

b) Rochester and Butler^106 observed two cases in a Wilson chamber. In one of them two particles arise in the gas of the chamber, emerging from one point; the angle between the directions of motion of both particles is about $65^\circ$. From the assumption that the point of intersection is the point of their production, it follows that the particles have charges of different signs. From the curvature of the tracks in the magnet—

*) The properties of the neutral complex are discussed in the paper by D. D. Ivanenko and A. A. Sokolov^125.

field and specific ionization, determined from the density of the droplets along the track, one may conclude that both secondary particles have a mass of about \(300\,m_e\). To explain the photograph, the authors assumed that the particles arose in the spontaneous decay “in flight” of a neutral particle with mass \(>800\,m_e\). In the second case, a sharp kink in the direction of motion of the particle was observed in the gas of the chamber. It is very difficult to explain the kink by nuclear scattering; the authors showed that this case is not inconsistent with the assumption of the decay in flight of a charged particle with mass about \(1000\,m_e\), with the emission of a secondary charged particle and one or several neutral particles.

c) Bradt and Peters, as a result of measuring the grain density in a large number of particle tracks in photographic plates exposed at considerable altitudes, put forward at the conference in Bristol in 1948 the suggestion that, in nuclear explosions, particles with mass about \(700\,m_e\) and small kinetic energy are sometimes emitted. However, these results must be treated with great caution because of the preliminary exposure of the plates and the effect of regression. The absence of tracks of spontaneous decay or interaction with nuclei at the ends of the particle ranges is also an unsatisfactory feature of these observations. As a result of subsequent experiments, the authors abandoned their assertions, explaining them by the preliminary exposure of the plates and by regression.

Other experimenters carried out similar observations, obtaining, however, different results. Friesen and collaborators (private communication) in Lund did not obtain, in photographic plates exposed by means of balloon probes at great altitudes, data testifying in favor of the existence of particles with masses in the interval \(500\)—\(1500\,m_e\). Brown and Fowler, studying plates exposed at an altitude of \(3300\,\text{m}\), obtained an analogous result. On the other hand, Alikhanian, Alikhanov and collaborators, using this method, asserted that they had obtained a result which confirms the conclusion about the existence of “varitrons.”

d) Leprince-Ringuet and collaborators \(^{10a}\) observed in a photographic emulsion a case characterized by the following features: 1) one of the recorded particles apparently has a mass smaller than the mass of the proton; 2) at the end of the track of this particle a disintegration was observed, in which a \(\pi^-\)-particle was emitted; 3) this \(\pi^-\)-particle produced a secondary disintegration. Assuming that the first track did indeed belong to the particle that caused the disintegration, the mass of this particle can be determined from the energy balance; the mass proved to be approximately \(700\,m_e\).

d) Brown and others observed in an “electron-sensitive” emulsion a case apparently corresponding to the spontaneous decay into three particles of a stopped particle with a mass of about \(1000\,m_e\). Such an interpretation is based on the fact that the total momentum of the secondary particles is, within the limits of error, equal to zero, and their total energy corresponds to the energy liberated in the disappearance of the rest mass of the primary particle. One of the secondary particles stopped in the emulsion, producing nuclear disintegration; consequently, this particle is a \(\pi^{-}\)-meson. From measurements of scattering and of grain density along the path, the second particle, which possessed a considerably larger energy, can likewise be identified with a \(\pi\)-meson.

After a considerable interval of time, during which there was no definite point of view on the essence of the question under discussion, new experimental data were obtained confirming the observations of Rochester and Butler. Thus, Anderson and others \(^{108}\) observed, at an altitude of \(3300\) m in a Wilson chamber, twenty examples of “V-shaped” tracks apparently due, as in the case observed by Rochester and Butler, to the decay of neutral mesons \(\tau^0\). In some cases the decay of a \(\tau^0\)-meson was accompanied by nuclear disintegration in a lead plate placed in the chamber. It is reasonable to suppose that the two events are connected and that \(\tau^0\)-mesons are formed in the disintegration of nuclei. The authors state that, if this supposition is correct, then the features of the “forks” indicate that the emission of neutral particles in the spontaneous decay of the primary neutral particle occurs rarely. Anderson and co-workers reported several examples corresponding to the second of the types of \(\tau\)-meson described by Rochester and Butler; as mentioned earlier, a photograph corresponding to this type was interpreted as the decay of a charged meson with a mass of about \(700\,m_e\) into a charged meson of smaller mass and into one or several neutral particles.

The results of Brown and others have been confirmed in a recent work by Harding \(^{109}\), who exposed photographic plates beneath \(3\) m of ice on the Jungfraujoch. Harding found two cases in which a particle with a mass of about \(1000\,m_e\), after stopping in the emulsion, decayed into three charged particles, the lines of their motion lying in one plane. A detailed analysis shows that the features of the tracks agree with the assumption of spontaneous decay into three charged \(\pi\)-particles.

From the data obtained by Harding, in one case it is possible to measure the total kinetic energy of the secondary particles; a value was found agreeing with the data of Brown and others, namely \(\simeq 80\) MeV. If the secondary particles are \(\pi\)-mesons, then this value of the energy corresponds to the mass of the primary \(\tau\)-meson

of the order of \((985 \pm 20)m_e\). Thus, the available data are consistent with the assumption of three types of decay. These decay schemes are represented by the following equations:

\[ 1)\quad \tau^0 \to \pi^+ + \pi^- + \pi^0 \]

Rochester and Butler, type 1

or

\[ \tau^0 \to \pi^+ + \pi^-, \]

\[ 2)\quad \tau^+ \to \pi^+ + \pi^0 + \pi^0 \]

Rochester and Butler, type 2

or

\[ \tau^+ \to \pi^+ + \pi^0, \]

\[ 3)\quad \tau^+ \to \pi^+ + \pi^+ + \pi^- \quad \text{Brown et al.} \]

It should be noted that the first four equations are of a very speculative character.

A number of experimenters studied the nature of mesons formed in nuclear disintegrations produced by particles of cosmic rays (protons and high-energy \(\alpha\)-particles). It was established that \(\tau\)-mesons sufficiently stable to come to rest in solid matter are formed in nuclear disintegrations comparatively rarely in comparison with \(\pi\)-mesons. Three cases of this type were observed at an altitude of 3300 m by Brown and others and by Harding under considerable thicknesses of matter; it is quite possible that such particles in this case are formed only with large kinetic energy. Then their observation is possible only when a considerable mass of matter surrounds the photographic plates. In the cases described by Rochester and Butler and by Anderson and others, the lifetime of the particles is hardly less than \(10^{-10}\) sec, while in the case given by Brown and others it is not less than \(10^{-12}\) sec.

Fig. 39. Apparatus of Alikhanian, Alikhanov, and Weisenberg for determining the mass of charged particles of cosmic rays.

9 (2). Varitrons

The above-mentioned experiments of Alikhanyan and others110, 111 were carried out at an altitude of 3250 m with the aid of an apparatus shown schematically in Fig. 39. Charged particles of cosmic rays, moving in directions making small angles with the vertical, passed through rows of counters \(C_1\) and \(C_2\).

Observing the discharges in the individual counters, one can determine the direction of motion of the particles. After passing through row \(C_2\), the particle moves between the poles of a permanent magnet producing a field of about 7000 gauss.

The particle is deflected so that it enters counter row \(C_3\), which does not lie in the direction of the initial motion. From the curvature of the path one can determine the particle momentum, with an accuracy governed by the finite dimensions of the counters.

After passing through the magnetic field, the particles traverse lead plates placed between rows \(C_3\) and \(C_4\); \(C_4\) and \(C_5\). By measuring the thickness of lead traversed by the particles before stopping, one can determine their range. The accuracy of the range determination is limited by the thickness of the lead plates. Assuming that the particles are stopped solely as a result of ionization energy losses, one can in principle, by combining both observations, determine the rest mass of the particle.

Fig. 40. Typical result of Alikhanyan et al.

Owing to the finite thickness of the lead plates, the values of the deflections of particles of one mass, stopped in a definite layer of lead, will be distributed as shown in Fig. 40, a. In interpreting their experimental results the authors concluded that there exist sharp “breaks” in their distribution curves.

definitions and, as a consequence of this, the existence of many types of charged mesons, which the authors called “varitrons.” This name indicates the diversity of the rest masses of the particles. A typical example of one of the observed distributions is shown in Fig. 40, б.

In a preliminary communication recently made by Brode \(^{55}\), the results are set forth of an experiment analogous to that described above. In Brode’s experiments the particle momentum was determined from the curvature of the trajectory in a Wilson chamber placed in a magnetic field; the stopping of the particles was studied as they passed through lead plates located in the Wilson chamber. In addition to \(\mu^+\)- and \(\mu^-\)-mesons and protons, Brode observed six positively charged particles with a mass of about \(1000\,m_e\). However, he has recently come to the conclusion that these six particles are also fast protons.

The results of Alikhanyan and his collaborators are in contradiction with the data obtained by Frascinetti \(^{80}\) and other authors, whose experiments were discussed earlier *).

It should be noted that in experiments with counters it is difficult to be guaranteed against the influence of unforeseen processes which may cause discharges in the counters. In the experiments of Alikhanyan and others it is possible, for example, that some cases were caused by particles moving upward. Such particles are sometimes produced in nuclear collisions of fast protons and neutrons passing through the surface layers of the earth; it is known that such particles have an appreciable intensity (Camerini et al. \(^{44}\)).

A second possible source of errors in these experiments is the nonionization energy loss of the main flux of particles directed downward. Some of them may suddenly be stopped as a result of nuclear collisions. On the other hand, electrons emitted in the spontaneous decay of a \(\mu^+\)-particle may cause a discharge in one of the counters of the lower row and, consequently, imitate an increase in range. In consequence of these and other possible processes, as well as the small statistical accuracy of the observations obtained so far and the absence of confirming results obtained with the aid of analogous apparatus, it is reasonable to treat the mentioned data with great caution \(^{112}\).

Brode’s experiments make it possible to carry out a more detailed investigation of the tracks of particles and of the physical processes occurring in the apparatus. It is also possible to eliminate some ambiguities which occur in experiments with counters. However, in this case too, particles stopping in the lead plates may be a source of secondary processes which will not be noticed.

*) The data obtained by Alikhanyan, Alikhanov, and collaborators are also in contradiction with the results of a number of works by Soviet authors \(^{126}\).

9 (3). Conclusions

The question of the existence of mesons of types other than the $\pi$- and $\mu$-particles is of great importance for the development of nuclear physics. The results presented above indicate the existence of particles of other types, sufficiently stable to come to rest in dense matter before they decay “in flight.”

However, they are encountered more rarely than $\pi$-particles. In order to establish the properties of $\tau$-particles and to remove doubts about their existence, it is extremely important to improve the accuracy and reduce the statistical errors of observations. This will help to lessen the difficulties encountered in constructing a satisfactory meson theory, which arise from the lack of precise knowledge. As was indicated at the beginning of the article, the discovery of the $\pi$-meson became possible soon after the sensitivity of the photographic method was increased. Consequently, one may say that there remains the conceivable possibility of the existence of other types of particles with even shorter lifetimes than the $\pi$- and $\tau$-mesons, whose observation presents still greater difficulties.

10. FORMATION OF MESONS IN THE ATMOSPHERE

As a result of the discoveries of the last five years, it seems possible to give a clear picture of the basic processes accompanying the passage of cosmic rays through the atmosphere. It is unlikely that the present picture will be preserved in its entirety; on the contrary, numerical calculations show that many details still require explanation. The study of these details may lead to the discovery of new fundamental phenomena, and various surprises may be expected along this path. Nevertheless, it should still be assumed that the most important features of the present picture are correct.

10 (1). The primary component of cosmic rays

The discoveries of Freier and others113 and of Bradt and Peters114 showed that, in addition to high-energy protons, which constitute a significant fraction of the primary radiation, it also contains a large number of heavy nuclei. Microphotographs X–XI show the track of one such particle, recorded in a photographic plate exposed at an altitude of more than 30 km.

Figure 41 presents the preliminary results of Bradt and Peters on the study of the mass spectrum of particles of the primary component. It follows from Fig. 41 that about 55% of the particles of the primary radiation are nuclei heavier than protons.

Bradt and Peters recently pointed out that in the mass spectrum of the primary component there are considerable gaps; in particular, the relative contribution of Li, Be, B, and F is small compared with the fractions of neighboring elements. This fact is interesting not only in itself; it also proves that the majority of primary particles do not undergo nuclear collisions while passing through interstellar space. On the other hand, the detailed structure of the mass spectrum remains uncertain (see, for example, micrograph XII). All theories of the origin of cosmic rays must explain these features of the primary component.

Fig. 41. Distribution of heavy particles of the primary component of cosmic rays by charge (Bradt and Peters^114).

Owing to the existence of the earth’s magnetic field, a particle possessing an energy greater than a certain minimum energy, which is a function of latitude, can enter the atmosphere at a given magnetic latitude. For example, for \(50^\circ\) north latitude this minimum energy for protons is equal to \(1500\) Mev. The energy of heavy particles is limited by analogous circumstances, but depends essentially on the value of

\[ \frac{Ze}{M}, \]

where \(Ze\) is the charge and \(M\) is the mass of the particle.

A sufficiently satisfactory approximation is the assumption that, for elements with average atomic weight,

\[ \frac{Ze}{M} \]

is equal to one half of the corresponding value for the proton; under this assumption the minimum energy of heavy particles is equal to \(500\) Mev per nucleon. Therefore the minimum energy of the nuclei entering into the composition of the primary component increases with their mass. Consequently, if we restrict our consideration to particles with energy greater than a certain value (say, \(10^{11}\) Mev), then heavy nuclei will make a considerably larger contribution than to the total particle flux. A more detailed investigation of this question depends on determining the energy spectrum of the particles of the primary component; the solution of this problem is of great interest for solving the problem of the origin of cosmic rays.

10 (2). Disintegrations of heavy particles of the primary component

Because heavy particles carry a large charge, they lose much energy to ionization and have a large effective cross section for interaction with nuclei. As a result, they rarely penetrate to depths below 18 km. Further, owing to the high probability of collisions with nuclei, heavy particles rarely reach the end of their range before disintegrating because of collisions; thus, the particle track shown in microphotographs X–XI is an exception. There is a great variety of types of nuclear explosions occurring as a result of collisions of high-energy heavy particles (Bradt and Peters[^114]); some examples are reproduced in microphotographs IX and XII. In some cases the incident nucleus disintegrates completely into its constituent nucleons. In other cases the disintegration is much less complete, apparently because of a large impact parameter (see microphotograph XII). Collisions sometimes lead to the formation of showers of $\pi$-mesons, analogous to the formation of showers

Fig. 42. Schematic representation of processes occurring in the atmosphere.

neutrons, protons, and α-particles moving with relativistic velocities. Since a large number of nucleons collide simultaneously, the number of mesons in such showers may be very large. As a result of processes of this type, besides primary protons, showers of relativistic nucleons also move simultaneously through the atmosphere. This phase in the development of secondary processes is shown in Fig. 42, a.

10 (3). Origin of the hard and soft components

Individual fast nucleons can penetrate to considerably greater depths in the atmosphere than heavy nuclei. However, as a result of nuclear collisions their intensity decreases exponentially with the mass of air traversed. Particles interacting with nuclei produce disintegrations and showers of fast charged π-mesons, many of which have energies below 1000 MeV. Because of their short lifetime, π-particles, when moving through the atmosphere, usually decay “in flight” after traveling a distance of less than 100 m from the point of their formation. In such decay μ-mesons are produced, constituting the main part of the hard component of cosmic rays.

Nuclear explosions are also accompanied by the emission of neutral π-mesons with a very short lifetime. The spontaneous decay of these particles into photons, and the subsequent cascade multiplication of electrons and photons due to pair production and bremsstrahlung, leads to the formation of the main part of the “soft” component. Consequently, both the hard and the soft components are produced in the same nuclear processes. The energy distributions of charged and neutral π-particles are very close to one another. The number of neutral particles is approximately equal to half the number of charged mesons; therefore almost the same fraction of energy passes into the hard and soft components, which is in agreement with Rossi’s observations^62. All these processes are represented schematically in Fig. 42, b.

We may suppose that many of the fast nucleons produced in the disintegration of “primary” heavy nuclei of high energy are capable of producing showers of π-mesons. If this is so, then this process is responsible for the formation of broad penetrating showers consisting of many hundreds of π-mesons, accompanied by soft radiation. In the collision of a primary nucleus, many nucleons are also formed. Some of these nucleons subsequently produce, in the atmosphere, showers of penetrating particles, appearing as if simultaneously; this apparent simultaneity is a consequence of the fact that their appearance at different depths cannot be traced with ordinary apparatus. Broad penetrating showers may be formed—

...both primary heavy nuclei and primary protons of sufficiently high energies. If an exact measurement is made of the distribution of particles of the primary component by charge and energy, it will prove possible to estimate the relative contribution of both processes.

There are some data indicating that the direct formation of charged and neutral $\pi$-particles in nuclear explosions of high energy is accompanied by the birth of $\tau$-mesons of considerable energies with a frequency of the order of 1% of the frequency of appearance of $\pi$-particles. These mesons, at least in some cases, can spontaneously decay into $\pi$-particles with a lifetime of about $10^{-10}$ sec.

High-energy $\mu$-mesons, owing to their weak interaction with nuclei, can penetrate to great depths underground. Sometimes, in interacting with nuclei, they can produce nuclear explosions accompanied by the emission of showers; however, it is possible that such an interaction has the character of an electromagnetic interaction with the protons of the nucleus.

The downward-directed flux of charged particles and photons at all depths in the atmosphere is accompanied by a flux of “neutrinos”—neutral particles with a small rest mass. At present there are no data on the fate of “neutrinos.”

11. PROBLEMS AND PROSPECTS

Experiments carried out during the last three years have established that $\pi$-mesons have properties close to those predicted for “heavy quanta.” These particles are formed in nucleon–nucleon collisions; they interact with all or almost all nucleons with which they collide; if they are stopped in a solid substance, then, despite the short lifetime $\simeq 10^{-8}$ sec., they usually have time to interact with the nuclei of all elements (even with hydrogen) before decay occurs. Therefore, for a time it seemed that, by modifying Yukawa’s original theory, one could create a satisfactory meson theory that would consistently describe the particles and their relation to nuclear forces.

For this purpose numerous variants of Yukawa’s theory were developed; in the mathematical formalism of these theories the meson field was characterized either by a scalar (the original theory), or by a vector, or by a pseudoscalar (terms depending on spin were added to the terms of the original “scalar theory” of the forces acting between two nucleons); many other variants were also developed. Recent experiments on the production of $\pi$-mesons by $\gamma$-rays, on the capture of $\pi$-particles by gaseous hydrogen, and also the scheme of decay of the $\pi^0$-particle into two photons give important information proving that many variants of meson theory are incompatible with the facts described.

Despite the considerable progress resulting from new discoveries, the question remains whether the basic features of Yukawa’s original idea are essentially correct. Although it is possible to identify the \(\pi\)-mesons with the “heavy quanta” of the nuclear field, in a formalism developed along such lines there is no place for \(\mu\)-mesons. These particles have a mass of \(215\,m_e\); they interact only weakly with the nucleus, so that they can pass through hundreds of nuclei without disintegrations; they have half-integral spin and decay with the emission of an electron and, probably, two neutrinos; they have a lifetime of \(2.1\cdot 10^{-6}\) sec.; negative mesons, when stopped in elements with \(Z\) greater than 15, interact with nuclei before decay. In such an interaction a neutrino and a neutron are emitted. The inadequacy of our present notions is well illustrated by the fact that they can hardly explain the existence and properties of \(\mu\)-mesons.

These difficulties already existed when we had not yet encountered the additional complications associated with the existence of other types of particles. However, additional evidence for the existence of \(\tau\)-mesons indicates that the situation is considerably more complex than was formerly supposed; there exist charged and neutral particles with a mass of about \(1000\,m_e\), which, at least in some cases, decay with the emission of \(\pi\)-particles.

Table IV presents the most important properties of the various types of particles which the theory must explain.

We have no grounds for assuming that the particles included in Table IV exhaust all possible forms of mesons. For example, it is known that neutral \(\pi\)-particles have a lifetime of less than \(5\cdot 10^{-14}\) sec. With the experimental means at our disposal it will be extremely difficult to establish the independent existence of many forms of mesons. Even without considering such possibilities, it is clear that any theoretical conception must explain the diversity and properties of the mesons presented in Table IV, although at the present stage of our understanding of this subject this diversity appears as a sequence of arbitrary, almost unrelated facts, which in reality, however, must be links in a single chain of phenomena unknown at the present time.

“Experimental sciences,” says Clerk Maxwell, “are continually discovering for us new data concerning the processes occurring in nature; and we must have new appropriate conceptual forms for these data.”

It is possible that important data still remain unknown which must open new paths toward the solution of the problem of mesons. Therefore, new proton-

Table IV

Types and properties of mesons discovered experimentally*)

Type	Reference	Mass in $m_e$	Mean lifetime in vacuum	Spin	Decay scheme
$\mu^+$	Anderson	$212 \pm 4$	$2.15 \cdot 10^{-6}$ sec.	$\left(\dfrac{1}{2}\right)$	$\mu^+ \to e^+ + \nu + \nu$
$\mu^-$	—	$212 \pm 4$	$2.15 \cdot 10^{-6}$ sec.	$\left(\dfrac{1}{2}\right)$	$\mu^+ \to e^- + \nu + \nu$ $\mu^- + x_A^Z \to x_A^{Z-1} + n + \nu$ (in heavy materials)
$\pi^+$ $\pi^-$	Lattes et al.	$276 \pm 4$ $278 \pm 4$	$1.6 \cdot 10^{-8}$ sec. $1.0 \cdot 10^{-8}$ sec.	$(0)$ $(0)$	$\pi^+ \to \mu^+ + \nu$ $\pi^- \to \mu^- + \nu$ $\pi^- + x_A^Z \to$ “star” $\pi^- + p \to \pi^0 + n$ $\pi^- + p \to h\nu + n$ (in hydrogen)
$\pi^0$	Bjorklund et al.	$\sim 270$	$< 5 \cdot 10^{-14}$ sec.	$(0)$	$\pi^0 \to 2h\nu$
$\tau^\pm$	Rochester and Butler	$\sim 903$	$\sim 2 \cdot 10^{-10}$ sec.	?	$(\tau^\pm \to \pi^\pm + \pi^0)?$ $(\tau^\pm \to \pi^\pm + \pi^0 + \pi^0)?$
$\tau^0$	Rochester and Butler	$903$	$2 \cdot 10^{-10}$ sec.	?	$(\tau^0 \to \pi^+ + \pi^-)?$ $(\tau^0 \to \pi^+ + \pi^- + \pi^0)?$
$\tau^+$	Brown et al.	$1033$	$10^{-12}$ sec.	$(0)$	$(\tau^+ \to \pi^+ + \pi^+ + \pi^-)$

*) $\nu$ is a particle which is not a proton and has small mass. Properties not yet definitively proved, or which are the consequence of various assumptions, are shown in parentheses. The difference in the lifetime values of the $\pi^+$ and $\pi^-$ particles has not been definitively established.

synchrotrons that are under development. Particles produced in synchrocyclotrons currently in operation do not possess enough energy, in accordance with the conservation law, to create particles with a mass of about \(1000\,m_e\). However, the design of the Birmingham proton synchrotron is calculated for obtaining protons with energies greater than \(1000\) MeV, which will make it possible to obtain artificial \(\tau\)-mesons.

The machines designed at Brookhaven and Berkeley, based on an analogous principle, are calculated, respectively, to accelerate protons to energies of 3000 and 6000 MeV. However, even if the new machines are successfully realized, there will remain a need for a natural source for studying nuclear transformations produced by particles of high energies. Experiments carried out with the aid of a controlled Wilson chamber in a magnetic field, and the successes of the new method for determining the energy of fast particles in photographic emulsion, make it possible to study in detail the splittings produced by protons and \(\alpha\)-particles with energies in the interval from \(10^9\) to \(10^{11}\) eV, and sometimes even by particles of still higher energy. As a result of these successes, it is impossible to draw a sharp boundary separating nuclear physics from the physics of cosmic rays. The latter must be regarded as nuclear physics in the region of ultrahigh energies.

In view of the possibilities of such technical development and the great concentration of human and material resources around the study of processes occurring at high energies, one may hope for a rapid development of our ideas about mesons. These particles, which decay when free, play an important role in ensuring the stability of nuclei.

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Microphotograph I. Four examples of successive $\pi$-$\mu$-$e$ decay. The increase in the density of grains at the end of the $\mu$-meson range is clearly visible, as is the low density of grains in the electron tracks.

To the article by C. F. Powell, “Mesons”

Microphotograph II. Splitting of nuclei of light elements present in the emulsion (carbon, oxygen, and nitrogen) upon capture of $\pi$-particles.

For the article by S. F. Powell, “Mesons”

Microphotograph III. Splitting of nuclei of heavy elements upon capture of π-particles.

For the article by C. F. Powell, “Mesons.”

Microphotograph IV. A splitting produced at point \(A\) by a particle (track \(p\)) moving with relativistic velocity. Two very slow particles and a negative \(\pi\)-meson were emitted. The latter stops at point \(B\) and produces a secondary splitting. In addition, one unidentified strongly ionizing particle was emitted, probably a proton.

To the article by S. F. Powel, “Mesons.”

Microphotograph V. A nuclear explosion accompanied by the emission of a \(\pi^+\)-particle. Two portions of the particle’s track are shown, meeting at point \(a\). The \(\pi^+\)-particle undergoes the successive \(\pi^+ - \mu^+ - e^+\) decay.

Microphotograph VI. Characteristic double star. One of the shower particles, created in the nuclear explosion, undergoes secondary splitting.

For the article by S. F. Powell, “Mesons.”

Microphotograph VII. As a result of a nuclear collision at point \(A\), the fast particle (track \(P\)) produced a shower of seven particles. Shower particle 3 created a secondary shower at point \(B\). The shower at point \(A\) is produced, possibly, as a result of the interaction of a proton with a proton.

To the article by S. F. Powell, “Mesons”

Microphotograph VIII. A high-energy α-particle, whose track is visible in the upper left corner of the microphotograph, interacts with a nucleus and produces 35 shower particles, most of which move in a narrow cone.

To the article by C. F. Powell, “Mesons”

Microphotograph IX. An aluminum nucleus \((Z = 13 \pm 2)\) undergoes a collision, as a result of which six \(\alpha\)-particles are emitted, moving inside a narrow cone with approximately equal velocities. It is possible that they belong to the primary nucleus.

For the article by C. F. Powell, “Mesons”

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Microphotographs X–XI. Successive sections of the track of an iron nucleus are bent in the lower right. The break in the track between sections 7 and 8 is explained by the strong scattering of an $\delta$-electron, with a decrease in the electron energy.

For the article by S. F. Powell, “Mesons.”

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\((Z = 26 \pm 2)\), which enters the emulsion in the upper left corner and [[unclear: word beginning “rema-”]] is due to the motion of the particle in the air gap between two emul- [[unclear: continuation missing]] the particle’s velocity, as well as other features accompanying capture by the nucleus.

Microphotograph XII. A sulfur nucleus \((Z = 16 + 1)\) collides in the emulsion with a silver or bromine nucleus. As a result of the collision, a fluorine nucleus and 25 shower particles—protons and \(\pi\)-mesons—are formed.

For the article by S. F. Powell, “Mesons”

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