Nuclear Fissions Induced by High-Energy Cosmic Particles

K. F. Powell, U. Camerini et al. *)

Introduction

During the last few years, experiments with Wilson chambers and counters have shown that the passage through matter of high-energy cosmic particles leads to the formation of showers of penetrating particles. Some authors believe that these events are caused by the passage through the nucleus of fast protons and neutrons and by the interaction of these “primary” particles with nucleons lying in their path. The difficulty of determining the rest mass of particles moving with relativistic velocities is well known, and the true nature of shower particles remains unclear. Furthermore, it is unclear whether shower particles are usually formed singly in successive interactions of the primary particle with nuclei along its path—the so-called “multiple-act” formation—or whether several particles may be formed as the result of a single nuclear collision—“multiple” formation.

In photographic emulsions exposed to cosmic rays, we have recently observed more than two hundred nuclear explosions accompanied by the emission of showers of fast particles with low specific ionization. Apparently, these events are identical with those that give rise to the “penetrating” showers observed in experiments with counters and the Wilson chamber. Thanks to the well-known advantages of the photographic method, we were able to study in detail some features of such events. The results of the observations provide information on nuclear fis—

) I. R. H. Brown, U. Camerini, P. H. Fowler, H. Heitler, D. T. King and C. F. Powell, Phyl. Mag. 40, No. 307 (1949).
II. U. Camerini, T. Coor, J. H. Davies, P. H. Fowler, N. O. Lock, H. Muirhead and N. Tobin, Phyl. Mag. 40*, No. 309, 1073 (1949). Translated by A. N. Gorbunov.

cleavages caused by particles with energies exceeding by more than 100 times the energies obtainable at present in large accelerators.

In the first part we describe the results obtained by scanning plates exposed at a high-altitude station situated at an altitude of about 3300 m on the Jungfrau. In the next part similar observations made at higher altitudes in balloon sondes are described; finally, in the last part the experimental results will be analyzed and discussed*).

I. OBSERVATIONS AT AN ALTITUDE OF 3300 m

Experimental part

The present observations were carried out on Kodak NT4 plates with emulsions 200 μ or 400 μ thick. The plates were developed in Ilford ID19 developer under a specified temperature regime in order to ensure uniform development. Examination of long rectilinear tracks formed by high-energy particles showed that even in the thicker emulsions no distortion of the tracks occurs, except in regions located at a distance of less than 3 mm from the edges of the plate.

Table I

Details of exposure

Information on the exposure of the plates is given in Table I. The different series of plates were developed under different development conditions. In Table I, for the plates of each series, the value of the grain density in the tracks of particles of charge $|e|$ with minimum ionization is also given.

) The third article, to which the authors refer, has not yet been published. (Translator’s note*).

“Fast” and “slow” charged particles

Among the “stars” formed in the emulsions, we found 1200 “stars,” with each of which there is associated at least one fast particle with a specific ionization close to the minimum value for charge \(|e|\). Figure 1 shows the grain-density distribution in the tracks of 300 particles associated with “stars,” from which at least seven strongly ionizing particles, mainly protons and \(\alpha\)-particles, emerge.

Fig. 1. Diagram showing a typical distribution of the grain density of tracks associated with stars. The measurements were restricted to tracks more than 300 \(\mu\) long, belonging to stars with seven or more particles.

The observations were restricted to tracks whose length exceeded 300 \(\mu\). The distribution curve has a maximum at a density of 400 grains per 1 mm. The same grain density in a track was recorded in this same emulsion for individual tracks of fast particles. It will be convenient to denote by the symbol \(i_{\min}\) the minimum value of the specific ionization of a particle with charge \(|e|\), and by \(g_{\min}\) the corresponding value of the grain density in the track.

In Fig. 1 there is a second maximum for tracks with a high grain density, of the order of 2400 grains per 1 mm. These tracks, which are an almost continuous sequence of grains, are caused mainly by protons of relatively low energy, 15–40 MeV. The remaining tracks are distributed continuously between the two maxima. (It should be noted that tracks with a grain density of less than approximately 1200 grains per 1 mm were not recorded by the less sensitive emulsions used until recently.) Below we shall call “slo-

“jet,” a particle that produces a track with a grain density less than \(1.5g_{\min}\), and the track of such a particle we shall call a “thin” track. The value of the ratio of the kinetic energy of such particles to \(mc^2\), where \(m\) is the rest mass, is greater than 2.

Let us denote by the symbol \(\Lambda_h\) the number of strongly ionizing particles in a star whose tracks have a grain density greater than \(1.5g_{\min}\). It will be convenient to call “gray” tracks those with grain density between 1.5 and \(5g_{\min}\), and “black” tracks those with \(g > 5g_{\min}\). Almost all gray tracks are produced by particles with charge \(|e|\). The energy of such particles, if they are protons, lies in the interval from 25 to 330 MeV.

Efficiency of registration of fast particles

In interpreting the results it is important to know the efficiency \(f\) with which the tracks of “fast” particles can be detected under our experimental conditions. A quantitative estimate of the efficiency can be made as follows: the overwhelming majority of \(\pi\)-mesons that stop in the emulsion and, decaying, produce \(\mu\)-mesons with energy 4.25 MeV are positively charged. In approximately 10% of such cases the range of the \(\mu\)-meson ends in the emulsion. We may assume that it then certainly decays with the emission of a fast electron, whose track has grain density equal to the minimum value \(g_{\min}\). Comparing the number of cases in which the decay electron is actually observed with the total number of \(\mu\)-mesons that have stopped in the emulsion makes it possible to determine the value of the efficiency \(f\).

In the plates studied we found 52 cases of \(\pi\)-meson decay in which the \(\mu\)-meson stopped in the emulsion; in 42 of these cases the track of the decay electron can be distinguished. Hence we conclude that \(f > 0.80\). This figure refers to the efficiency of registering tracks of particles for which both the point of origin and the direction of motion are distributed arbitrarily. We shall see, however, that the majority of fast particles associated with stars move in directions making angles of less than \(50^\circ\) with the plane of the emulsion. Since the value of \(f\) is calculated from observation of decay electrons, it represents a lower limit for the efficiency for fast particles associated with stars.

Energy released in stars with different numbers of particles

The second quantity that is important for the interpretation of the results is the mean energy released in stars consisting of different numbers of “black” and “gray” tracks (tracks for which the grain density is greater than \(1.5g_{\min}\). We have determined this quantity

methods described in the Appendix; the measurement results are presented in Fig. 2. Apparently these results agree quite well with the results of the experiments at Berkeley on disintegrations produced by artificially accelerated deuterons and α-particles of known energy, and with observations of disintegrations produced when π-mesons stop in emulsion (if one assumes that all the energy corresponding to the rest mass of such a particle is distributed among the nucleons of the nucleus which it disintegrates). The curve drawn through the points in Fig. 2 is calculated from the empirical relation

Fig. 2. Mean energy released in “stars” in which different numbers of heavily ionizing particles are formed. The energy values correspond to the energy of the emitted nucleons and do not include the energy of the “shower” particles.

Fig. 3. Distribution of the quantities θ for “thin,” “gray,” and “black” tracks. In this case the observations were restricted to tracks whose length was greater than 300 μ, associated with stars with seven or more rays (\(N_h > 7\)).

\[ E\;(\mathrm{Mev}) = 37N + 4N^2 . \]

Orientation of the tracks of fast particles associated with stars

During irradiation the plates were set up so that the emulsion lay in a vertical plane. This made it possible to determine the direction of motion of the particles relative to the vertical as they passed through the emulsion. For simplicity we usually preferred to measure only the angle θ formed by the projection of the track on the plane of the emulsion relative to the vertical.

In Fig. 3, a is shown the distribution of the measured values of \(\theta\) for all “thin” tracks longer than \(300\ \mu\) and formed in stars that are accompanied by at least seven strongly ionizing particles \((N_h \geqslant 7)\). In Fig. 3 and in other diagrams of this type, \(0^\circ\) corresponds to the direction toward the nadir from the center of the disintegration. From Fig. 3, a it is seen that the directions of motion of the fast particles in cases of this class are inclined to the vertical by less than \(40^\circ\). These results suggest that the overwhelming majority of tracks above the stars are produced by particles that move toward the nucleus and cause its disintegration. This conclusion is also confirmed by other observations described in the following paragraphs.

Fig. 4. Distribution of the values of \(\theta\) for tracks of all fast particles associated with “stars.” \(\theta\) is the angle between the vertical and the projection of the track onto the plane of the emulsion; \(0^\circ\) corresponds to the direction of the vertical drawn downward from the center of the star.

Fig. 3, c shows the corresponding distribution of the values of \(\theta\) for strongly ionizing particles that form “black” tracks \((g > 2100\) grains per \(1\ \mathrm{mm})\). From Fig. 3, c it is seen that for these particles, in contrast to the fast ones, an approximately isotropic distribution of emission directions is observed. The results of similar observations for tracks with intermediate grain-density values are given in Fig. 3, b. A tendency for the emission of gray tracks downward is clearly noticeable; however, these tracks are not as sharply oriented as the tracks of fast particles. In Fig. 4 the angular distribution is given for all thin tracks (irrespective of their length) of stars accompanied by at least three strongly ionizing particles \((N_h \geqslant 3)\).

We carried out a similar analysis for all stars accompanied by one or two fast particles. It was found that the directions of motion of the fast particles in most cases are confined to directions making only small angles with the vertical (Fig. 5). Here again the results suggest that the track on the upper side of the star is due to a “primary” particle.

In some cases, when the star contains two fast particles, both of them turn out to be in the upper hemisphere.

If we assume that in all cases the primary particle forms the track that makes the smallest angle with the vertical, then we can determine the angular distribution of the secondary fast particles (Fig. 5, b, III).

Fig. 5. Distribution of the values \(\theta\) for tracks of fast particles; a—for stars with one fast particle; b—for stars with two fast particles. In Fig. 5, b, the initial observations (I) were extrapolated to show the distribution of the values \(\theta\) for incident particles (II) and for emerging particles (III).

Fig. 5, b, II shows the corresponding distribution of primary particles, which, as follows from the above assumption, are absent for \(\theta \leqslant 90^\circ\). Fig. 6 gives the distribution of the observed values of the difference between the directions of motion of two fast particles associated with cases of this class.

Fig. 6. Diagram showing the distribution of the angles between the directions of motion of two fast particles in cases of type \(1_p\).

In making these careful observations, we determined no longer the projection of the track onto the plane of the emulsion, but the true direction of each track \(\delta\), taking into account its angle of inclination in the emulsion. It can be seen that the difference in the directions of the tracks is usually less than \(50^\circ\). However, in some cases much larger values of the deviations were found.

Classification of Stars

On the basis of the considerations presented in the preceding paragraphs, it seems reasonable to classify the “stars” that are accompanied by fast particles in the following way. A star is characterized by the number of fast particles \(n_s\) formed in the nuclear interaction, i.e. by the number of “shower” particles. If the track of a fast particle, also associated with the star, is the track of the particle that caused the disintegration—which we may assume from the direction of its motion—then we shall add the subscript “\(p\)” to the number \(n_s\). If no such tracks are visible, then we assume that the star was formed by some neutral radiation. In this case we add the subscript “\(n\)” to the number \(n_s\). This interpretation will be incorrect if the particle producing the disintegration has charge \(2e\) or greater, or if the velocity of the primary particle of charge \(|e|\) is less than the velocity corresponding to the ionization minimum.

Fig. 7. Schematic representation of stars of various types.

Examples of this classification are shown in Fig. 7, in which various classes of stars are represented schematically. For a further description of a star it is sometimes convenient to determine the number of strongly ionizing particles \(N_h\) \((g > 1.5g_{\min})\) entering into its composition.

Although we shall sometimes make an error by assuming that a track is the track of a particle approaching the nucleus, the directionality of the tracks of the generating particles at an altitude of 3300 m is sufficiently clearly expressed for us to be confident that the effect of errors on the results is negligible.

Stars of Types \(1_p\) and \(1_n\)

Fig. 8, a shows the relative frequency of cases of types \(1_n\) and \(1_p\), in which the formation of a single fast particle is accompanied by the emission of various numbers \(N_h\) of “slow” charged particles. The figure (above) also gives the values of the mean energy released by the nucleons in stars with different numbers of slow particles (the results shown in Fig. 2 were used).

Examples of disintegrations of type \(1_p\) are shown in microphotograph I (see at the end of the issue). From Fig. 8, a it can be seen that the distributions

for cases of types \(1_n\) and \(1_p\) have the same form, and that the frequency of occurrence of stars of these types is the same to within statistical fluctuations.

This striking result shows that the neutral and charged particles that initiate disintegrations of these types have the same intensity in cosmic radiation at an altitude of 3300 m above sea level.

Fig. 8. Distribution of stars of types \(0_n\), \(0_p\), \(1_n\), and \(1_p\) by the number of tracks \(N_h\). Stars of types \(0_p\), \(1_n\), \(1_p\) with \(N_h > 10\) occur equally often. Types \(1_n\) and \(1_p\) are observed equally often for all values of \(N_h\).

In Fig. 8,b is shown the distribution of the magnitude of the energy released in stars of type \(0_p\), analogous to the distribution for stars of types \(1_n\) and \(1_p\) given in Fig. 8,a. A comparison of Figs. 8,a and 8,b shows that the frequency of occurrence of the three types of stars (\(1_n\), \(1_p\), \(0_p\)) with a large number of emitted charged particles is the same within the corresponding statistical errors, but that the number of stars of type \(0_p\) with a small number of charged particles is almost twice as large as the number of such stars of types \(1_n\) or \(1_p\). Stars of class \(0_n\) are more frequent than stars of any other classes for any number \(N_h\). Examples of stars of these classes are shown in microphotographs II and III.

Showers of Fast Particles

The most surprising phenomenon discovered in the present work is nuclear disintegrations accompanied by the emission of “showers” of fast particles. Microphotographs IV and V show mosaics of two showers. Table II shows the ratio of the grain density in the tracks of fast particles formed in these two cases to the value characterizing the minimum ionization for particles with charge \(e\). Each of the showers of fast particles shown in microphotographs IV

and V, is accompanied only by four slow heavy charged particles that have flown out of the initial nucleus, apparently in arbitrary directions. In other cases, showers of this type are accompanied by the emission of a large number of heavy particles. Two typical examples of such cases are shown in microphotographs VI and VII. Microphotograph VIII reproduces a star made with the aid of a projection microscope.

Table II

Analysis of “showers” of fast particles

In Fig. 9 the distribution of the angles \(\theta\) is given for fast particles associated with showers of three and a larger number of shower particles.

It can be seen that the form of the distribution is similar to the distribution shown in Fig. 5, a. Consequently, in this case the observations also confirm the supposition that at least the majority of the tracks of fast particles “above” the stars correspond to charged generating particles causing

of fragmentation. To obtain one more argument, we determined the true direction of the tracks of all fast particles in cases of this type. Illustrative examples are given in Fig. 10.

Each target shown in Fig. 10 depicts the points of impact of “shower” particles on the lower hemisphere. A filled circle indicates the direction of motion of a “shower” particle, and a cross—the direction of the incident particle, on the assumption that it is approaching the nucleus. In some cases a shower particle is emitted in the direction of the upper hemisphere. In this case the direction of its motion is shown by an open circle. The position of this point on the diagram corresponds to the position of a particle moving along the same line of motion as all the particles under consideration, but in the opposite direction.

It is seen from Fig. 10 that, in those cases in which the track of the incident particle can be distinguished, the direction of its motion lies close to the “center of gravity” of the shower particles by which, apparently, it was produced. This connection is clearly noticeable in the case of showers of 10–12 particles, especially if the shower particles are concentrated in a narrow beam. We see in this decisive evidence that a single isolated particle, at least in the overwhelming majority of cases of this type, is in fact the primary particle responsible for the fragmentation. Diagrams like those shown in Fig. 10 make it possible for us to determine the distribution of the directions of motion of shower particles relative to the direction of the charged

Fig. 9. The magnitude \(\theta\) for tracks of fast particles associated with “showers” with \(n_s \geqslant 3\); a—shows the distribution for all tracks; b—for tracks of incident particles; c—for “shower” particles.

of the primary particle. The results obtained in this way are shown in Fig. 11.

The graph in Fig. 11 gives the number of shower particles per unit solid angle for various deviations of these particles from the direction of motion of the charged primary particle.

In almost half of the cases in which showers of five or more charged particles were produced, we were unable to detect tracks with a grain-density value corresponding to minimum ionization (such tracks could have been produced by the generating particles). On this basis, we conclude that in such cases the particle producing the disintegration is electrically neutral.

Fig. 10. “Targets” showing characteristic cases of the orientation of the tracks of “shower” particles relative to the vertical. In the cases shown on the three “targets” at left, the charged primary particle can be detected, and the point corresponding to the direction of its motion is denoted as: \(+p\).

Formation of \(\pi\)-mesons

Among stars of all classes we found examples of disintegrations accompanied by the emission of slow mesons. Typical examples of such cases are shown in microphotograph VI. In 70% of the cases, when such a meson comes to rest in the emulsion, it produces disintegrations with the emission of heavy charged particles. In not a single case did we detect the decay of such mesons with the emission of electrons. In previous works of our labora-

…tory it was shown that at least 95% of the slow mesons formed in stars and stopping in the emulsion are negatively charged. This result was attributed to the influence of the nuclear charge, under the action of which the emitted positive mesons acquire greater energy than the negative ones. Thus, positive mesons stop in the emulsion only in rare cases.

Axis labels in Fig. 11: vertical — “Number of particles as a function of the shower angle”; horizontal — “Deviation of shower particles in degrees.”

Fig. 11. Distribution of the directions of motion of shower particles relative to the direction of the primary particle.

The observations presented are consistent with previous experiments in establishing the fact that at least the overwhelming majority of slow mesons emitted during nuclear explosions are \(\pi^-\)-mesons. The observations agree with the assumption that all slow mesons belong to this type.

Axis labels in Fig. 12: vertical — “Number of cases”; horizontal — “Number of shower particles, \(n_s\).” The labels above the first bins are [[unclear: small numerical labels]].

Fig. 12. Observed frequency of nuclear explosions accompanied by different numbers of shower particles \(n_s\).

Relative frequency of the formation of showers with different numbers of shower particles \(n_s\)

Table III gives the relative frequency of formation of nuclear explosions at an altitude of 3300 m in which the emission of \(n_s\) shower particles is accompanied by the emission of \(N_h\) more strongly ionizing particles (gray and black tracks). Cases with which fast ionizing primary particles are associated are marked by the index \(p\), and neutral particles by the index \(n\).

Table III

Number of stars with given \(n_s\) and \(N_h\)

(To obtain the numbers of stars per \(1\ \mathrm{cm}^2\) per day, the observed values must be multiplied by \(x=2.2\cdot10^{-3}\). The numbers then obtained give the approximate intensity of stars of different types in the absence of an absorber above the plates.)

Continuation of Table III

Figure 12 shows the relative frequency of formation of stars with different numbers of shower particles, independently of the number of accompanying strongly ionizing particles, \(N_h\). The curve in Fig. 12 indicates a continuous decrease in the frequency of appearance of stars with increasing value of \(n_s\). Nevertheless, there is an indication of a noticeable decrease in the number of stars at \(n_s=6\), along with an almost constant frequency of formation of stars with \(n_s\) between 7 and 12. If such an effect exists, then it apparently must be connected with the problem of the multiplicity of formation of “shower” particles in nucleon–nucleon collisions. It is therefore important to increase the statistics of observations.

APPENDIX

Energy released in stars with different numbers of particles

In order to determine the mean value of the energy released as a result of nuclear disintegrations with the emission of different numbers of particles, we first divided the observed cases into 4 groups, according to the value of \(N_h\): \(N_h=4\) or 5, \(N_h=7\) or 8, \(N_h=12\)—16 inclusive, and \(N_h=16\)—25 inclusive. For each of these classes we distinguished three types of tracks:

a) short tracks of length \(<70\ \mu\), formed by particles stopping in the emulsion;

b) “black” tracks with \(g>2100\) grains per 1 mm, formed by particles emerging from the emulsion or stopping after a path in the emulsion exceeding \(70\ \mu\), and

c) “gray” tracks with \(2100>g>600\) grains per 1 mm.

For each class of stars we can calculate the average number of particles in a star that are emitted with a range \(<70\ \mu\). Many of these particles leave the emulsion without stopping in it; however, we can introduce a correction for the thickness of the emulsion by means of a simple geometrical calculation, i.e., the observed number of tracks that reach the end of their ranges in the emulsion (tracks of class a) allows us to calculate the total number of tracks that we should expect in an emulsion of infinitely great thickness.

We assume that the majority of these tracks are formed by \(\alpha\)-particles, but some of them may be formed by nuclear fragments of greater mass and sufficiently large energy, or by protons with a short range. We estimated that the average amount of energy required for the formation of each of these particles is \(15\) MeV; \(10\) MeV is the kinetic energy of the particle and \(5\) MeV is the binding energy. By means of similar observations of tracks of type b, we calculated the true number of “black” tracks formed by particles with range \(>70\ \mu\). We assume that

the overwhelming majority of these tracks are formed by protons and deuterons, and that the formation of each track requires an energy of 21 MeV, independently of the class of the star in which it is formed. Apparently, this assumption is justified by the fact that the grain-density distribution in the “black” tracks does not depend on \(N_h\), and that the grain-density curves for stars of all classes show a steep drop for values \(g\) smaller than 2100 grains per 1 mm (Fig. 1). The emitted protons must be accompanied by neutrons, and we assume that the latter release an energy 25% greater than the protons, in accordance with the ratio of the numbers of neutrons and protons in bromine and silver nuclei.

In Fig. 13: vertical axis: “number of stars”; horizontal axis: “number of ‘grey’ tracks”; panels marked \(N_h = 4.5\), \(N_h = 7.1\), \(N_h = 12\text{–}15\), \(N_h = 16\text{–}25\).

Fig. 13. Diagram showing the distribution of the number of “grey” tracks in stars of different classes.

In Fig. 14: vertical axis: “number of stars”; horizontal axis: “number of grains per 1 mm.”

Fig. 14. Diagram showing the distribution of the grain density of “grey” tracks associated with stars of different classes.

A large part of the energy released in nuclear explosions is carried away by the particles forming the “grey” tracks. Figure 13 shows the relative frequency of occurrence, in stars of the four indicated classes, of different numbers of “grey” tracks. The spread in the values for any class is only slightly greater than the spread,

corresponding Poisson distribution. Since most of the energy is represented by the “gray” tracks, this result suggests that the total energy liberated in a star with a given value of \(N_h\) never differs greatly from the mean value of the energy for stars of its class. Fluctuations depend on whether the emitted fast nucleons with energies between 40 and 400 \(Mэv\) are neutrons or protons.

The distribution of grain density in “gray” tracks for the four different classes of stars that we considered is shown in Fig. 14. From these observations we can determine, for each class, the mean energy of the particles forming the “gray” tracks. We can also determine the mean number of “gray” tracks in stars with different values of \(N_h\) (Fig. 15). Combining all these results, one can find the mean total energy liberated in a star, represented by “gray” tracks, for various

Fig. 15. Mean number of “gray” tracks as a function of the total number of strongly ionizing particles \(N_h\) in a star.

Table IV

quantities \(N_h\). We again assume that the energy carried away by neutrons is 1.25 times greater than the energy of the protons. The results are presented in Table IV and shown in Fig. 2.

II. OBSERVATIONS AT HIGH ALTITUDES WITH BALLOON-SONDES

Experimental part

During exposures at high altitudes the plates were enclosed in a Dewar vessel, as shown in Fig. 16, in order to protect them from large changes of temperature. In several cases the plates were placed above or below lead (see the figure), in order to observe effects connected with the generation of secondary radiation in lead.

Fig. 16. Set of plates with lead blocks in a Dewar vessel.

The gondola, attached to the balloons, was equipped with a radiosonde device, so that the altitude of the apparatus and its direction from the station could be observed throughout the flight. Three characteristic curves illustrating the change with time of the altitude of the balloons are shown in Fig. 17. The flight corresponding to curve \(a\) in this figure was made with two balloons weighing 4 kg, made of natural latex, each of which after inflation gave a net lift of 5 kg; the total load was 6 kg. From the figure it can be seen that the balloons rose with an average speed of 270 m per minute until one of them burst. The remaining balloon thereafter descended at a speed of 210 m per minute.

In the flight corresponding to curve \(b\) in Fig. 17, three 4-kg balloons were used, two of which were inflated so that on the ground they were just able to support the weight of the gondola. The third balloon was inflated more strongly, in order to provide lift; a device was made for releasing this balloon at an altitude of about 26 km. This was accomplished by means of a “barometric switch,” which closed an electric circuit at this altitude. The electric current passed through a wire resistance, which heated up and burned through the cord attaching the balloon to the gondola. This flight was made under conditions of good visibility,

so that the ascent of the balloons could be observed visually. At an altitude of 26,100 m the third balloon separated from the gondola. The two remaining balloons thereafter flew at an approximately constant altitude, until, 40 minutes later, the second balloon burst. After this a rapid fall began.

In the flight represented by curve c, three 4-kg balloons were used, filled in such a way that on the ground any two of them were just capable of supporting the weight of the gondola. Each of the three balloons was equipped with an automatic release device, so that, if a balloon burst, its remnants would fall downward. This method had the advantage that horizontal flight took place at the maximum altitude reached by the least strong balloon, and it was precisely the burst balloon that was cast off downward.

Fig. 17. Change of altitude with time during three characteristic flights. The altitude is determined by means of a “barometric switch,” whose calibration before and after each ascent coincides. The apparent increase in the rate of ascent at great altitudes during flight a may be connected with a change in the temperature of the instrument; however, the large number of tracks of heavy particles found on plates exposed during this flight makes it reasonable to assume that the plates were at an altitude exceeding 30 km for a time interval approximately equal to that indicated in the figure.

By launching sounding balloons in a light wind of favorable direction, and arranging that at least one of the balloons should still remain filled when the gondola reached the ground and serve as a signal for locating the gondola, we succeeded in finding the plates after 95% of the ascents. In order to estimate the intensity of the radiation generated by stars of different types at a given

at the altitude in question, we assumed that the intensity of the radiation which produces stars of a given magnitude \(n_s\) varies with atmospheric depth in accordance with the relation \(I=I_0 e^{-x/k}\), where \(x\) is the mass of the column of overlying air, expressed in \(\mathrm{g}/\mathrm{cm}^2\). On the other hand, we used Gross’s formula, which takes into account the effects associated with the isotropic distribution of the directions of motion of the incident particles at the boundary of the atmosphere:

\[ I=I_0\left\{e^{-x/k}-\frac{x}{k}\int_{x/k}^{\infty}\frac{e^{-z}}{z}\,dz\right\}. \]

Next we can compute the number of days of exposure at Jungfraujoch to which each flight is equivalent for any assumed value of \(k\). Comparing the number of stars formed in \(1\ \mathrm{cm}^3\) of plates exposed at high altitudes with the number of stars formed under an equivalent exposure at an altitude of \(3300\ \mathrm{m}\), we can determine \(k\). For horizontal flights (of the type in Fig. 17, c) the contribution to the exposure during ascent and descent amounts to 20–30%.

It is well known that the assumption of an exponential law of absorption of “star-producing” radiation meets with serious objections, since the absorption process is usually not a one-act process*). However, this law apparently gives a sufficiently close approximation, and therefore it may be used to determine the equivalent increase in the duration of a horizontal flight at maximum altitude owing to the time of ascent and descent. Furthermore, the application of this law enables us to compare our results with those of other investigators, who analyzed their observations in terms of the exponential law of absorption.

Table V

Table V gives the absorption coefficients of particles generating stars of various types, obtained by the above-mentioned method as a result of a series of balloon flights.

*) The exponential law, as is known, describes a one-act absorption process. (Translator’s note.)

Orientation of the tracks of fast charged particles associated with “stars”

In plates exposed at great altitudes, we determined the angular distribution of the directions of tracks with a minimum grain density \(g_{\min}\), associated with stars. The results are given in Fig. 18. This distribution may be compared with the corresponding distribution obtained from observations at an altitude of 3300 m (see Fig. 4). From the comparison it is seen that at great altitudes the vertical directionality of the tracks is less sharply expressed.

At great altitudes the same types of stars were found—with “shower” particles and without them—as at an altitude of 3300 m. However, the ratio of the number of “showers” to the number of stars with a large number of rays is considerably greater at great altitudes. Table VI gives the numbers of stars of different classes found in the present work.

Fig. 18. Distribution of the values of \(\theta\) for all thin tracks associated with stars observed in a series of plates exposed at great altitude. \(\theta\) is the angle between the vertical and the projection of the track onto the plane of the emulsion.

Fig. 19. Frequency of formation of stars with different numbers \(n_s\) at altitudes of 21,200 m and 3300 m. For comparison, the dotted curve is shown, illustrating the results relating to the altitude of 21,200 m and normalized so that the total frequencies of star formation at 21,200 m and 3300 m are equal.

In Fig. 19 is shown the frequency of formation of stars with different numbers of shower particles, \(n_s\), observed at two altitudes: 3300

Table VI

Number of stars with given \(n_s\) and \(N_h\) \((x=1.5,\) see Table III)

and 21,200 m. The results clearly show that at greater altitudes the majority of stars are formed by high-energy particles.

The second important feature of the results obtained at high altitudes is associated with the generating particles of those stars in which showers of fast particles are formed. At an altitude of 3300 m, charged and neutral primary particles produce approximately equal numbers of “showers,” whereas at high altitudes the percentage of cases in which “showers” are produced by charged particles is noticeably higher.

In Fig. 20, a is shown, for plates exposed at high altitudes, the relative frequency with which nuclear

Fig. 20. Number of observed stars with different values of \(n_s\).
\(a\)—at high altitudes; \(b\)—at an altitude of 3300 m; \(c\)—sum of \(a\) and \(b\).

explosions are accompanied by various numbers of shower particles, \(n_s\), having grain density \(g < 1.5\,g_{\min}\).

The form of the distribution is similar to the corresponding curve given in Fig. 12; for comparison it is reproduced in Fig. 20, b. The results of these two groups of observations, combined together, are shown in Fig. 20, c.

Energy of Shower Particles

In some cases a “shower” particle is emitted in a direction almost parallel to the plane of the emulsion, so that its track has the greatest length, in some cases exceeding \(10\,000\,\mu\).

An estimate of the energy of such a particle can sometimes be made by observing the deviations in its track due to Coulomb scattering. We investigated ten such long tracks. Of these, seven tracks were formed by “shower” particles and three by primary particles generating a “shower.” It is to be expected that the latter should possess such a large energy that Coulomb scattering in their tracks will be imperceptible under the conditions

of our experiments, and all noticeable deviations of their tracks will be due to distortions of the emulsion and to errors in the readings of the instruments.

In such cases we can calculate the lower limit of the energy of the corresponding particles and estimate the magnitude of the errors that can be allowed in observing tracks formed by particles with energies less than the shower energy.

Fig. 21 gives a characteristic image of elements (200 μ each) of the track of a fast primary particle, obtained with the aid of a projection microscope. We determined the mean direction

Fig. 21. Image of successive elements (each of which is 200 μ long) of the track of a shower particle with a total length of 10,000 μ. The track is rectilinear to an accuracy of 0.05°, and the energy of the particle that forms it must be greater than \(1.5 \cdot 10^9\) eV.

of the track in successive elements 200 μ long, and the mean magnitude of the difference in the direction of the elements at intervals of 800 μ. Such measurements enable us to determine the quantity

\[ \frac{m_0 \beta^2 c^2}{\sqrt{1-\beta^3}}, \]

which is equal to \(pv\), where \(p\) is the momentum of the particle and \(v\) is its velocity.

Table VII gives the mean magnitudes of the deviations determined by this method and the corresponding values of the particle energies, calculated under various assumptions concerning their rest masses. The very small deviations observed in the case of the “primary” particles convince us that the large values of the deviations found in the tracks of shower particles are real and that the corresponding values of the energies of these particles are not very erroneous. The tracks described in detail in Table VII were selected from the total number only because of their very great length, which is a consequence of their favorable direction. But one may object to this that, for tracks with lower energy, the scattering should be greater and, consequently, the probability of remaining in the emulsion smaller; therefore there should be a tendency to select for measurements only the tracks of particles with the greatest energy. However, if the shower particles are mesons or heavier particles, they must inevitably have energies of at least \(5 \cdot 10^7\) eV, if they form tracks with grain density,

Table VII

Comparison of the observed grain-density values in the tracks of “relativistic” particles associated with stars with the theoretically calculated values under various assumptions about the rest mass of the particles

Continuation of Table VII

close to the minimum value. The scattering angles that may be expected for such particles are so small that deflections of the tracks due to scattering will not noticeably affect the number of particles emerging from the emulsion. This conclusion is not applicable to electron tracks with energy less than \(40\) MeV; but there is reason to think that electrons of such low energy constitute only a small part of the shower particles.

The considerations set out above show that the tracks selected for measurement are random examples of shower particles emitted in directions making small angles with the vertical. This latter restriction follows from the fact that less vertically directed particles, for purely geometrical reasons, will have a small probability of producing a track of very great length.

Furthermore, at an altitude of \(3300\) m the tracks of charged primary particles usually make only small angles with the vertical. Hence it follows that the long tracks of shower particles will usually be inclined at a small angle to the track of the primary particle that produced them. In addition, it is reasonable to suppose that the mean energy of such shower particles considerably exceeds the mean energy of shower particles whose directions of motion are distributed more widely.

Method for determining the rest mass of shower particles

The results given in Table VII show that some shower particles have energies of order \(\sim 3 \cdot 10^8\) eV. This value is still sufficiently small that we can decide whether such a particle is a meson or a proton. A proton track has a grain density \(g\) significantly exceeding \(g_{\min}\) only if its energy is less than \(5 \cdot 10^8\) eV, whereas, for example, a \(\pi\)-meson with energy exceeding \(10^8\) eV will already produce a track with grain density \(g = g_{\min}\). It follows that, if the energy of the particle is less than \(5 \cdot 10^8\) eV, observation of its scattering and of the grain density in its track will in favorable cases allow us to determine its rest mass or to estimate the order of this mass.

The method indicated above is analogous to the method usually employed in experiments with Wilson chambers operating in a magnetic field. In such experiments the particle velocity is calculated from its specific ionization, determined by counting drops, and its momentum from the curvature of the track.

In the photographic method, however, measurement of the grain density makes it possible to determine the particle velocity, and investigation of scattering—the value \(pv\). For the four shower particles that are described in detail in Table VII, we may conclude that their mass is less

mass of the proton. In three other cases it is impossible to draw any conclusions.

This method is especially well suited for studying the nature of particles that form “gray” tracks, and we used it in three cases of stars suitable for measurements. It was found that the corresponding particles are protons.

Formation of π-Mesons at High Altitudes

It is well known that slow π-mesons observed at mountain altitudes are, in many cases, formed locally (either in the material of the photographic plates themselves, or in other matter in the immediate vicinity of the plates). In the case of high-altitude balloon flights the density of matter around the plates is greatly reduced, and we should therefore expect a decrease in the number of π-mesons relative to the number of stars. We investigated plates exposed at two altitudes in order to check the correctness of this view. The results of the investigation, given in Table VIII, give the number of cases actually registered, without introducing corrections connected with allowance for geometrical and other effects. The number of mesons actually stopping in the emulsion must be greater than the observed number. In the last row of the table an estimate of the true value of this quantity is given.

Table VIII

Relative number of mesons and stars observed at different altitudes

The results obtained at high altitudes are divided into two groups according to whether a lead block was placed around the plates or not (see Fig. 16).

The results summarized in Table VIII show that the ratio of the number of π±-mesons to the number of stars is almost three times smaller.

for plates exposed without lead during balloon flights, as compared with plates exposed at an altitude of 3300 m. The results also indicate a rapid increase in the number of mesons formed even for small thicknesses of lead.

Using the numerical data of Table VIII, we estimated the frequency of formation of mesons with energies less than approximately 60 MeV in lead at an altitude of \(\sim 24500\) m. We assumed that the difference between the numbers of \(\pi\)-mesons observed in the experiments with lead and without lead is due to the generation of mesons in lead. These mesons will stop in the plates if they are emitted in suitable directions and if their energy is less than about 60 MeV.

The calculations lead to the conclusion that, in a certain energy interval, the number of mesons formed in a star in Pb is equal to 0.06. This quantity may be compared with the frequency of formation of shower particles in the emulsion, namely 0.05 particles per star.

Our results, therefore, show that the greater part of the mesons arising in the interaction of cosmic radiation with dense materials is emitted with an energy less than 60 MeV. It should be emphasized that the exact value of the maximum energy of the mesons recorded in these experiments is somewhat uncertain. Further experiments are continuing; and a more detailed analysis will be given in subsequent communications.

Secondary nuclear interactions of shower particles

In the present experiments it was sometimes observed that a charged particle, emitted in a nuclear explosion with a velocity close to relativistic, can interact with nuclei and cause secondary disintegrations. Microphotographs IX and X show two cases of this type. In microphotograph IX the first star is of type \(2_n\), and in microphotograph X—of type \(1_n\). A similar case was described by Terc, in which the first “star” belonged to type \(1_n\).

Such observations are important for the problem of identifying shower particles. Indeed, by measuring the mean path length of shower particles in the emulsion before they produce a nuclear collision, we can obtain some idea of the forces of interaction of these particles with nucleons. This estimate is analogous to the experiments with a Wilson chamber, in which the penetrating power of shower particles in lead plates placed inside the chamber is studied.

Our observations are still not sufficiently extensive to permit us to draw any conclusions; but it may be interesting to note that the total observed length of the “thin” tracks formed in stars of types \(1_n\), \(2_n\), \(1_p\), and \(2_p\) in the emulsion is equal to 60 cm, which corresponds to the passage of particles through an absorber

with a mass of 240 g/cm\(^2\). The particles forming these tracks produced three nuclear collisions. On the other hand, the total length of the tracks of fast particles formed in stars with a large value of \(n_s\) is 65 cm; however, not one of them produced a nuclear disintegration. This circumstance will be discussed in greater detail in Part III.

Showers of fast protons produced by heavy primary particles of high-energy cosmic rays

On plates exposed at great altitudes there are many examples of tracks of heavy nuclei of cosmic radiation. Microphotograph XI shows an example of the interaction of one such particle with a silver or bromine nucleus. This case is apparently a striking example of a nuclear collision of the type described by Brad and Peters. It is clearly seen that the track of particle 1 is accompanied by a large number of \(\delta\)-electrons, characteristic of heavy nuclear fragments moving with high velocity. The track shows no deviations in direction exceeding \(1^\circ\) over the extent of the emulsion of four successive plates, corresponding to a mass of about 8 g/cm\(^2\). The number of \(\delta\)-electrons per unit length of track is approximately constant over the whole observed path of the particle. This means that the particle was moving with a velocity close to the speed of light. By determining the number of \(\delta\)-electrons per unit length of track, one can calculate the charge of the particle. For the above-mentioned particle, the magnitude of the charge thus obtained is equal to \((17 \pm 2)e\), where \(e\) is the charge of the electron. At present, in our laboratory and in other laboratories, several examples have been found of heavy nuclear fragments with energies of the order of 200 MeV, emitted during explosive disintegrations of silver and bromine nuclei. However, in the present example the energy of the heavy particle was greater than \(10^4\) MeV. Further, since this particle was approaching the “star,” it was moving downward at an angle of \(\sim 60^\circ\) to the vertical, and its line of motion was very close to the “axis” of the cone of fast particles formed in the disintegration. Thus it has been established that this particle is one of the heavy nuclei of “primary” cosmic radiation and that it,

Fig. 22. Diagram showing the magnitude of the grain density in the tracks of all particles associated with the star shown in microphotograph XI.

colliding with the nucleus, produces a nuclear disintegration and is not one of its products.

Figure 22 shows a diagram giving the distribution of grain density \(g\) for all tracks associated with this event. It can be seen that fourteen secondary particles have a specific ionization less than \(1.3\,g_{\min}\), where \(g_{\min}\) is the minimum ionization of particles with charge \(|e|\). In Fig. 23 we have shown the distribution of the directions of motion of the secondary particles relative to the direction of motion of the heavy fragment, assuming that the latter approaches the disintegrating nucleus.

Fig. 23. Distribution of the deviations of the directions of motion of all particles associated with the star shown in microphotograph XI from the direction of the primary particle.

Axis labels in the figure: vertical—“number of particles”; horizontal—“angle of deviation in degrees.”

▧ — magnitudes of deviations for tracks with minimum ionization,

▧ — for “gray” tracks,

▧ — for “black” tracks.

Most of the tracks of the fast particles are emitted in directions forming angles of less than \(30^\circ\) with the direction of the presumed “primary” particle. The arithmetic sum of the charges carried by these particles is equal to \(12e\).

The observations described lead to the idea that this event corresponds to the interaction of a fast chlorine nucleus with a bromine or silver nucleus, and that as a result of the collision the incident particle is almost completely destroyed and its nucleons are emitted in the form of a narrow beam. Further evidence supporting this conclusion will be given in Part III.

Microphotograph I. Two examples of splittings of type \(1_p\), in which the collision of a relativistic particle with a nucleus is accompanied by the emission of a single “fast” particle.

The small angular difference in the directions of the fast particles in each of these cases is characteristic for the majority of splittings of this class. Both cases are exceptional in the sense that they demonstrate electrons with energies of several MeV (tracks “e”), which emerge from points near the centers of the splittings. Changes in the directions of electron motion owing to scattering can be clearly distinguished. At least in some cases these electrons are formed in the \(\beta\)-decay of unstable nuclear fragments with a short range.

Microphotograph II. A star of type \(0_n\), which is accompanied by the emission of a beryllium nucleus with an energy of 150 MeV and an electron. The beryllium nucleus, identified by the observation of \(\delta\)-electrons, does not emit an electron at the end of its path. Consequently, it probably had a mass of 10, 11, or 12 mass units. The scattering of the electron track can be clearly seen.

K. F. POUELLI, W. CAMERINI, ET AL.

Microphotograph IV. Star of type $6_n$ ($N_h = 4$).

Microphotograph V. Star of type \(6_p\) \((N_h = 4)\).

Microphotograph VI. Three examples of stars of type \(\theta_{\rho}\) that are accompanied by the emission of mesons. In two cases the mesons produce secondary scatterings. This agrees with the supposition that the slow mesons formed in stars of this type are invariably negative \(\pi\)-mesons.

Microphotograph VII. Mosaic of a “shower” of type \(10_n\) \((N_h = 9)\).

Microphotograph VIII. Reproduction of a shower of type \(20_n\) (\(N_h = 23\)), made with a projection microscope.

Microphotograph IX. The particle forming the track \(P_1\) interacts with a nucleus at point \(A\) and produces a nuclear explosion of type \(2_p\) \((N_h = 8)\), in which two “relativistic” particles with charge \(e\) arise. One of the fast secondary particles, \(P_2\), emerging from the star \(A\), produces a secondary nuclear explosion at point \(B\) of type \(0_p\) \((N_h = 9)\). In Part III of the present series of articles it will be shown that cases of type \(2_p\) in 75% of cases correspond to the passage of a particle through the nucleus without the formation of a single charged “shower” particle; while the majority of cases of type \(0_p\) \((N_h \geqslant 9)\) correspond to the passage through the nucleus of an incident proton which, changing its charge, turns into a neutron. A more probable explanation of the present case is that it corresponds to the passage of a fast nucleon successively through two nuclei. Under this explanation, this photograph is a clear example of the principal mode of energy loss of primary protons with energies in the range from \(3 \cdot 10^9\) to \(10^{10}\) eV as they pass through the atmosphere.

Microphotograph X. A case analogous to that shown in the preceding microphotograph. We believe that a star of type \(1_n\) \((N_h = 7)\) was formed at point \(A\) by a neutron which in this process acquires a charge, is deflected like a proton, and forms at point \(B\) a star of type \(0_p\) \((N_h = 2)\). The interpretation of this case is connected with the analysis that will be given in Part III and which shows that 80% of stars of type \(1_n\) are formed by the passage of a proton through a nucleus with a change of charge.

Microphotograph XI. Track 1 can be followed in the emulsions of four plates. The almost constant number of electrons per unit length of track shows that the charge of the particle is equal to \((17 \pm 2)e\). This case, therefore, is interpreted as a collision of a chlorine nucleus with a bromine or silver nucleus in the emulsion.

As a result of the collision, the incident nucleus disintegrates almost completely; its nucleons are ejected in the form of protons and neutrons moving in directions lying within a narrow cone. Most of the more strongly ionizing particles are formed by evaporation of the struck nucleus. Track 32 belongs to a Li nucleus; track 9 to an \(\alpha\)-particle; track 4 to a fast particle that produces a second disintegration at a point lying outside the field of view shown in the photograph.