OBSERVATION OF COSMIC RADIATION USING PLATES SENSITIVE TO ELECTRONS

R. Brown, U. Camerini, P. H. Fowler, H. Muirhead,
C. F. Powell and D. M. Ritson*)

Recently we have made observations using new emulsions intended for nuclear research and described by Dr. Berriman[^1]. These emulsions, which make it possible to detect the tracks of particles with charge \(e\) even in the case of minimum ionization, represent a technical improvement of great importance. They enable us to penetrate considerably more deeply into the nature of nuclear processes than was possible with the old emulsions and, in addition, greatly extend the field of application of the photographic method in solving physical and biological problems. In Part I of the present paper we describe the most interesting phenomena produced by charged mesons and detected in observations of cosmic radiation with the aid of the new plates. These phenomena include cases of disintegration caused by \(\pi^-\)-particles and cases of decay of \(\mu\)-particles. In approximately \(10\%\) of all cases the track of the particle formed in the emulsion in the decay of a \(\mu\)-meson has a length exceeding \(1000\,\mu\). By studying the Coulomb scattering undergone by these particles in the emulsion, it is possible to estimate their energy. A characteristic feature of all the exposed plates is the presence of a large number of tracks with a grain density corresponding to particles situated near the minimum of ionization.

These tracks make it possible very simply to monitor the “fading” (regression) of the latent image, the change in the degree of development with depth, the sensitivity, and also other characteristic properties of the emulsions. In Part II a phenomenon is described which serves as still another proof of the existence of mesons with a mass greater than that of the \(\pi^-\)-particles[^2]. It consists in the fact that a particle with mass (determ—

*) Nature 163, 47, 82 (1949). Translated by V. A. Troitskaya.

... counted grains in the emulsion), equal to \(\sim 1000\,m_e\), emits three charged particles, one of which reaches the end of its path in the emulsion and causes the splitting of a nucleus. We consider that this phenomenon corresponds to the spontaneous decay of a heavy particle. Assuming that the three charged particles are the only products of the decay, the obtained photograph can be analyzed by applying the laws of conservation of mass and energy. Within the limits of measurement error our observations agree with the assumption that the three secondary particles are \(\pi\)- or \(\mu\)-particles. Before considering the correctness of such an interpretation established, it is necessary to study a further number of similar cases. We nevertheless give this preliminary interpretation of the observed phenomenon, since the number of particles of this type, compared with the number of \(\pi\)- and \(\mu\)-particles at moderate altitudes, is small (\(3500\) m).

Moreover, if our assumptions are correct, then, for purely geometrical reasons, only a small fraction of such phenomena can be analyzed by means of the method we used. However, other phenomena of a similar type which may prove less suitable for analysis may nevertheless, in the light of the observations presented here, provide valuable information confirming or refuting the correctness of our assumptions.

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

In the experiments described, plates with Kodak experimental emulsions of type NT4, kindly provided to us by Dr. Berriman, were used. They were delivered to Jungfraujoch immediately after manufacture. Some of them were placed under lead \(10\) cm thick for a period of 8 to 16 days, while the other part was exposed unshielded. The lead was intended to reduce the intensity of the soft component. However, this precaution proved superfluous, since the number of tracks on the unshielded plates was not too large.

The plates were developed at Jungfraujoch immediately after their exposure. In order to determine the most favorable conditions for development, different plates were developed in different ways. In this connection, on different plates, for the same particles, different grain densities in the tracks occur. Owing to the short exposure, the number of events recorded per unit area is comparatively small. However, the greatly increased grain density in the tracks, due to the greater sensitivity of the emulsion, makes it possible to examine the plates under the microscope with a considerably smaller magnification than that used previously. Thus, in searching for mesons we used an objective with tenfold magnification and an eyepiece with sixfold magnification.

Such an arrangement, together with a binocular microscope, gives a total magnification of only 90.

Work at low magnifications makes it possible to speed up the process of examining plates. In the examination of \(300\ \mathrm{cm}^2\) of new plates, many examples were found of related processes in which charged mesons participate.

Disintegrations caused by \(\pi^-\)-particles

We succeeded in finding 30 cases of disintegrations caused by \(\pi^-\)-particles (Fig. 1) and 30 cases of \(\mu\)-decay of \(\pi^+\)-particles. A distinctive feature of the new plates is the large number of tracks of slow electrons that are clearly visible under the microscope. In Fig. 1, for example, two electrons are visible which are associated with the star formed when a \(\pi^-\)-particle is captured by a nucleus.

Electron tracks only in rare cases begin at the end of the track of a \(\pi^-\)-particle, i.e. at the point at which the disintegration occurs (Fig. 2). Thus, among 30 cases of disintegrations caused by \(\pi^-\)-particles, only in three cases are tracks of electrons associated with them visible.

The observed electrons may be attributed to the \(\beta\)-decay of the residual nucleus formed in the disintegration, or, possibly, to internal conversion of \(\gamma\)-rays. If the meson sometimes loses its energy in emitting Auger electrons, then the number of such electrons with energy greater than 15 keV must be small.

Particles with low specific ionization

In addition to phenomena with which we were already familiar earlier, in the new plates we distinguish the tracks of a large number of particles with low specific ionization, passing in the direction from the surface toward the glass. The deflection which they undergo as a result of scattering does not exceed several degrees. These tracks may be attributed to fast particles, most likely electrons and mesons, possessing a specific ionization approximately equal to the minimum ionization value for a particle with charge \(e\). In order to confirm this point of view, a count was made of the grains in 25 tracks of this type, of length greater than \(1000\ \mu\), chosen arbitrarily from plate No. K47. The results of this investigation are presented in Fig. 3. The graph shows the relative frequency of occurrence of tracks with various values of the mean grain density. The plate was taken from a series of plates exposed under lead. It follows from Fig. 3 that there is a sharply separated group of tracks with a mean grain density of 0.22 grain per micron. We believe that this group of tracks is formed by particles whose specific ionization lies near the minimum value.

The observations presented in Fig. 3 can be explained by the fact that the ionizing power of particles whose momentum is greater than \(2mc\) (where \(m\) is the rest mass) changes slowly with change of energy. It follows from Fig. 3 that phenomena due to the “fading” (regression) of the latent image are small, since “fading” leads to a reduc-

Fig. 1. Splitting caused by a \(\pi\)-particle. The photograph shows the tracks of electrons associated with the splitting.

Fig. 2. Splitting caused by a $\pi$-particle.

tion of grain density. If these phenomena were significant, then instead of the sharply delineated group of tracks found, one would have to expect, for particles with minimal ionization, a smeared distribution of grain density corresponding to the presence of tracks of different ages. The tracks under consideration run in the direction

Fig. 3. Histogram showing the distribution of values of the mean grain density in the tracks of particles with small specific ionization.

from the emulsion to the glass. Therefore they can be studied in order to determine the change in the degree of development with depth. The grain density along the tracks was measured as a function of depth in the emulsion, and in Fig. 4 the mean results for 25 tracks are presented. We see that the grain density corresponding to the minimum of ionization changes with depth, in particular for the plate studied, from 23.5 per 100 μ at the surface to 21.5 at the glass. It follows from this that the relative changes in the grain density of a track caused by changes in the degree of development with depth are less than 8%. Moreover, for tracks of particles with small specific ionization, which are of special interest, one can introduce a correction that takes into account the small observed changes.

Fig. 4. Mean values of grain density in tracks of 25 particles with small specific ionization at different depths in the emulsion.

In the study of cosmic radiation by means of plates sensitive to electrons, a large number of long tracks with low grain density are observed. Therefore the methods described above can be used as standard methods for determining:

a) the degree of regression at a given exposure;

b) the degree of development with depth;

c) the density of grains corresponding to the minimum value of the specific ionization, for particles with charge \(e\).

The results presented in Fig. 3 make it possible to draw one further conclusion. The value of the minimum specific ionization of a particle is proportional to the square of its charge. The sharply defined peak in Fig. 3 indicates that most of the fast particles detected in the emulsion have, to within 5%, equal charges. This circumstance indicates with great certainty that this charge must be equal to \(e\).

Decay of \(\mu\)-mesons

We observed the tracks of 100 \(\mu^+\)- or \(\mu^-\)-particles which stop in the emulsion and emit one charged particle possessing a small specific ionization. Fig. 5 reproduces a photomicrograph of such a decay. Phenomena of this type are easily distinguished from the formation of a \(\mu\)-meson in the decay of a \(\pi\)-meson, because the track of a \(\mu\)-meson arising in the decay of a \(\pi\)-meson at rest has a considerably greater grain density. In addition, the particles formed at the end of the range of \(\mu\)-mesons and emitted in a direction approximately parallel to the surface usually have a range in the emulsion of the order of several thousand microns. These particles undergo almost no scattering, and the grain density in their tracks is approximately equal to the grain density corresponding to minimum ionization. This indicates that their charge is equal to the electron charge. Fig. 6 shows a photomicrograph in which a \(\pi\)-particle stops in the emulsion and emits a \(\mu\)-particle with a range approximately equal to \(600 \mu\). In the photograph, a particle with small specific ionization, emerging from the end of the track of the \(\mu\)-particle, is clearly visible.

In the other eight observed cases of this type, the characteristics of all the secondary particles are indistinguishable from the characteristics of particles arising at the end of the range of \(\mu\)-mesons formed outside the emulsion and then entering it. These new observations, together with the evidence obtained in the preceding experiments, constitute one more basis for the supposition that these \(\mu\)-mesons are identical with some of the ordinary mesons of the penetrating component of cosmic radiation, and that \(\pi\)- and \(\mu\)-mesons have an electric charge equal to \(e\).

Approximately 10% of the mesons that stop in the emulsion and are formed outside it produce particles whose track length is greater than \(1000 \mu\). We considered the possibility of determining the momentum of these particles by observing the change in the direction of their motion under the influence of a magnetic field of 50,000 gauss. A simple calculation shows, however, that the deflections will be of the same order of magnitude as the deflections caused by scattering. Therefore the momentum of the particles was determined from the magnitude of the scattering in the absence of ...

Fig. 5. A characteristic example of the track of a particle produced in the decay of a $\mu$-meson and having a small specific ionization.
The track of the secondary particle is given in two parts, which must be joined at the point marked $a$.

Fig. 6. Successive decay $\pi \to \mu \to \eta$. It is usually assumed that the $\eta$-particle arising in the decay of a $\mu$-meson is an electron; however, this assumption still requires final proof. Near the end of the range of the $\mu$-meson, several grains of the track of a secondary particle with small specific ionization can be distinguished, but this particle is not connected with the main event. Several tracks of $\delta$-electrons produced by the $\mu$-meson can also be distinguished. One such track is visible near the decay point of the $\pi^+$-particle. In all cases observed so far, the $\eta$-particle leaves the emulsion.

Fig. 7.

magnetic field.^4 The values given below, which are typical for data obtained by this method, indicate the degree of accuracy that can be obtained in favorable cases: \(15 \pm 3,\ 25 \pm 5,\ 38 \pm 6,\ 42 \pm 2,\ 44 \pm 4,\ 48 \pm 6\ \mathrm{MeV}/c\). Deviations from the mean correspond to probable errors associated with statistical fluctuations. It is natural to suppose that in the coming months we shall find several hundred traces of such particles suitable for measurements, and that these measurements will make it possible to carry out a detailed investigation of the momentum distribution of such particles. The values obtained from the study of the first twenty traces of particles with a range greater than \(1000\,\mu\) indicate that the momentum of the decay particle is not constant.

Of all the \(\mu\)-particles stopped in the emulsion, approximately \(40\%\) do not produce distinguishable tracks of secondary particles. One may suppose either that these particles were negatively charged and were captured by atoms of silver or bromine before the time required for their decay had elapsed, or that we are dealing with events in which the decay particle escapes observation because of the direction of its motion. In order to estimate the number of cases that should be attributed to the latter cause, measurements were made of the lengths of the projections of decay particles onto the plane coinciding with the surface of the emulsion. From the distribution of the values thus obtained one can estimate the total number of \(\mu\)-mesons producing secondary particles. This problem is purely geometrical and can be solved in a manner similar to that used previously in the case of the \(\mu\)-decay of \(\pi\)-mesons.^5 We found in this way that, of all the observed \(\mu\)-mesons, \(65 \pm 10\%\) emitted secondary particles, while \(35 \pm 10\%\) did not give secondary particles. This result is apparently in agreement with the preceding estimate of the fraction of \(\mu^{-}\)-particles stopped in gelatin and silver bromide.

We have already mentioned that observations of disintegrations caused by \(\pi\)-particles indicate that the formation of Auger electrons with energy greater than \(15\ \mathrm{KeV}\) during the “capture by an atom” of a negative meson occurs very rarely. An analogous conclusion can be reached by studying the tracks of \(\mu\)-particles. Among 10 cases in which we can distinguish the track of the fast particle arising in the decay of a \(\mu\)-meson, there is not a single case in which a short track of an electron formed at the point of decay was seen. It is reasonable to suppose that in approximately \(1/3\) of events of this type we observe the spontaneous decay of a negative meson. It follows from this that, for \(\mu^{-}\)-particles as well, the emission of Auger electrons with energy greater than \(15\ \mathrm{KeV}\) in the process of their capture by an atom is a rare phenomenon. It is, of course, desirable to carry out a more detailed investigation of this problem, since in the case of spontaneously decaying \(\mu^{-}\)-particles the picture of this phenomenon is not distorted by the \(\beta\)-decay of the residual nucleus, which sometimes follows the capture of the meson.

Showers of penetrating particles

In studying the “stars” formed in the new emulsions, we found eight cases in which five or more charged particles diverge from a single point; the grain density in the tracks of these particles has a value close to the minimum.

In all cases these particles moved downward in directions making small angles with the vertical, so that their tracks formed a narrow cone. They were accompanied by protons and α-particles of low energy, emitted in arbitrary directions. We suppose that each of these events corresponds to the interaction of a fast particle with a silver or bromine nucleus, as a result of which several penetrating particles are formed, the heavy particles subsequently “evaporating” from the nucleus as a result of its increased “temperature.” These events belong to processes for whose existence evidence has been given in recently published photographs (obtained in Wilson chambers) showing the formation of showers of penetrating particles (Hazen, Yanoshi, Rochester, and other authors).

The existence of such processes was indicated by Hamilton, Heitler, and Peng in their theory of meson formation in the interaction of fast nucleons with nuclei.

Relation between grain density and specific ionization

The possibility of determining the specific ionization of a charged particle from the observed grain density in its track is of great practical importance. We see that curves of the type shown in Fig. 3 enable us to determine the grain density in the tracks of particles with charge \(e\), possessing minimum ionization. Further, from observation on the same plate of the tracks of μ-mesons and protons with long range, we can determine the grain density corresponding to a wide region of values of specific ionization. Having made such determinations, from the range–energy curve for protons one can obtain the value of the energy loss corresponding to the given value of the residual range of a particle of known mass. In this way we obtained the results shown in Fig. 8. The point corresponding to the minimum of ionization on this curve is indicated by the sign \(+\). The ionization in this case was determined by the formula derived by Bloch, under the assumption that the atomic composition of the new emulsion is identical with the atomic composition of Ilford emulsions. Fig. 8 shows an analogous curve for Ilford C2 emulsions. We see that, as a result of the increased sensitivity of Kodak NT4 emulsions, there is a decrease in the resolving power for tracks with a specific ionization of the order of 6 KeV per micron. On Kodak plates the track of a particle in the region of large ionization appears as an almost continuous sequence

of developed grains, which cannot be separately resolved. Thus, in order to determine the masses of particles of the order of \(1000\,m_e\), it is necessary to have tracks of considerably greater length than in the case of less sensitive emulsions. Despite the difficulties encountered in studying the tracks of particles with large specific ionization, the calibration curve shown in Fig. 8 makes it possible to estimate the magnitude of the energy loss experienced by weakly ionizing particles, which is of great importance in connection with the material considered in Part II of the present article.

II. FURTHER EVIDENCE FOR THE EXISTENCE OF UNSTABLE CHARGED PARTICLES WITH MASS EQUAL TO \(1000\,m_e\), AND OBSERVATIONS OF THEIR DECAY

One of the first phenomena discovered in examining plates sensitive to electrons and exposed on Jungfrau Joch is shown in the microphotograph of Fig. 7. There are two centers \(A\)

Fig. 8. Relation between the energy loss of particles and the density of grains in the track. The points marked by circles were obtained in the study of tracks of \(\mu\)-particles with a range exceeding \(2000\,\mu\), and the points marked by crosses—from analogous measurements with protons.

and \(B\), connected by a common track \(t\), from which tracks of charged particles diverge.

Owing to the shortness of the exposure and the small number of decay events occurring in the plate, the probability that the observed trajectories were caused by the accidental superposition, at one point, of tracks

particles not connected with one and the same event is very small and is of the order of \(10^{-7}\). Therefore such a probability may be neglected. Further arguments confirming this assumption are given in the next paragraph. Examination of track \(k\) shows that the particle producing it approaches the center \(A\). The range of the particle in the emulsion exceeds \(3000\,\mu\), and, as it approaches \(A\), there is a continuous increase in the density of grains along the track. Near \(A\) the grain density is indistinguishable from the density of grains produced by a particle with charge \(e\), found on the very same plate. The determination of the direction of motion of the particle, based on counting the grains, is confirmed by observations of small-angle deflections due to Coulomb scattering. These deflections are most frequent near point \(A\), while at points distant from it the scattering is less noticeable. Thus it may be concluded that particle \(k\) approached point \(A\), that it possessed one elementary charge, and that at point \(A\) it reached, or was near, the end of its range. We therefore believe that particle \(k\) excited the whole set of phenomena reflected in the tracks emerging from \(A\) and \(B\). It may be supposed that the particle producing track \(t\) originated in star \(A\) and caused the disintegration at \(B\). In order to analyze this phenomenon, we first attempted to determine the mass of particle \(k\).

Determination of the Mass by Counting Grains

About a year ago, experiments were undertaken in our laboratory with the aim of determining the mass ratio of \(\pi\)- and \(\mu\)-mesons, \(m_{\pi}/m_{\mu}\). This determination was made by counting the number of grains\(^5\) and by studying the scattering of particles through small angles as they passed through the emulsion\(^4\). The values obtained by these methods were, respectively, \(m_{\pi}/m_{\mu}=1.65\pm0.11\) and \(m_{\pi}/m_{\mu}=1.35\pm0.10\). (The indicated error limits in the determination of \(m_{\pi}/m_{\mu}\) from the magnitude of the scattering are smaller than those given in Goldschmidt’s article, for the following reason. Previously, the mass values for different mesons, classified phenomenologically, were given separately. Now, however, it is known that at least the majority of \(\sigma\)-mesons are \(\pi\)-particles, while \(\rho\)-mesons are \(\mu^{+}\)- and \(\mu^{-}\)-particles. The different results can therefore be combined and give values of \(m_{\pi}/m_{\mu}\) with greater statistical accuracy.) The latest experiments carried out at Berkeley indicate that the true value is apparently \(1.33\pm0.02\). This result casts serious doubt on the reliability of the method based on counting grains. However, because of the great advantages of this method and the important conclusions based on it, a series of experiments was undertaken to determine the conditions under which reliable results can be obtained. In the first experiments\(^5\) the two most serious experimental difficulties were caused—

were caused by regression of the latent image and by the change in the degree of development with depth. This forced us to turn to the study only of tracks formed simultaneously and to compare the grain density along the tracks of $\pi$- and $\mu$-mesons of one and the same pair.

As a result of this restriction, the $\pi$-meson tracks suitable for measurements were in most cases shorter than $400\,\mu$. In subsequent experiments it proved possible to obtain considerably more favorable conditions for measurements, thanks to the short exposure time (in this case the effect of regression can be neglected), and also thanks to the method of developing plates used by Dilworth, Occhialini, and Payne$^{7}$, by means of which an approximately identical degree of development with depth was achieved. On plates developed in this way it is permissible to compare the grain density

Fig. 9. Dependence of grain density on range for protons and $\mu$-particles.

in the tracks of unrelated particles. Moreover, it is now known that the majority, and possibly all, of the mesons that form “stars” are $\pi^{-}$-particles,$^{6,8}$ and that the majority of $\rho$-mesons are $\mu^{+}$- and $\mu^{-}$-particles. In determining $m_{\pi}$ and $m_{\mu}$ we therefore made measurements along the tracks of $\pi^{+}$- and $\pi^{-}$-, $\mu^{+}$- and $\mu^{-}$-particles with lengths greater than $1000\,\mu$, and compared the results obtained with the results of analogous measurements along proton tracks. Under these conditions we found that $m_{\pi}/m_{\mu}=1.33 \pm 0.05$. A detailed description of the observations will be published separately, but for the purposes pursued in the present article it is sufficient to note that the results are apparently in good agreement with the results obtained by other methods. From this it may be concluded that, using Ilford C2 emulsion under the new conditions, reliable results can be obtained. We saw that with the new Kodak emulsions there were achieved

conditions of equal development with depth and absence of regression. Therefore we tried to measure the mass of the particles by methods analogous to those used for Ilford plates. Fig. 9 shows the results obtained from observations of four proton tracks and four \(\mu\)-particle tracks found on one and the same plate. In this graph the number of grains per unit length of track is plotted as a function of the values of the residual range. The mean values for tracks of one type are shown by solid lines. The ratio of the masses of the two types of particles can be derived by comparing the residual-range values at which the grain densities are the same. The result obtained in this way is

Fig. 10. Dependence of grain density—range for particle \(k\), protons, and \(\mu\)-particles.

\[ m_\mu = (220 \pm 20)\,m_e. \]

Using analogous methods, we estimated the mass of particle \(k\). The results of the measurements are presented in Fig. 10. In this graph are shown the mean values of the grain density in the tracks of four \(\mu\)-mesons and four protons, as well as the corresponding results for particle \(k\). All the tracks considered were recorded on one plate.

Table I gives the values of the mass of particle \(k\), obtained by comparing the grain density in the track of this particle with the mean curve for protons. All the values obtained in this way are independent, and their mean is equal to \(m_k = (1080 \pm 160)\,m_e\). The limits of the error indicated above were derived as follows. We compared the grain density in the tracks of four separate protons with the mean curve for the same particles (see Fig. 9) and thus obtained a certain number of independent values for the apparent mass of each of these particles. The distribution of these values allows us to calculate the “probable error” associated with the mass determined

from observations on any given track, and express it as a percentage of the apparent mass of the particle. It is then assumed that the relative error for the calculated mass of particle \(k\) has the same value. Studying, by means of the methods described earlier,\(^{4}\) the scattering of particles through small angles, we also determined the mass \(m_k\) and obtained the value \(m_k=(1800\pm400)\,m_e\). If the true value of the particle mass is \(1080\,m_e\), then the probability that the value obtained from the observation of scattering will be equal to or greater than \(1800\,m_e\) is \(1/4\). In view of the large statistical fluctuations characteristic of the scattering phenomenon, we consider the measurements based on grain counts to be more reliable.

Table I

Ratio \(m_p/m_k\) (i.e., of the proton mass to the mass of particle \(k\)), obtained by counting the grain density

From these observations it seems evident that the true value of \(m_k\) lies between 700 and \(1800\,m_e\), and we consider it very probable that this mass is substantially smaller than the proton mass. Indeed, in Fig. 10 it is seen that each individual point giving the grain density in track \(k\) at a certain value of the residual range lies below the corresponding points for each of the four protons.

Scattering \(B\)

Tracks \(c\) and \(d\)—of two particles emitted from point \(B\)—correspond to protons or heavier particles which, in our opinion, are formed as a result of the disintegration caused by particle \(t\). This particle, passing through the emulsion, underwent frequent scattering, indicating that it had a low velocity. The observational results agree with the supposition that it reaches the end of its range at point \(B\). The only known slow charged particle capable of producing a disintegration of the star-\(B\) type is the \(\pi^{-}\)-particle.\(^{6,8}\) Therefore we assume that at point \(A\) a negative meson of mass \(286\,m_e\) was created, which, on reaching the end of its range, caused disintegration \(B\).

Transformation A

In order to explain transformation \(A\), we made a detailed study of the tracks of the emitted particles. Of the two tracks \(a\) and \(b\), the first has a length in the emulsion greater than \(2000\,\mu\) and ends at the surface, while the second has a length of \(116\,\mu\) and ends on the glass. The grain densities in both tracks are equal, within the limits determined by statistical fluctuations.

The mean grain density in the long track \(a\) is equal to 49.0 grains per \(100\,\mu\), i.e. 2.17 times greater than the value corresponding to the ionization minimum for a particle with charge \(e\). Since we do not allow the existence of fractional values of the elementary charge, we arrive at the conclusion that both particles which formed tracks \(a\) and \(b\) had a charge equal to \(e\). In order to determine the possible values

Fig. 11. Dependence of the energy-loss magnitude of a particle with charge \(e\) on the ratio \(E/m\), where \(E\) is the kinetic energy and \(m\) the particle mass; both quantities are measured in MeV.

of the energies of the particles which formed tracks \(a\) and \(b\), we calculated, from the formula of Halpern and Hall\(^9\), the variation of the specific ionization of a particle possessing charge \(e\) as a function of the energy, assuming that the atomic composition of the new emulsion is identical with that of Ilford C2 plates. The formula used by us is a modification of Bloch’s formula. It is applied to particles moving in a solid medium and gives results in good agreement with experiment for particles of low energy. The results obtained are shown in Fig. 11. In the graph, the specific ionization is plotted as a function of \(E/m\), where \(E\) is the energy and \(m\) the mass of the particle, with both quantities measured in MeV. In Fig. 11 we determined the possible energy values of particles \(a\) and \(b\) corresponding to the observed grain densities in the tracks, assuming

consequently, that the particles are protons, \(\pi\)-mesons, \(\mu\)-mesons, or electrons. The results obtained are collected in Table II. The transformation caused in \(A\) by particle \(k\) can be explained in two ways. We may assume either that the particle was captured by the nucleus, or that it decayed spontaneously. Using the measured values of the particle mass, one may, on the basis of the law of conservation of mass and energy, suppose that at the end of its path in the emulsion the particle was captured by a nucleus, which led to the emission of two protons of high energy and a \(\pi\)-particle.

Table II

Values of the energy and momentum of the particle producing track \(a\), derived from the observed grain densities and scattering under various assumptions about the mass of the particle

However, the almost certain liberation in the nucleus of such a large amount of energy will lead to the evaporation of many nucleons (a process usually observed on plates exposed to cosmic radiation). Thus, the two high-energy protons will represent only two components of a complex star (it should be noted that we cannot suppose that particle \(k\) was captured by one of the rare nuclei of heavy hydrogen contained in the gelatin. In such an interaction the algebraic sum of the charges of the two initial particles must be equal to \(0\) or \(2e\), and the alge-

...the algebraic sum of the charges of the newly formed particles is equal to \(e\) or \(3e\)). Below we shall see that there are still other objections which do not allow one to accept the hypothesis that tracks \(a\) and \(b\) were formed by protons or by heavier nuclei with charge \(e\).

From the arguments given it follows that if we are to describe the transformation using particles whose existence has already been established, then we must attribute tracks \(a\) and \(b\) either to electrons or to \(\pi\)- or \(\mu\)-mesons. Considering the first of these possibilities, we must suppose that the electrons possess an energy greater than the energy corresponding to minimum ionization, namely greater than 1000 MeV. The observed ionization corresponds to a lower energy limit of 300 KeV. A particle with such an energy would have a range in the emulsion of only 100 \(\mu\) and would undergo frequent scattering. Therefore the assumption that particles \(a\) and \(b\) were electrons is not consistent with the law of conservation of energy and may be rejected. Thus it remains to decide whether the tracks were formed by \(\pi\)- or \(\mu\)-mesons.

If particles \(a\) and \(b\) were mesons, then in order for the law of conservation of mass and energy to be satisfied we must assume that their kinetic energies were 27 MeV or 37 MeV, respectively for the case of \(\mu\)- or \(\pi\)-mesons (see Fig. 11). In any case it is very difficult to reconcile the observations with the assumption that the particles were emitted as a result of the release, in the nucleus, of an energy corresponding to the rest mass of particle \(k\). We are therefore forced to consider the possibility of explaining the observations by the spontaneous decay of this particle.

Assumption of the spontaneous decay of the \(k\)-particle

In studying the assumption that the transformation in \(A\) corresponds to the spontaneous decay of particle \(k\), we must determine the relative directions of motion of the three emitted particles. For this purpose it is necessary to determine the shrinkage of the emulsion, i.e. the ratio \(S\) of the thickness of the emulsion at the time of exposure of the plate to its thickness after development, fixing, and drying. We measured this quantity by studying the tracks of \(\alpha\)-particles formed in the emulsion by accidental radioactive contaminations. Among such “stars,” some can be identified as having been produced by an atom of radiothorium, from which a thorium \(\alpha\)-particle \(C'\) is emitted. The shrinkage was measured by determining the lengths of the projections of the corresponding tracks on the surface of the emulsion and their apparent angles of “entry.” The value of the shrinkage found in this way was \(S = 2.7 \pm 0.1\). Knowing the value of \(S\), in favorable cases one can determine the initial direction of a track in the emulsion before development with an accuracy of the order of \(1^\circ\). This can be done by observing the apparent angle of “entry” of the particle and the direction of the projection of its track on the plane defined by the surface of the emulsion. With the aid of these methods it was found that the initial direc...

directions of motion of the three particles were coplanar. The deviation of the direction of motion of any particle from the plane defined by the directions of motion of the other two particles is less than \(4^\circ\). The error with which this determination was made is due chiefly to the fact that the length of track \(t\) is small and that the particle producing it had a low velocity and often underwent scattering. The angles between the directions of motion of the particles in the common plane are shown in Fig. 12. The observed coplanarity is the basis for the assumptions that the three particles arise as a result of the spontaneous decay of a \(k\)-particle at the end of its path in the emulsion, that they are the only products of its decay, and that in this decay there is no emission of neutral particles, which

Fig. 12. Reproduction, made with the aid of a projection microscope, of the event shown in Fig. 8. The true angles \(\alpha\) and \(\beta\), measured in the plane common to all three tracks, are equal to \(\angle \alpha = 9.8^\circ\); \(\angle \beta = 76.6^\circ\).

escape observation. It follows from this that the vector sum of the momenta of the three particles must be equal to zero. If we correctly assign track \(t\) to a \(\pi^-\)-particle, then from the observed range, equal to \(45\,\mu\), it follows that the kinetic energy of emission was \(1.04\ \mathrm{MeV}\). The corresponding value of the particle momentum is \(17.5\ \mathrm{MeV}/c\). Next, from the observed directions of motion, the momenta of the particles producing tracks \(a\) and \(b\) were determined. They proved to be \(98 \pm 5\) and \(104 \pm 5\ \mathrm{MeV}/c\), respectively. These values should be compared with the values corresponding to electrons and mesons, given in Table II and derived from the observed grain density in the tracks. We see that the values indicated in Table II for the momenta of the two particles, on the assumption that these particles are electrons, are many times larger. It follows that the momentum balance is far from being satisfied if tracks \(a\) and \(b\) are attributed either to protons or to electrons. Moreover, the momentum values derived from observations of particle scattering do not agree with the results obtained from the grain count if it is assumed that these particles are either electrons or protons (see Table II).

Agreement among the series of values for the mesons is striking and serves as a strong argument in favor of the assumption of spontaneous decay of the \(k\)-particle.

Let us note that, if the obtained result is regarded as accidental, then such an accident has occurred as a result of an extremely rare coincidence of such mutually unrelated characteristics as the coplanarity of the directions of motion of the particles, the range of particle \(t\), and the specific ionization produced by the particles that formed tracks \(a\) and \(b\). The values of the momenta of the particles forming tracks \(a\) and \(b\), determined by three different methods, agree within the limits of measurement errors with the assumption that spontaneous decay of the \(k\)-particle took place, as a result of which either \(\mu\)-mesons or \(\pi\)-mesons were formed. We can carry out a further check of our assumptions by calculating the values of the rest mass of the particle \(k\) that correspond to the two different assumptions. The results obtained are given in Table III. (In calculating the energies of the particles forming tracks \(a\) and \(b\), it is assumed that track \(t\) was formed by a \(\pi^-\)-particle with momentum \(17.5\ \mathrm{MeV}/c\); knowing the relative directions of motion of the three emitted particles, one can determine the momenta of the remaining two particles and, consequently, also the energies corresponding to the masses that would be adopted.)

Table III

Determination of the mass of particle \(k\) for two proposed decay schemes

From Table III it is seen that the assumption of two \(\mu\)-mesons gives, for the rest mass of the \(k\)-particle, the value \(869\,m_e\), while the assumption of two \(\pi\)-mesons gives the value \(985\,m_e\). If it is assumed that different particles arise in the decay, namely one \(\pi\)- and one \(\mu\)-meson, then an intermediate value is obtained, approximately \(925\,m_e\). Owing to the errors in the direct determination of the value of \(m_k\), this result does not make it possible to decide the question of the decay scheme. If one attempts to explain the transformation considered by us with the aid of previously known particles, then four variants of interpretation of the nature of the particles forming tracks \(a\) and \(b\) are possible. They are considered schematically in Table IV.

Case 3 in Table IV is the least probable for the following reasons. If track \(a\) belongs to a \(\pi\)-meson, then we can calculate the momentum

and the density of grains that we may expect in track \(b\). Thus we obtain a value of 34 grains per 100 microns instead of the observed value \(51.0 \pm 6.0\). On the other hand, in case 4, when track \(a\) is formed by a \(\mu\)-meson, the calculated grain density for track \(b\) is 64. This value differs from the observed one by only two standard deviations. The observed grain densities agree best of all with the assumption that both particles are of the same type. Observations of the scattering of the particle forming track \(a\) are in better agreement with the assumption that this particle is rather a \(\pi\)-meson than a \(\mu\)-meson (see Table II), but the results obtained

Table IV

Comparison of the calculated and observed values of the grain density in track \(b\) under various assumptions about the nature of the particles forming tracks \(a\) and \(b\)

(Grain-density values are given in grains per 100 microns)

again cannot unambiguously decide the question of the nature of the particles. We may combine this result with the results obtained in determining the masses by grain counting, asserting that there is some evidence in favor of the three decay particles being \(\pi\)-mesons; however, in this case one cannot exclude the possibility of decay into one \(\pi\)- and two \(\mu\)-mesons or two \(\pi\)- and one \(\mu\)-meson.

Probability of the Superposition of Unrelated Phenomena

In the light of the analysis carried out in the preceding sections, we may return to the original assumption that this phenomenon should not be regarded as an accidental superposition of tracks. The lack of accuracy with which the mass of particle \(k\) is determined does not allow us to exclude the possibility that the particle has the mass of a proton, although the results obtained by grain counting make this possibility unlikely. Suppose that the proton,

not associated with the particles forming the other tracks, ends its path at point \(A\). Even under this assumption the observed phenomenon is very difficult to explain in the usual way. In our laboratory many cases of emission of \(\pi^{-}\)-particles in stars have been observed.\(^{8}\) However, in the case under consideration we have a nuclear interaction in which two mesons of high energy are emitted. This nuclear interaction is not accompanied by the emission of slow protons and \(\alpha\)-particles, which requires its own explanation. An analogous difficulty arises if we assume that the particle which formed one of the tracks \(a\) or \(b\) reaches \(A\) and produces a transformation. If, on the other hand, the tracks \(c\) and \(d\), diverging from star \(B\), correspond to an unbound disintegration caused, for example, by a \(\gamma\)-quantum, then we may suppose that track \(t\) was produced by a proton. In this case we encounter difficulties connected with explaining the features of star \(A\), which under this assumption must have been formed by a slow charged particle. The difficulties arising here were discussed in the preceding paragraph.

The considerations set forth are one more argument in favor of the initial assumption that all the tracks shown in the microphotograph constitute a sequence of connected processes.

Relation between the Results Presented and Other Observations

If a particle possessing an elementary charge undergoes spontaneous decay, then according to the law of conservation of charge the number of decay particles with charge \(e\) must be odd. From this point of view the sign of the charge of the primary particle may be either positive or negative. If the particles forming tracks \(a\) and \(b\) have charges of opposite sign, then the primary \(k\)-particle must be negatively charged. The only other possibility is that both these particles are positively charged. In that case the particle \(k\) is also positively charged. It is therefore possible that our observations correspond to the decay of positively charged particles with mass approximately equal to \(900\,m_e\), and that in the Leprince-Ringuet observations particles of the same mass, charged negatively, are captured by a nucleus; a star is formed in the process and a \(\pi^{-}\)-particle is emitted.

Rochester and Butler published a photograph obtained in a Wilson chamber which corresponds, apparently, to the spontaneous decay of a neutral particle with mass about \(900\,m_e\) into two oppositely charged particles whose rest mass is approximately \(300\,m_e\). We therefore decided to consider the possibility that the decay process consists of two stages, namely, the emission of a \(\pi^{-}\)-particle of low energy and the subsequent decay of the resulting neutral particle. In doing so, however, it is necessary to assume that

neutral particle has a lifetime of the order of \(10^{-14}\) sec. On the other hand, as a result of recoil the neutral particle will move away from the original point of decay, and therefore the two charged particles into which it is transformed will arise at a point removed from the beginning of the track of the \(\pi\)-particle. It follows from this that we cannot identify the postulated unstable neutral particle with the particle whose existence was proved in the experiments of Rochester and Butler. In conclusion we shall consider the possible connection between our results and the results reported by Bradt and Peters\(^2\), who obtained evidence for the existence of particles with a mass of about \(800\,m_e\), which they called \(\tau\)-mesons. A distinctive feature of their experiments is that these mesons do not form observable secondary particles at the end of their range. It is possible that in the decay of these particles three charged mesons also arise, but that in this transformation there is a considerably more uniform distribution of kinetic energy than in the case observed by us. It would follow from this that, in Ilford C2 emulsions, the decay products usually escape observation. If this point of view is correct, then we must regard the case discovered by us as a rare example of the usual decay scheme of these mesons, which by chance enabled us to make a detailed analysis of this phenomenon. If this is so, then the \(\tau\)-meson of Bradt and Peters, recorded with the aid of an emulsion sensitive to electrons, should form tracks of three weakly ionizing particles whose directions of motion are coplanar.

Note added in proof

When this article had been written, Dr. Peters informed us that he and Dr. Bradt had observed in an Ilford C2 emulsion, exposed at an altitude of \(27\,000\) m, the following three cases. A particle, whose mass they consider approximately equal to the mass of their \(\tau\)-mesons, apparently comes to rest and emits a particle of smaller mass, which produces a nuclear disintegration at the end of its range. The ranges of the secondary particles in these three cases are \(20\), \(25\), and \(45\,\mu\), respectively. The authors did not know our results when they informed us that their observations possibly correspond to the spontaneous decay of heavy mesons. According to their description, these phenomena correspond exactly to those which should be expected in a C2 emulsion as a result of the spontaneous decay of heavy particles of the type postulated by us: particles with small specific ionization are not recorded by Ilford plates.

The observations of Peters and Bradt are apparently further evidence for the supposition that the observations described were not caused by an accidental superposition of tracks. They also indicate that in the near future further examples will be found which will make it possible to carry out a detailed analysis.

References

1. Berriman, Nature, 162, 992 (1948).
2. Leprince-Ringuet, C. R. 226, 1897 (1948); Rochester and Butler, Nature 160, 855 (1947); Bradt and Peters, Report to the Bristol Symposium, 1948 (in press); Alichanian, Alichanov and Weissenberg, J. Exp. and Theoret. Phys. USSR 18, 301 (1948), and others.
3. Camerini, Muirhead, Powele and Ritson, Nature 162, 433 (1948).
4. Goldschmidt-Clermont, King, Muirhead and Ritson, Proc. Phys. Soc. 61, 138 (1948).
5. Lattes, Occhialini and Powele, Proc. Phys. Soc. 61, 173 (1948).
6. Serber, Report of Solvay Conference for 1948.
7. Dilmorth, Occhialini and Payne, Nature 162, 102 (1948).
8. Occhialini and Powele, Nature 162, 168 (1948).
9. Halpern and Hall, Phys. Rev. 73, 447 (1938).
10. Livingston and Bethe, Rev. Mod. Phys. 9, 263 (1937).
11. Camerini and Lattes (private communication); see also Powell and Occhialini, UFN 35, 213, 384 (1948).