OBSERVATIONS ON THE TRACKS OF SLOW MESONS IN PHOTOGRAPHIC EMULSIONS*)

C. M. G. Lattes, G. P. S. Occhialini, C. F. Powell
and F. C. Frank)

INTRODUCTION

In some recent experiments it was shown that charged mesons stopping in photographic emulsions sometimes lead to the formation of secondary mesons. These experiments were continued by studying plates exposed in the Bolivian Andes at an altitude of 5500 m, and a total of forty cases of a process leading to the formation of secondary mesons was found. In eleven of these the secondary particle stopped in the emulsion and, thus, its range could be determined. In Part I of the present article the measurements of the tracks are described, and it is shown that they give data supporting the existence of mesons with different masses. In Part II additional data on meson production are presented, making it possible to show that many of the observed mesons are generated locally in “explosive” disintegrations of nuclei. These data also make it possible to discuss the question of the connection between the various types of mesons found in photographic plates and the penetrating component of cosmic radiation investigated in experiments with a Wilson chamber and counters.

I. THE EXISTENCE OF MESONS WITH DIFFERENT MASSES

As in our previous communications, by the term “meson” we shall mean any particle with a mass intermediate between the mass of the electron and the mass of the proton. It should be emphasized that, in using this term, we by no means wish to assert that the corresponding particle necessarily interacts strongly with nucleons or that it is closely connected with intranuclear forces.

) Translated by L. N. Bell.
) Parts I and II of the present article were written by C. M. G. Lattes, G. P. S. Occhialini, and C. F. Powell and published in Nature, 160, 453, 486 (1947). Part III, written by F. C. Frank, was published in Nature, 160, 525 (1947). (Editor’s note.*)

We have now observed a total of 644 meson tracks that stopped in our plates. Of these, 451 tracks were found in plates of various types exposed at an altitude of 2800 m on the Pic du Midi in the Pyrenees; the remaining 193 tracks were obtained

Fig. 1. Track of a μ-meson. The track is shown in two parts. The place of the joint is indicated by the letter a and an arrow.

in similar plates exposed at Chacaltaya (Bolivian Andes) at an altitude of 5500 m. The 451 tracks in the plates exposed at an altitude of 2800 m were found upon examination of 5 cm³

Fig. 2. Track of a μ-meson. The track is shown in two parts. The place of the joint is indicated by the letter a and an arrow.

of emulsion. This corresponds to the stopping of approximately 1.5 mesons per 1 cm² per day, and this figure is a lower limit, since some of the tracks may remain unnoticed because of destruction of the latent image or owing to the small length of the track. The true number of them, therefore, will be somewhat higher. In any case,

this value agrees in order of magnitude with what should be expected in delayed-coincidence experiments at an altitude of 2800 m, if for the estimate one takes the data obtained at sea level and makes reasonable assumptions concerning the increase in the number of slow mesons with altitude. Thus the mesons observed by us are undoubtedly a constituent part of cosmic rays. Microphotographs of two examples of secondary-meson formation (Nos. III and IV) are shown in Figs. 1 and 2. Table I gives detailed information on the characteristics of all cases observed up to the present time in which the secondary particle stopped in the emulsion.

Table I

The mean range of the secondary meson is \(614 \pm 8\mu\); coefficient of scatter \(\sqrt{(\sum \Delta i)^2/n} = 4.3\%\), where \(\Delta i = R_i - R\); \(R_i\) is the range of the secondary meson and \(R\) is the mean value for \(n\) particles of this type.

The distribution of secondary particles by range is shown in Fig. 3. The values given refer to the lengths of the projections of the true trajectories of the particles onto a plane parallel to the surface of the emulsion. The true ranges, however, cannot differ greatly from the values given above, since throughout the main part of their length each track is inclined to the plane of the emulsion at small angles. In addition to the results pertaining to slow mesons that stopped in the emulsion (shown in Fig. 3 by black squares), the lengths are indicated of a number of tracks of mesons that arose as a result of the same process but left the emulsion at the end of their range (shown in Fig. 3 by unshaded squares).

μ-decay of mesons

Two important conclusions follow from these measurements. Our observations show that secondary mesons are emitted in all directions with equal probability. This makes it possible to calculate the probability that the trajectory of a meson created in such a process and observed by us will remain, over a length greater than

Fig. 3. Distribution of 10 secondary mesons by ranges. Mesons indicated by the symbol ■ stopped in the emulsion; 3 mesons indicated by □ left the emulsion near the end of their range. The mean range of the secondary mesons is 606 microns. Results relating to events Nos. VIII and XI are not included in the figure.

500 μ, inside an emulsion of thickness 50 μ. If, as a first approximation, we assume that the trajectories are straight lines, we obtain for this probability a value of the order of 1:20. In reality, the noticeable Coulomb scattering of mesons in the emulsion will increase the probability of “escape.” Thus the six cases observed by us in plates exposed at an altitude of 2800 m, in which the secondary particles traverse in the emulsion a path greater than 500 μ, correspond to \(120 \pm 50\) cases of this type. Our observations, therefore, prove that decay with the formation of secondary mesons is widespread among those mesons which stop in the emulsion.

Furthermore, there is a remarkable constancy in the lengths of the ranges of the secondary mesons: the differences in the individual values are very close to those which would be expected as a result of the scatter of the ranges of particles emitted with the same velocity. From this we conclude that the secondary mesons have identical masses and are always emitted with one and the same kinetic energy.

If, in a process of another type, mesons of smaller range are emitted, then they must be produced considerably more rarely than the mesons observed by us, for the geometrical conditions and the greater mean density of the grains of the tracks would favor their detection. In fact, such mesons with short ranges have not been found by us. We cannot, however, be entirely certain that mesons of long range are not formed. Both the smaller ionization at the beginning of the track and the still greater difficulties of detecting them over a considerable section of the track would substantially hinder observation of such a group or groups. Since a significant part

mesons, as we have seen, can be attributed to the observed process; it is reasonable to suppose that other modes of decay, if they exist, are less frequent than the mode of decay observed by us. Thus there are solid data in favor of the formation of a single homogeneous group of secondary mesons with constant mass and identical kinetic energy. This convincingly indicates the existence of an elementary process not connected with the interaction of the primary meson with any definite nucleus in the emulsion. In what follows it will be convenient to call this process \(\mu\)-decay. We shall denote primary mesons by the symbol \(\pi\) and secondary ones by the symbol \(\mu\). At present we still have no data that would make it possible to establish the sign of the electric charge of these particles. In all cases in which the particles came to rest in the emulsion, it was not observed that the stopping occurred as a result of the disintegration of a nucleus with the emission of heavy particles.

Knowing the dependence of the range of a proton in the emulsion on its energy, and taking a definite value for the mass of the particle, one can derive the energy of emission of the secondary mesons from their observed ranges. The values thus calculated for various masses are given in Table II.

Table II

For protons with energies above 13 MeV there are no generally accepted data for the dependence of range on energy, and one has to be content with extrapolation of the relation established for small energies. According to our estimates, the energies given in Table II are correct to within 10%.

Data Indicating a Difference in the Masses of \(\pi\)- and \(\mu\)-Mesons

It had already been noted earlier\(^1\) that it is difficult to explain \(\mu\)-decay by the interaction of the primary meson with the nucleus of an atom of the emulsion, leading to the formation of a meson with greater energy and the same mass as the primary one. It was therefore proposed to regard our observations as an indication of the existence of mesons with different masses. Since the argument in favor of this supposition was based entirely on the principle of conservation of energy, other possible processes were also considered which, independently of other

arguments in their favor, could have led to the release of the necessary amount of energy.

F. C. Frank examined such possibilities in greater detail, and his results are given in the third part of the present article. His analysis shows that it is very difficult to explain our observations by a process of nuclear fission or by any process of “synthesis” of nuclei with the release of binding energy as a result of the penetration of protons into the nuclei of light elements following the presumed combination of a negative meson with a hydrogen nucleus. We find that this general argument in favor of the existence of mesons of different masses can now be supported by data based on the counting of grains.

We have repeatedly emphasized,^1 that great caution is necessary when determining the mass of particles from grain density. The main source of errors in such a determination lies in the instability of the latent image created in the silver-halide grains as a result of the passage of a fast particle. In the case of the $\mu$-decay process there is an essential simplification. It is natural to assume that both meson tracks are formed within a small interval of time, one after the other, and undergo destruction to the same degree. The whole double track in the process under consideration lies within a very small region of the emulsion, and the processing conditions are therefore identical for both tracks, if one does not count the dependence of the degree of development on depth. These factors provide favorable conditions for determining the mass ratio of $\pi$- and $\mu$-mesons.

In determining the grain density in a track we counted the number of individual grains in a series of consecutive intervals of the track, each $50 \mu$ long; for the observation we used optics with high magnification ($\times 2000$) and with the greatest resolving power available to us. Typical results for protons and mesons are shown in Fig. 4. These results were obtained for tracks in one and the same plate and, as can be seen, the separation of the curves corresponding to particles of different types is quite satisfactory. The scatter of the results for different particles of the same type may be attributed to different degrees of destruction of the latent image, associated with the difference in the time at which the particles passed through the emulsion during the six-week exposure.

Applying these methods to cases of the $\mu$-decay process in which the ranges of the secondary mesons end in the emulsion, we find that in all cases the curve representing the observations on the primary meson lies above the curve for the secondary meson. We can, therefore, conclude that there is a significant difference in the grain density in the tracks of the primary and secondary mesons, and, consequently, a difference in the mass of the particles. This conclusion, of course,

is based on the assumption that the charge of the $\pi$- and $\mu$-mesons is the same. The grain density at the ends of the tracks of particles of both types is compatible with the view that the charges have magnitude $e$.

A more accurate determination of the masses of the $\pi$- and $\mu$-mesons can be made in those cases where the length of the track of the primary meson

Fig. 4. Dependence of the logarithm of the total number of grains in the track on the magnitude of the residual range $R$ (in scale divisions). 1 scale division $= 0.85$ micron.

in the emulsion is of the order of $600\,\mu$. The probability of such a favorable case is rather small, and the only cases observed so far are given in Table I under Nos. III and VIII. In Fig. 1 a mosaic of microphotographs is shown of only part of the first of these cases, since the length of the $\mu$-meson track in the emulsion exceeds $1000\,\mu$. The logarithms of the number of grains in the tracks of the primary and secondary mesons for this case, as functions of the logarithm of the residual range, are presented in Fig. 5. Comparing those residual ranges for which the grain densities in both tracks are the same, one can determine the mass ratio. We thus obtained $m_{\pi}/m_{\mu}=2.0$. Similar

measurements for event No. VIII gave the value 1.8. In discussing the meaning of the result obtained, it should be borne in mind that, in addition to the standard deviations in the number of grains counted, there are also other sources of error. For example, certain difficulties arise as a result of the fact that the distribution of silver-halide

Fig. 5. Dependence of the total number of grains in a track on the value of the residual range \(R\) (on logarithmic scales). One scale division = 0.85 micron. The line running at \(45^\circ\) intersects the curves for mesons and the proton at points of equal grain density.

grains in the emulsions is not entirely uniform. There exist “islands” in which the concentration of grains is substantially higher or lower than the average values, and these deviations considerably exceed the deviations associated with random fluctuations. Measurements of other cases of \(\mu\)-decay are substantially less reliable owing to the limi-

...of the path length in the emulsion; they give results that are smaller than those presented. We consider it unlikely, however, that the true ratio should have so low a value as 1.5.

The preceding result is of great importance for the interpretation of the process of μ-decay. Suppose that it corresponds to the spontaneous decay of the heavier π-meson, with the momentum of the μ-meson equal to and opposite in sign to the momentum of the emitted photon. For any given value of the μ-meson mass one can compute the energy of emission of this particle from its observed range and hence determine its momentum. This determines the momentum, and consequently also the energy, of the emitted photon; the mass of the π-meson then follows from the relation

\[ c^{2}m_{\pi}=c^{2}m_{\mu}+E_{\mu}+h\nu . \]

It can be shown in this way that the ratio \(m_{\pi}/m_{\mu}\) is less than 1.45 for any value of \(m_{\mu}\) in the interval between 100 and \(300\,m_e\), where \(m_e\) is the electron mass (see Table III). A similar result is obtained if it is assumed that a particle of small mass, such as, for example, an electron or a neutrino, is emitted in the direction opposite to the direction of emission of the μ-meson.

Table III

On the other hand, if it is assumed that equality of the momenta in μ-meson decay is ensured as the result of the emission of a neutral particle with a mass equal to the mass of the μ-meson, then the calculated ratio turns out to be approximately \(2.1:1\).

Our preliminary measurements, therefore, indicate that the emission of the secondary meson cannot be regarded as the result of a process of spontaneous decay of the primary particle in which conservation of momentum is ensured by the emission of a photon or of a particle with a small rest mass. On the other hand, the results obtained are compatible with the assumption that a neutral...

... particle with a mass approximately equal to that of the \(\mu\)-meson. A final judgment will become possible only after the discovery of new cases of \(\mu\)-decay that provide favorable conditions for determining the number of grains.

II. ORIGIN OF SLOW MESONS

In the first part of the present article we showed that there exist two types of mesons, and the supposition was advanced that the heavy \(\pi\)-mesons decay with the emission of the lighter \(\mu\)-mesons. In the second part we shall discuss the origin of the slow mesons observed in photographic plates, and their relation to the mesons constituting the penetrating component of cosmic rays, for which data from Wilson chambers and counters are available. We shall also present photomicrographs which show that some of the slow mesons emitted by nuclei during “explosive disintegration” can penetrate into other nuclei and cause their secondary disintegration. Most of the plates exposed at an altitude of \(5500\) m had an emulsion with an admixture of boron, and the plates considered are mainly of precisely this type. The nature of the admixed material has a substantial effect on the rate of destruction of the latent image, but, thanks to the procedure described above, it is possible to compare the results of experiments at different altitudes.

Disintegrations caused by mesons

Of 644 mesons that stopped in our emulsions, 145 led to the formation of secondary particles. In 40 cases the characteristics of the track of the secondary particle indicate that it is a meson. We therefore consider that these cases were caused by the decay of \(\pi\)-mesons, although in some cases the range of the secondary particle is too short to vouch for the accuracy of the identification. In the remaining 105 cases the mesons produce disintegrations with the emission of a heavy particle. We had earlier published photographs of such disintegrations; Fig. 6 shows a case with the emission of a single proton. Although there is no proof that they are all of one type, it will nevertheless be convenient to denote provisionally all slowly moving mesons that cause nuclear disintegrations as \(\sigma\)-mesons. Since the characteristic nuclear interaction between mesons and nucleons can be regarded as effective only at small distances, and since Coulomb repulsion would prevent a slow positive meson from approaching the nucleus, we believe that the observed disintegrations caused by \(\sigma\)-mesons indicate the negative charge of the latter. In another paragraph it will be shown that some data indicate that \(\pi\)-mesons and, at least, part of the \(\sigma\)-mesons are respectively positively and negatively charged particles of one type.

In Fig. 7 the relative frequency of occurrence of disintegrations with different numbers of emitted heavy charged particles is shown, it being assumed that the disintegrations were produced by mesons. W. Heitler has noted that the observed cases probably do not represent all cases of disintegrations actually caused by slow mesons in the region of the plate under consideration. In some cases, for example, a single fast neutron may appear as the result of the interaction of a negative meson with a nuclear proton. Further, for the same

Fig. 6. A σ-meson, coming to rest, causes a disintegration with the emission of a single, strongly ionizing particle, probably a proton.

reasons as in the cases considered below, we probably sometimes do not detect single fast protons emitted from the nucleus, owing to the large angle of inclination of the track with respect to the plane of the emulsion.

It is interesting to compare the distribution shown in Fig. 7 with the results obtained by Gardner[^2], who studied disintegrations produced in photographic emulsions by deuterons accelerated in the 184-inch synchro-cyclotron. In these experiments disintegrations with the emission of two, three, or four charged particles were usually observed; only in a few cases were five charged particles emitted. Our results are therefore compatible in this respect with the view that the absorption of a σ-meson sometimes leads to the release from the nucleus of an amount of energy corresponding to the rest mass of a particle of the order of \(400m_e\).

Total number of meson tracks in the emulsion

In discussing the question of the origin of the mesons observed in our experiments, it is important to determine the frequency of occurrence of their various types; and for this purpose we cannot use the number of observed tracks without the appropriate corrections. If the inclination of the track

if the length of its projection onto the plane of the emulsion is less than 50 μ, there is some probability that it will not be noticed, or that there will not be sufficient grounds to regard it as the trace of a meson. A certain fraction of mesons, consequently, will not be counted. This “loss” of tracks will not affect observations of mesons of different types in the same way. In the case of σ-mesons, for example, the observation of tracks is facilitated by the existence of secondary particles from disintegrations, which draw the investigator’s attention to the given event. Similarly, in those cases when π-mesons create μ-mesons stopping in the emulsion, observation of the μ-meson track makes it possible to observe the primary π-meson, although this track is short.

Fig. 7. Relative frequency of disintegrations produced by mesons, in which \(N\) charged heavy particles are emitted.

To overcome these difficulties, we proceed as follows. Fig. 8 shows the distribution of the lengths of the projections onto the plane of the emulsion of the tracks of those mesons which stop without the formation of secondary heavy particles. These results were obtained with 50-μ plates with an admixture of boron, exposed on Pic du Midi.

Simple geometrical considerations make it possible to compare the distribution in Fig. 8 with the distribution that would be expected if all tracks without exception were observed in the given volume of emulsion.

We shall assume that the tracks are rectilinear and that the ranges of the particles are infinitely large, and also that the positions of the ends and the directions of the tracks are randomly distributed. Then it is easy to show that the number of tracks \(N(t)\,dt\), the lengths of whose projections lie in the interval \(t, t+dt\), is given by the relation

\[ N(t)\,dt=\frac{2N_0}{d}\left(1+\frac{t}{(d^2+t^2)^{1/2}}\right)dt,\ldots, \tag{1} \]

where \(\Sigma N_0\) is the total number of tracks in the portion under consideration and \(d\) is the thickness of the emulsion. Further, the number of tracks \(\Sigma N_t\), whose projections are

Fig. 8. Histogram giving the distribution of the observed lengths of the projections of meson tracks on the surface of the emulsion. The dotted line shows the distribution expected on the assumption that the tracks are straight.

greater than \(t\), is related to the total number of tracks \(\Sigma N_0\) by the equation

\[ \Sigma N_t=\Sigma N_0\left[\left(d^2+t^2\right)^{1/2}-t\right]\ldots \tag{2} \]

From equation (2) one can calculate the value of \(\Sigma N_0\) from the observed values of \(\Sigma N_t\) corresponding to the measurements presented in Fig. 8; the results are shown in Table IV.

Table IV

C-2 type emulsions with boron admixture. Meson tracks without secondary heavy particles. Exposure: 40 days on Pic du Midi. Total volume of emulsion examined: \(3.5\ \mathrm{cm}^3\)

The dotted line in Fig. 8 was calculated by means of equation (1) for 795 mesons terminating in the emulsion. From the figure

and from Table IV it is seen that the results are consistent with the supposition that no meson tracks of this class, with a projected length exceeding \(100\ \mu\), remain unnoticed. On the other hand, for shorter tracks there are serious “losses.” We may therefore assume that the total number of tracks in the emulsion can be determined from observations of tracks for which \(t\) is greater than \(100\ \mu\); in doing so we use the result \(\sum N_0=795\), obtained on the basis of the value \(\sum N_{100}\), as the most reliable value. This number includes those \(\pi\)-meson tracks for which the tracks of secondary mesons were not observed, and also any \(\sigma\)-mesons that produce disintegrations without visible secondary particles.

From similar observations of \(\sigma\)-mesons leading to visible disintegrations, we conclude that the total number of such particles in the measured area of the emulsion is \(122 \pm 20\), and, consequently, the total number of slow mesons of all types is \(917 \pm 70\).

Number of \(\pi\)-Mesons

The analysis of the preceding paragraph can also be applied to determine the total number of \(\pi\)-mesons in the emulsion. Thus, in the boron plates exposed at Pic du Midi, we observed six tracks of \(\pi\)-mesons for which the length of the secondary \(\mu\)-meson track exceeds \(500\ \mu\). Using equation (2), we find that this figure corresponds to the appearance of \(120 \pm 50\) events of this class in the area of emulsion studied. In many of these cases the \(\mu\)-meson track will be very short and will remain unnoticed, as will the track of the associated \(\pi\)-meson. The total number of events that we have derived must therefore be compared with the total number of mesons, equal to 917, because, as we have seen, examination of the tracks of those \(\mu\)-mesons for which the track length is greater than \(500\ \mu\) guarantees that we shall detect the trace of the primary \(\pi\)-meson, however small its range in the emulsion may have been.

Another estimate of the number of \(\pi\)-mesons can be obtained from those observed cases for which the secondary \(\mu\)-meson has a limited range in the emulsion. The result obtained in this way is \(115 \pm 20\), a value which differs little from the value obtained by the first method. Combining both results, we obtain for the number of \(\pi\)-mesons the value \(117 \pm 20\).

Relative Number of Slow Mesons of Various Types at 2800 m and 5500 m above Sea Level

Of the 917 slow mesons which, as we suppose, should be present in the measured area of the emulsion of the plates exposed at Pic du Midi, we have seen that \(122 \pm 20\) should be ascribed to \(\sigma\)-mesons and \(117 \pm 20\) to \(\pi\)-mesons. An approximately equal number

μ-mesons from the decay of π-mesons stopped in glass or another substance in the immediate vicinity of the emulsion will end in the emulsion. These results are summarized in Table V and show that the origin of approximately one third of all the observed mesons can be explained as π- and σ-mesons stopped in the measuring plates, and as μ-mesons arising from their decay. The remaining tracks, if one does not count the small number possibly due to disintegrations caused by σ-mesons with emission of neutrons, remain unexplained.

Very similar results were obtained with plates exposed at an altitude of 5500 m; the corresponding figures are given in Table V. These results show that there is no essential difference in the distribution by classes of mesons observed at different altitudes. However, there were differences in the exposure conditions at the two altitudes; moreover, the time between exposure and development was also different in the two cases. We therefore cannot be fully confident in the correctness of the absolute intensities given in the table.

Table V

Summary of results obtained in examining emulsions with boron exposed for 40 days at Pic du Midi (2800 m) and at Chacaltaya in Bolivia (5500 m). Thickness of the emulsion at 2800 m was 50 μ; volume of emulsion examined—3 cm³. Thickness of the emulsion at 5500 m was 100 μ; volume of emulsion examined—1.1 cm³

Fig. 9. Mosaic of microphotographs. The $\sigma$-meson, emitted in the explosive disintegration of the nucleus $P$, at the end of its range produces a second disintegration $S$. The tracks marked “$b$,” “$c$,” and “$k$” are due to protons that stop in the emulsion. Most of the other tracks terminate on one of the surfaces of the emulsion.

Emission of mesons from disintegrated nuclei

A mosaic of microphotographs showing the emission of a meson from a disintegrating nucleus was given in the preceding communication. We have already observed five cases of this kind, including two cases in which the emitted meson at the end of its range causes the disintegration of a nucleus. Microphotographs of these two events are shown in Figs. 9 and 10, the number of charged particles from the secondary “stars” being, respectively, 4 and 2. In the terminology used in the present article, it may be said that these two events prove that σ-mesons can be produced in the disintegration of nuclei by high-energy particles present in cosmic rays.

Fig. 10. Mosaic of microphotographs. A σ-meson, emitted in the explosive disintegration of nucleus P, stops and creates a secondary disintegration of nucleus S.

We have also observed a case in which one of the emitted mesons, at the end of its range, gives rise to the formation of a single fast secondary particle. In this case the length of the track of the secondary particle in the emulsion before passing into the glass was only 150 μ. We therefore cannot assert that the secondary particle was not a fast proton but a μ-meson, although the grain density of the track agrees with the latter supposition and, in our opinion, it is the correct explanation of the event considered. If this is so, then this observation corresponds to the generation of π-mesons in processes associated with the explosive disintegration of nuclei. Further observations will be required for final conclusions. If our present view is correct, we should expect the appearance of such cases of decay of an emitted π-meson, for which the secondary ...

ric particle stops in the emulsion after traversing a path of approximately \(600\,\mu\).

Two of the five mesons emitted in the explosive disintegration of nuclei stopped without producing secondary particles with visible tracks. We have seen that \(\sigma\)-, and possibly \(\pi\)-mesons, can be formed in explosive disintegration; an important question arises as to whether mesons of other types, for example \(\mu\)-mesons, can also arise in such processes. We believe that our data are insufficient for answering this question. The two emitted mesons under consideration stopped near the surface of the emulsion. If they were \(\pi\)-mesons, the probability of detecting the track of the corresponding \(\mu\)-meson, if it existed, would be less than 0.5.

The formation of a meson requires, we shall suppose, an energy of the order of \(100\ \mathrm{MeV}\). As we have already emphasized, the probability of emitting such a particle with kinetic energy of the order of several \(\mathrm{MeV}\) must be small. Furthermore, one may hope to identify such a meson only in the case where it is emitted in a direction almost parallel to the surface of the emulsion. The new observations thus support the point of view that meson emission is usually connected with the explosive disintegration of nuclei. The probability of observing two slow mesons emerging from one and the same nucleus must be small, even if the formation of several mesons at once as a result of the interaction of a fast particle with a nucleus occurs, as many believe, rather often.

Origin of Slow Mesons

We have already observed 4000 cases of explosive disintegrations of nuclei (in plates exposed at an altitude of \(2800\ \mathrm{m}\)), for which the total amount of energy released, judging by the number of emitted charged particles and their ranges, is greater than the energy released in similar events accompanied by the emission of slow mesons. In the thickness of a solid substance, for example that which forms the box for photographic plates, nuclear explosions accompanied by the emission of slow mesons will arise. Some of these mesons will stop in the emulsion of the photographic plate. It is of great interest to determine what fraction of the mesons observed by us can be ascribed to such processes.

As a first approximation one may assume that, in the solid substance, those of the emitted mesons will stop whose ranges are less than the linear dimensions of the mass under consideration. Furthermore, the ends of the meson tracks will be distributed randomly in the mass of the solid substance, and their density will be equal to the density of the primary nuclear explosions. We estimate the energy of a meson required to traverse the layer of solid substance surrounding our plates during exposure at approximately \(50\ \mathrm{MeV}\). Mesons emerging with lower energy,

will stop in the emulsion or glass, whereas mesons of higher energy may be regarded as escaping altogether.

In plates exposed on the Pic du Midi, we observed 4 disintegrations for which the energy of the emitted meson lay between 1 and 3 MeV. Taking the geometry also into account, one may estimate that this number corresponds to at least 12 cases of this type occurring in the volume of emulsion under consideration; the remaining ones were not detected because of the large angles of inclination of the meson tracks. If we assume that the energies of the emitted mesons are distributed randomly between 0 and 50 MeV with equal probability, then the expected number of mesons with energies between 1 and 3 MeV will correspond to the appearance in our emulsions of mesons at the end of their range in the amount of \(0.6 \pm 0.3\) per \(1\ \mathrm{cm}^3\) per day. This estimate is based on certain quantities that are not known exactly, but the agreement, in order of magnitude, with the number of \(\pi\)- and \(\sigma\)-mesons is nevertheless remarkable. This supports the view that a considerable part of the observed mesons of this type is produced in locally generated disintegrations. The observations are not sufficiently accurate to enable us to determine the fraction of \(\pi\)- and \(\sigma\)-mesons that should be attributed to analogous processes in the material surrounding the plates during exposure and removed from the plates by distances of several meters; this question is especially interesting in connection with the problem of determining the lifetime of these mesons.

Interpretation of the Observations

Owing to the complexity of the phenomenon and the limited number of tracks of different types of mesons observed by us, we cannot draw definitive conclusions regarding many questions arising as a result of our observations. We have nevertheless considered a number of possible interpretations of the present experiments and of experiments with Wilson chambers or counters. The following working hypothesis is the simplest of the hypotheses we have considered that makes it possible to account for all the principal experimental results without serious contradictions.

We suppose that \(\pi\)-mesons and the majority of \(\sigma\)-mesons are respectively positive and negative particles of the same type, formed in processes associated with explosive disintegration of nuclei such as those we have observed. Positive \(\pi\)-mesons undergo \(\mu\)-decay and form \(\mu\)-mesons, about whose fate our data say nothing. On the other hand, negative \(\pi\)-mesons, which in our experiments appear as \(\sigma\)-mesons, are captured by nuclei and produce disintegrations with the emission of heavy particles. This hypothesis enables us to explain the approximate equality of the numbers of \(\pi\)- and \(\sigma\)-mesons, which can be inferred from our observations, and also the fact that the relative frequency of appearance of mesons of different types does not change noticeably with altitude.

Further, since those particles which are produced in the decay of stopped \(\pi\)-mesons are regarded as carrying a positive charge, it must be expected, in accordance with the observations, that they will not react with nuclei and produce disintegrations with the emission of heavy particles.

It remains to explain the origin of those mesons which are neither \(\pi\)- nor \(\sigma\)-mesons and which cannot be attributed to \(\mu\)-mesons arising in the decay of \(\pi\)-mesons stopped in the photographic-plate apparatus. We attribute them to \(\mu\)-mesons arising as a result of the decay of moving positive and negative \(\pi\)-mesons, generated in nuclear processes which take place at some distance from the apparatus. Under such an assumption our observations can be arranged in a simple, non-contradictory scheme, in many respects similar to schemes proposed by other authors[^3].

If the proposed point of view is correct, we shall be able to attribute the penetrating component observed at sea level to particles of the same type as the \(\mu\)-mesons formed by high-energy \(\pi\)-mesons arising in the upper layers of the atmosphere and decaying in flight. It may be assumed that these \(\mu\)-mesons have both positive and negative charge. If one accepts the general conclusions usually drawn on the basis of delayed-coincidence experiments, then we should expect that those negative \(\mu\)-mesons which stop in the grain of the plate should be captured by heavy nuclei. On the other hand, those mesons which stop in the gelatin should undergo \(\beta\)-decay. At present it is impossible to determine accurately the relative probability of these two processes, since this requires knowledge of the atomic stopping powers of the various components of the emulsion for an energy interval of \(\sim 20\ \mathrm{KeV}\); corresponding measurements in this energy region, however, do not exist. Further, Freilich has drawn our attention to the fact that the range–energy curve will be different for positive and negative mesons, since the latter do not capture and do not lose electrons while passing through the emulsion. Rough estimates show, however, that the probability of a meson stopping in the gelatin is approximately twice the probability of its stopping in a silver-halide grain. Under these assumptions the mesons in line (г) of Table V constitute approximately five-sixths of those \(\mu\)-mesons which stop in the emulsion; the remaining sixth interacts with nuclei. If we suppose that these latter mesons, like negative \(\pi\)-mesons, lead to disintegrations with the emission of heavy particles, then they will be classified as \(\sigma\)-mesons. In Wilson chambers, however, cases of disintegration by slow mesons at sea level have not been observed. This may be because the interaction of negative \(\mu\)-mesons with nuclei leads to a process different from the disintegration caused by \(\sigma\)-mesons.

If the point of view proposed above is adopted, then it remains to explain why negative \(\pi\)-mesons, despite the short lifetime attributed to them, undergo nuclear capture both in gelatin and in silver bromide, whereas negative \(\mu\)-mesons, which are presumed to have a longer lifetime, undergo \(\beta\)-decay before capture by light nuclei. We can resolve this difficulty only by assuming that the time required for a negative meson to approach the nucleus is less than the lifetime of both types of mesons. At present the magnitude of this interval of time is still being debated. If, however, it is assumed that a close passage near the nucleus can occur before the decay of the meson, irrespective of the type of the latter, then it will further be necessary to assume that the interaction of \(\mu\)-mesons with nucleons is much weaker than that of \(\pi\)-mesons. If the genetic connection between the different types of particles has been described by us correctly, i.e. if \(\pi\)-mesons decay with the formation of \(\mu\)-mesons, which in turn emit \(\beta\)-particles responsible for delayed coincidences, then from experiments with counters it follows that the sum of the lifetimes of \(\pi\)- and \(\mu\)-mesons must be equal to \(2 \cdot 10^{-6}\) sec. The only available data relating to the decay constants of the two types separately are obtained from the fact that the flight time of \(\pi\)- and \(\mu\)-mesons in our emulsions is of the order of \(10^{-11}\) sec. Consequently, the lifetime of both types is in any case greater than this value.

Let us suppose, as one possibility, that the lifetime of the \(\pi\)-meson is equal to \(2 \cdot 10^{-6}\) sec, while for \(\mu\)-mesons it is much smaller. Then the majority of cosmic-ray mesons at sea level, observed by means of counters or in Wilson chambers, must be attributed to \(\pi\)-mesons. In this case, in order not to violate agreement with the experiments on delayed coincidences, we must assume that those negative \(\pi\)-mesons which stop in gelatin undergo \(\mu\)-decay, whereas those which have stopped in grains of silver bromide produce disintegration. This compels us to expect the appearance of five times more \(\pi\)-mesons than \(\sigma\)-mesons. Further, according to this hypothesis a fraction of the negative \(\pi\)-mesons will undergo \(\mu\)-decay, emitting negative \(\mu\)-mesons which can interact with nuclei. To explain the absence of disintegrations from the eleven mesons observed by us, which undoubtedly appeared as a result of \(\mu\)-decay and some of which we must regard as negatively charged, it is necessary either to attribute to them a sufficiently short lifetime or else to suppose that they do not react with nucleons.

Even if the above-mentioned difficulties are eliminated, two serious objections to this hypothesis still remain. First, contrary to experiment, one would have to observe \(\mu\)-decay of mesons in Wilson chambers. Secondly, at present we cannot propose an explanation of the contradiction between the weak interaction of mesons with nucleons

at sea level, which follows from experiments on delayed coincidences and experiments of other types, and by the fact of the observed generation of $\sigma$-mesons. In view of these considerable difficulties, we reject the second hypothesis in favor of the first assumption, that $\pi$-mesons have a short lifetime and interact strongly with nucleons.

We have already emphasized that, at the present stage of our knowledge, it is not possible to draw definitive conclusions. In fact, it is quite probable that the phenomena under discussion are much more complicated than we have represented them here. Consequently, it is important to continue the observations, in order to reduce the statistical errors and also to determine, by every possible means, the masses of mesons of different types. In this connection it may be noted that the large number of tracks now available makes it possible to apply statistical methods. Thus $\pi$- and $\mu$-mesons probably constitute separate classes; therefore it will be possible to carry out a statistical study of the scattering of particles during their passage through the emulsion, with the aim of determining their mass. It is possible that $\sigma$-mesons, which, as we suppose, consist mainly of negative $\pi$-mesons, also contain some number of negative $\mu$-mesons. In this case, however, a statistical study of scattering through small angles would also make it possible to settle this question and to prove whether the majority of $\sigma$-mesons have the same mass as $\pi$-mesons or not. Such studies, as well as experiments to determine the lifetimes of $\pi$- and $\sigma$-mesons, are being carried out at present.

Conclusions

We may summarize our results as follows. We believe that our observations establish:

1) that there exist two types of mesons, denoted by us as $\pi$- and $\mu$-mesons and possessing different masses;

2) in agreement with the observations of Perkins, that a fraction of slow mesons can penetrate into nuclei and produce disintegrations with the emission of heavy particles, we believe that these mesons are negatively charged and provisionally call them $\sigma$-mesons; finally,

3) that $\sigma$- and, possibly, $\pi$-mesons can be created in processes connected with the explosive disintegration of nuclei.

Our observations indicate:

4) that $\pi$- and a considerable fraction of $\sigma$-mesons are, respectively, positively and negatively charged particles of one type, which interact strongly with nucleons; moreover, negatively charged mesons are captured by both light and heavy nuclei with the formation of disintegrations accompanied by the emission of heavy particles;

5) that the heavier $\pi$-mesons undergo spontaneous decay, accompanied by the emission of lighter $\mu$-mesons; in this decay process the momentum of the $\mu$-meson is compensated by the momentum of a neutral particle of approximately the same mass.

Moreover, the main features of the present experimental results and the result obtained in delayed-coincidence experiments and in Wilson chambers can be explained on the assumption that

6) the greater part of the mesons observed at sea level are μ-mesons formed in the decay of flying π-mesons, and

7) that the lifetime of positive and negative π-mesons is small and lies in the interval between \(10^{-6}\) and \(10^{-11}\) sec.

III. HYPOTHETICALLY POSSIBLE SOURCES OF ENERGY FOR EXPLAINING OBSERVATIONS OF “SECONDARY MESONS”

Lattes, Occhialini, and Powell*) showed that rather often cosmic-ray mesons, stopping in the emulsion of a photographic plate, create secondary mesons with a kinetic energy of the order of 4 MeV, not accompanied by other visible particles. To interpret this observation, apparently, the existence of two sorts of mesons is required, the source of the observed kinetic energy of the secondary particle lying in the difference of the masses of the two particles. In view of the importance of this conclusion, we have made an attempt to explain the observations by some reasonable process not requiring the introduction of a new elementary particle, namely, by a process in which the energy is obtained from the material of the photographic plate and not from the meson itself. Below we give arguments which make it possible to deny with considerable confidence the possibility of the existence of such processes.

We come to the conclusion that, for elements existing in sufficient quantity in the emulsion, none of the following processes can cause the release of the required amount of energy.

1) β- or K-capture processes: these processes are unacceptable because of the known mass defects of light nuclei and the general regularities for heavy nuclei present in the emulsion. In such processes energy must be released (although in amounts insufficient to explain the experiments) for \(K^{40}\), \(Rb^{87}\), \(Lu^{176}\), \(Os^{187}\) and for each of the following pairs: \(In^{113}\), \(Cd^{113}\); \(Sn^{115}\), \(In^{115}\); \(Te^{123}\), \(Sb^{123}\); not one of these elements is present in sufficient quantity. It is improbable that any natural nucleus should possess a more stable neighboring isobar not yet discovered in nature.

2) Induced emission of single nucleons: unacceptable because of the known mass defects of light nuclei and the general regularities for heavier ones; in natural nuclei such processes always absorb energy.

3) Induced emission of α-particles: excluded for light nuclei because of the known mass defects. In general it is not exclu—

) See parts I and II of the present article. (Ed. note*)

…for heavy nuclei, since the mass defects are not known with sufficient accuracy and, according to the Geiger–Nuttall relation, the lifetimes of sources of low-energy α-particles are too large for its determination. However, if there are no nuclei heavier than silver, then energies exceeding 2 MeV are excluded on this basis, since they would lead to spontaneous decay at a noticeable rate. In addition, the Coulomb repulsion from a nucleus of medium mass would in any case impart to the α-particle an energy sufficient for the particle to leave a visible track.

4) Induced fission: in this case as well, Coulomb repulsion would certainly produce a visible track of the fission fragments; moreover, it is extremely improbable that a meson could excite such a process, say in silver—the only element of significance from the point of view of energy reserves.

5) Processes accompanied by a change of charge by 2 units, such as, for example,

\[ \mathrm{At}^{A}_{Z}+Y^{-}\to \mathrm{At}^{A}_{Z-2}+Y^{+}, \]

where \(Y^{-}\) and \(Y^{+}\) denote negative and positive mesons. It should be expected that, if this process does occur, energy should be liberated in approximately half of the nuclei having stable isobars with charge reduced by two units. In the case of the transition \(\mathrm{Zn}^{64}\) to \(\mathrm{Ni}^{64}\), the measured mass defects give an energy yield of the order of \(9.8 \pm 3\) MeV. The conditions necessary for this process are not satisfied by any of the nuclei present in sufficient quantity in the photographic emulsion, namely by the isotopes of hydrogen, boron, carbon, nitrogen, oxygen, silver, bromine, iodine, and sulfur; of them only \(\mathrm{S}^{36}_{16}\), which is the rarest (0.016%) of the sulfur isotopes, and itself occurs only in insignificant quantities, has the stable isobar \(\mathrm{A}^{36}_{18}\). It also requires that the inverse process, beginning with a positive meson, take place, which is unlikely.

6) Induced decay of naturally stable nuclear isomers; this would mean the existence of isomers with lifetimes \(10^{12}\) times greater and energy reserves 10 times greater than any known values—an extremely improbable combination.

This, apparently, exhausts the possibilities associated with the degradation of nuclei. On the other hand, in order to exclude processes of “synthesis” of nuclei, in which a proton is added to another nucleus, a more careful consideration is required: almost all processes of this kind are exothermic. The possibility of such processes follows from the special properties of the combination proton—negative meson, which may be called a mesonic atom of hydrogen or, if desired, an excited neutron.

A meson stopping in an emulsion loses kinetic energy from, say, 100,000 eV to 2000 eV, which corresponds to a fraction of a micron. This slowing down may occur in silver bromide or in gelatin with comparable probability. In the latter case it will most probably find itself in the vicinity of a proton, the number of which exceeds by more than a factor of two the number of all other nuclei in gelatin. It must therefore first find itself in a hydrogen-like orbit about a proton. The resulting compact neutral atom (its radius in the “Coulomb ground state” is approximately \(1/200\) of the Bohr radius, i.e. \(2.6\cdot 10^{-11}\,\text{cm}\), and the binding energy is approximately 200 times greater than that of the hydrogen atom, i.e. 2700 eV) at distances exceeding \(10^{-9}\,\text{cm}\) will resemble a slow neutron. It will be able easily to pass through the electron cloud of atoms and to come close to nuclei without Coulomb repulsion. Indeed, the polarization of the mesonic atom in the field of another nucleus should lead to an initial attraction.

The next step, most probably, must consist in the capture of the meson by a nucleus of higher charge and in the ejection of the proton. However, there must also be some probability that the proton will be captured and the meson will fly out. At least in one case, namely when the second nucleus is a deuteron, the probability of the second process must be large. In fact, by analogy with the molecular ion of hydrogen \( \mathrm{H}_2^- \), the combination of a deuteron, a proton, and a meson must be stable with respect to Coulomb interactions at intramolecular distances \(10^{-8}/200 = 5\cdot 10^{-11}\,\text{cm}\). At such a distance and with a low potential barrier both nuclei should combine readily, the meson acquiring kinetic energy in a process that may be called “internal conversion.” Thus one may formally expect the reactions:

\[ \mathrm{H}_1^{1}(e^{-}) + Y^{-} \longrightarrow \mathrm{H}_1^{1}(Y^{-}) + e^{-} + 2700\,\mathrm{eV}, \]

\[ \mathrm{H}_1^{1}(Y^{-}) + \mathrm{D}_1^{2} \longrightarrow \mathrm{H}_1^{1}\mathrm{D}_1^{2}(Y^{-}) + 500\,\mathrm{eV}, \]

\[ \mathrm{H}_1^{1}\mathrm{D}_1^{2}(Y^{-}) \longrightarrow \mathrm{He}_2^{3} + Y^{-} + 5.46\,\mathrm{MeV}. \]

It is very unlikely that the small quantities of deuterium present in a normal emulsion are the cause of the observed phenomena. The corresponding process, but with a second proton (with the formation of deuterium, since \(\mathrm{He}^{2}\) is unstable), requires the emission of a positron and a neutrino, which would carry away the greater part of the available (and already insufficient) 1.43 MeV. For heavy nuclei the details of the interaction will be more complicated, since, among other circumstances, adhesion to the molecular ion will occur only when the latter is in an excited state.

The mesonic atom of hydrogen will be attracted to the second nucleus owing to polarization. Some amount of energy may go into the formation of the molecular combination as a result of the Auger effect,

which ceases to act when the nucleus and the meson come together to a distance considerably smaller than the radius of the \(K\)-shell for electrons. This combination dissociates when the meson, as a result of a radiative transition, falls to a level on which it is concentrated around the nucleus with the larger charge. The time of this transition must be of the order of \((hc/e^2)(\lambda/r)^2(1/\omega)\), which is approximately \(10^8 Z^{-2}\) periods of the emitted radiation (as also in hydrogen-like spectra), independently of whether we consider mesons or electrons. The characteristic frequency must be 200 times greater than the frequency of the corresponding electronic spectrum, i.e., for example, \(10^{18}Z^2\), while the frequency of molecular vibrations is \(200^{3/2}\) times greater than the frequency in the case of the electronic bond of hydrogen atoms, i.e. approximately \(3\cdot 10^{17}\). We estimate from this that the lifetime in the bound state must be of the order of \(10^{-10}Z^{-4}\) sec, or approximately \(3\cdot 10^{7}Z^{-4}\) periods of oscillation of the mesonic molecular ion.

The potential barrier which must be overcome by the proton extends from some distance between the nuclei in the excited molecular ion \((r_1)\) to the distance at which the nuclei touch \((r_0)\). In this interval of distances the meson still provides some screening, and we therefore assume that the potential energy is \(E=(Z-1)e^2/r\). We take \(r_1\) equal to that distance at which the polarizing action of the second nucleus on mesonic hydrogen (which we regard as a linear function of the field strength) produces an equivalent displacement of the meson equal to its Bohr radius, \(a_\gamma=2.6\times 10^{-11}\) cm. Thus

\[ r_1=3a_\gamma\sqrt{Z/r}=5.5\times 10^{-12}Z^{1/2}\ \text{cm}. \]

For \(r_0\) we have taken the value

\[ 1.45\times 10^{-13}(A^{1/3}+1)\ \text{cm}, \]

where \(A\) is the mass number of the second nucleus. Consequently, if we write

\[ \lambda^*=\frac{h}{\sqrt{2M(E-E_0)}} \]

(\(M\) is the proton mass) and neglect the initial kinetic energy \(E_0\), the transparency of the barrier for the proton wave must be of the order

\[ \exp\left\{-\pi\int_{r_0}^{r_1}(1/\lambda^*)\,dr\right\} = \exp\left\{-\frac{5\pi e\sqrt{2M(Z-1)}}{h}\left(r_1^{1/2}-r_0^{1/2}\right)\right\} = \]

\[ =\exp\left\{-3.33\sqrt{Z-1}\left(7.4Z^{1/4}-0.4\sqrt{A^{1/3}+1}\right)\right\}, \]

which is approximately \(10^{-27}\) for \(\mathrm{B}^{11}_{5}\). This expression, which is in general rather inaccurate, for example because of the uncertainty of \(r_1\), gives the probability that, on the incidence of a single proton, the latter will pass through the barrier. Multiplying by the number of oscillations before dissociation, we find that the probability of penetration before dissociation will in this case be \(10^{-21}\). This result may differ from the true value by several orders of magnitude, but nevertheless the result remains that, if the adopted model corresponds in any degree to the true state of affairs, the probability of penetration is negligible for all nuclei except the deuteron. For the latter, a similar calculation with

Neglect of internal screening, i.e., taking \(Z-1\) as 1 instead, gives a penetration probability equal to \(10^{-9}\) per oscillation, so that the passage may occur in approximately \(10^{-8}\) sec.

The specific forces of the meson have not been taken into account here. There is an obvious possibility that the meson will undergo nuclear capture or annihilation before the two nuclei can interact; this probability, however, is reduced by the fact that, during the entire time required for this process, the meson is in excited states. If, on the other hand, the meson forces lead to a somewhat closer bond of the proton with the meson than the one we have considered (different from that of the neutron), then it may quite well interact with any nucleus.

For the saturated nuclei \(C_6^{12}\) and \(O_8^{16}\), the proton binding energy is small (1.96 and 0.51 MeV, respectively). For almost all other nuclei it is of the order of 5 MeV or more. The next most frequently occurring nucleus in gelatin is \(N_7^{14}\), which gives 7.3 MeV, which would be sufficient to explain the experiments if \(O_8^{15}\) were formed with an excitation of the order of 3.5 MeV. Boron was also present in these emulsions and could supply more than the necessary amount of energy by proton binding, but in this case the most probable reactions proceed with the emission of \(\alpha\)-particles.

This process can in any case be rejected statistically. Of the total number of 380 mesons stopped in the emulsion, four secondary mesons had tracks at least \(500\,\mu\) long inside \(50\,\mu\) emulsions and with mutually well-agreeing energy yields. Geometrical considerations show that there were at least 30 times as many such cases in which the secondary meson left the emulsion after traversing a shorter path; in this case it could have remained unnoticed or else have been indistinguishable from a proton. On the other hand, the projection of the end of a meson track \(50\,\mu\) long would not have remained unnoticed. Thus the four observed secondary mesons in reality represent \(120\pm 60\) mesons (the deviations refer to the probable error), whereas the 380 observed stopped mesons represent no more than 900 mesons actually stopped in the emulsion. For randomly directed straight tracks ending at all possible depths in an unlimited layer of thickness \(H\), the statistical fraction of all tracks ending in this layer and having ranges whose horizontal projections inside the layer exceed \(R\) will be \(\sqrt{R^2/H^2+1}-R/H\). For \(R/H=1\) this gives 0.414. (For \(R/H>1\), a good approximation will be \(H/2R\), but if \(R/H \gg 1\), the curvature of the tracks will lead to some reduction of this quantity.)

Thus it follows that the formation of a secondary meson with an energy of 4 MeV occurs in \(13\pm 7\) percent of all cases of meson stopping in emulsion. Apparently only half of the mesons

negative, and of them only half can form mesonic atoms of hydrogen (since \(H\) constitutes 40 atomic percent of the whole emulsion); if we assume that the interaction with the second proton is small, so that mesonic hydrogen will with the greatest and nearly equal probability be attracted to carbon, nitrogen, or oxygen (with every eighth nucleus in gelatin being \(N^{14}\)), we shall have an expectation of about 3%, if each collision of a mesonic hydrogen atom leads to capture of the proton and if in every case there occurs an “internal conversion” of the released energy, leading to the formation of a secondary meson with an energy of 4 MeV. The unaccounted-for circumstances are still less probable, and therefore, even with the small number of observed cases available, it is statistically unlikely that they represent this process.

Furthermore, this simple theory shows that one should expect an even larger number of readily observable secondary mesons with energies of 2 MeV and possibly \(\frac{1}{2}\) MeV, appearing as a result of the attachment of a proton to \(C_6^{12}\) or \(O_8^{16}\); however, a simple and probable addition to the theory will be the assumption that these reactions are relatively “forbidden.”

It should be added that such processes may be of importance under other circumstances; if it is correct to assume that mesons can exist for, say, \(10^{-8}\) sec in hydrogen-like orbits about a proton, then there is a finite probability that the meson can induce a nuclear fusion reaction, causing the attachment of the proton to a deuteron. However, in dealing with two or an even larger number of cosmic-ray mesons, it will be necessary to review all the factual material on mesons.

Addition in proof. Later observations make it possible to refine the “corrected observed” fraction of mesons forming secondary mesons: instead of \(13 \pm 7\) percent we obtain \(12.8 \pm 2.5\) percent (\(117 \pm 20\) out of \(917 \pm 70\)), which only lends greater confidence in the correctness of neglecting other possible processes.

CITED LITERATURE

1. C. M. G. Lattes, G. P. S. Occhialini and C. F. Powell, Nature, 159, 93, 186, 624 (1947).
2. E. Gardner, Phys. Rev. (in press).
3. Bethe and Marshak, Phys. Rev. (in press).
   Moller and Pais also considered the possibility of a genetic relationship between different types of particles of intermediate mass.