HIGH-ENERGY NUCLEAR INTERACTIONS

Part I

EVIDENCE FOR THE FORMATION OF HEAVY MESONS

R. R. Daniel, J. H. Davies, J. H. Malvey
and D. H. Perkins*)

1. INTRODUCTION

In recent papers from our laboratory**) the results were given of an analysis of several hundred high-energy stars accompanied by the production of showers of mesons. These stars were selected in examining photographic plates exposed by means of balloon sondes at high altitudes, near geomagnetic latitude \(55^\circ\) N. In these papers the conclusion was drawn that almost all mesons produced in nuclear collisions of primary particles with energy less than \(10\) Bev (the greatest value of the energy that could be measured directly) are \(\pi\)-particles.

In the present work an analysis will be given of showers formed by protons whose energy lies in the interval from \(50\) to \(3000\) Bev. These showers were recorded in several ascents, at geomagnetic latitude \(\sim 55^\circ\) N. For these ascents rubber balloons and non-stretch balloons made of plastic were used. In each flight it was possible to keep the plates for several hours at an approximately constant altitude, lying within the limits from \(22\) to \(32\) km.

It has been suggested\(^9\) that the number of observed \(K\)- and \(\tau\)-particles stopping in photographic emulsions can be explained if it is assumed that they are created in nuclear interactions caused by primary protons with energy greater than \(10\) Bev.

The results presented show that heavy mesons are indeed emitted in showers formed by protons of such

*) See Uspekhi Fizicheskikh Nauk, vol. 40, no. 1, p. 76, 1950, and vol. 43, no. 1, p. 54, 1951.

**) R. R. Daniel, J. H. Davies, J. H. Malvey and D. H. Perkins, Phil. Mag. 42, 342, 753 (1952).

...of high energy. In the more detailed analysis carried out in the present article and in the following Part II, an attempt is made to determine how the disintegration energy is distributed among the resulting mesons of various types. Although this analysis is based on the consideration of data having small statistical weight, the results obtained are of great significance and serve as an illustration of various approaches to the problems arising in the study of nuclear collisions of very high energy.

In the course of the work evidence was obtained making it possible to assert that the neutral meson has a second possible mode of decay, described by the scheme \(\pi^0 \to \gamma + \beta^+ + \beta^-\). This result was obtained in the same experiments as the preceding ones, and the corresponding evidence is examined in detail at the end of the article.

It is convenient to use the notation for stars of various types proposed by Camerini et al.\(^2\). In this notation \(n_s\) denotes the number of shower particles associated with the disintegration, for which the grain density along the track \(g^*\) exceeds the minimum density \(g_0\) by no more than a factor of 1.5. \(N_h^*\) denotes the number of heavily ionizing particles with \(g^* > 1.5g_0\). \(E_p\) denotes the energy of the primary particle that produced the disintegration. Mean values are indicated by angle brackets: \(\langle n_s\rangle\), \(\langle E_p\rangle\), etc.

2. MASS SPECTRUM

Method of measurement

To determine the mass and energy of the secondary particles emitted in nuclear disintegrations, measurements were made of the mean scattering at small angles \(\bar{\alpha}\) and of the grain density \(g\) along the track. Ilford G5 emulsion 400 \(\mu\) thick was used for the experiments.

Systematic errors of measurement were carefully eliminated. Particular attention was paid to establishing the conditions for counting grains. To this end, subjective errors were reduced by counting all unresolved groups of grains (“blobs”) as a single grain. This facilitated rapid grain counting. The statistical error for a given determination of the grain density was taken to be

\[ \frac{0.67}{\sqrt{n}}, \]

where \(n\) is the total number of grains counted. There are indications that the distribution of the number of grains falling on a given segment of track has a sharper maximum than follows from the normal statistical distribution. If this is so, then the error in grain counting is well described by the formula given above. In practice, for each of the measured tracks

$n$ was not less than 1000. Recent measurements have shown that if the particle velocity approaches the speed of light, then the grain density in its track increases. It reaches a minimum for the value

\[ \frac{p\beta}{\mu c^2}=3.5 \]

(here $p$ is the particle momentum, and $\mu$ is its rest mass) and increases by 8% as

\[ \frac{p\beta}{\mu c^2}\to 10. \]

Other experiments have shown that for large values of $\frac{p\beta}{\mu c^2}$ the grain density remains constant within the limits of experimental errors.^{12, 13, 14}

It follows from this that, as the value of the minimum grain density, denoted by $g_0$, one may take the grain density produced by extremely relativistic particles $\left(\frac{p\beta}{\mu c^2}>10\right)$. Whenever possible, such “events” were selected for study in which the primary particles had $\frac{p\beta}{\mu c^2}>10$, and the length of their tracks was greater than 4 mm. These measurements gave the value $g_0$ with an error of less than $2\frac{1}{2}\%$. The values of the grain density for the tracks of secondary particles of one and the same “star” were then compared with the value $g_0$ for the primary particle. In several cases the tracks of two or more secondary particles, for which $g/g_0<2$, were sufficiently long and could be used for measurements.

The degree of agreement of the results obtained in this way served as an additional check on the correctness of the observations. For 25% of the secondary particles, the values of the grain density were normalized by comparison with the grain density of the corresponding primary particles. For the remaining secondary particles, the normalization was carried out by comparison with the grain density in the tracks of primary particles that had produced disintegrations nearby, in the same plate. The variation of grain density with depth was investigated, and in several cases, when this proved necessary, appropriate corrections were introduced. Events observed within a few millimeters of the edge of the plate were not considered, since in this part of the plates there are usually inhomogeneities in the emulsion and anomalies in the grain density. The scattering parameter $\bar{\alpha}$ was determined by a method analogous to that described by Fowler.^8 The microscopes used (magnification 4000) had a table “noise” of less than $0.1\,\mu$ for regions with dimensions equal to $\sim 200\,\mu$. It was assumed that the statistical error in measuring the quantity $\bar{\alpha}$ is given by the expression $0.6/\sqrt{m}$, where $m$ is the number of independent sections into which the track is divided. The size of the sections was chosen so that the mean deviation $\bar{d}$ exceeded the “noise level” by a factor of 5. All tracks that proved too short to obtain a reliable value of $\bar{d}$ were not considered by us.

Let us list the remaining possible sources of error in the determination of \(a\).

(a) Distortion of the emulsion. It was detected from the rapid increase of \(\bar d\) with increasing area size. Tracks showing such an effect were not considered.

(b) The influence of single scatterings through large angles was eliminated by excluding from consideration cases for which the deviation exceeded \(\bar d\) by more than a factor of 4.

(c) The “smoothing” effect, or “narrow-chamber” effect. This effect was especially noticeable in the case of long tracks produced by mesons with energy less than \(100\) MeV. Its influence was reduced to a minimum by using segments of the smallest possible sizes for the determination of scattering.

(d) In order to simplify the determination of masses, in calculating the parameter \(p\beta\) for each track, curves of the dependence of the change in the scattering constant \(K_{c0}\) on the dimensions of the area and on \(\beta\gamma\) were used.

Fig. 1. Relationship between the grain density \(g^*\) and \(p\beta =\) momentum \(\times\) velocity for particles charged in stars, according to various observers. The solid lines for \(\pi\)-mesons and protons were drawn so as to satisfy the experimental data in the best way. The dotted line corresponds to the theoretical calculations of Voyvodich.

In Fig. 1 the relationship is shown between the normalized grain density \(g = g'/g_0\) and \(p\beta\). The points correspond to results obtained by three groups of experimenters: 1) Danich, Locke, and Ecutielli, 2) Voyvodich, and 3) the authors of the present work. As is seen from this figure, there is satisfactory agreement among the results, despite the fact that three different methods were used in calculating the grain densities. The dotted curve corresponds to the theoretical value of the ionization losses in silver bromide ...

re, normalized in such a way as to satisfy the observed “plateau” in the limiting relativistic region. The solid curve, drawn in such a way as to satisfy the experimental data, shows that the increase of the specific ionization with velocity occurs much more rapidly than follows from the theoretical consideration.

Masses of secondary particles produced by protons with energy \(\sim 15\) Bev

In Fig. 2 the values of \(p\beta\) and \(g^*\) are plotted for secondary particles from showers with \(N_h > 5\) and \(n_s \leqslant 12\). In these cases the energy of the primary particle is usually greater than \(5\) Bev and less than \(50\) Bev, while the mean

Fig. 2. Result of measurements of the tracks of particles arising in stars of type
\(N_h > 5,\ n_s \leqslant 12,\ \langle E_p\rangle \sim 15\) Bev.

energy value \(\langle E_p\rangle\) is equal to \(\sim 15\) Bev. We assumed that for \(1.1 < g^* < 2.0\) the points corresponding to particles of different mass lie on straight lines. This assumption agrees especially well with the results presented in the case where the “drop” counting method applied by us is used.

The two straight lines that best satisfy the experimental data correspond to 1) \(\pi\)-mesons and 2) particles whose masses

which are close to the proton mass. The second straight line almost coincides with the straight line obtained for protons by recalculating the first straight line for π-mesons, made under the assumption that the mass ratio is \(\frac{m_p}{m_\pi}=6.66\).

This result indicates that almost all particles of group (2) are protons, and that heavy mesons, if they are present at all in the showers under consideration, occur very rarely in comparison with π-mesons. Fig. 2 also includes 4 points obtained in determining \(\alpha\) and \(g^*\) for the tracks of four π-particles that stopped in the emulsion and showed at the end of their range the characteristic phenomenon of decay into a μ-meson.

Using the results presented in Fig. 2, one can, for each plotted point, calculate the value of the mass by making use of the position of the point relative to the fitted straight line. Fig. 7, a shows the mass spectrum obtained by this method for all points with a value of \(g^*\) between 1.1 and 2.0, under the assumption that the mass of the π-meson is \(276\,m_e\). The small horizontal bars in this figure show the half-width of the expected distributions corresponding to particles of a given mass, calculated on the basis of an estimate of the errors in measuring the quantities \(\alpha\) and \(g^*\). From the median values of these two distributions it follows that the mass ratio is \(\frac{m_p}{m_\pi}=6.6\pm0.25\).

The results shown in Fig. 7, a include data obtained for some stars of type \(1p\). This was done in order to increase the number of protons. Therefore Fig. 7, a does not give the correct ratio between the number of π-mesons and protons.

Mass spectrum for secondary particles produced by high-energy protons. “Jets”

By measuring the energy of secondary particles for a large number of showers, it proved possible to determine the relation between the mean value of the total energy of charged particles emitted in a nuclear disintegration and the number of shower particles \(n_s\) for different values of \(N_h\). The results are given in Fig. 3. Referring further to Fig. 3 presented in paper \({}^2\), we see that, for a given value of \(n_s\), the observed width of the angular distribution of shower particles increases with increasing \(N_h\). These data indicate that secondary interactions play a significant role in the formation of stars with large values of \(N_h\) and \(n_s\).

In contrast to cases of this type, well-collimated showers, or “jets” (jets), of fast particles are observed (see the photographs at the end of the article). These jets are observed in stars containing a small number of tracks of strongly ionizing particles, usually formed in the “evaporation” of a highly excited nucleus, or in stars where such particles are entirely absent.

It will be shown below that many of these cases should be regarded as caused by single collisions of a nucleon with a nucleon. Such cases occur when the primary proton collides either with a hydrogen nucleus or with a nucleon located at the periphery of the nucleus. It was reasonable to assume that the absence of secondary interactions in such collisions will lead to the result that, among the secondary particles produced, there will be only a small number of protons. If this is so, then in these cases, apparently, the most favorable conditions are fulfilled for observing heavy mesons whose mass is close to the proton mass. A second advantage of such cases is that the energy of the secondary particle can be estimated from the observed angular distribution of the secondary particles. Thus, if \(\eta\) is the mean value of the angle at which the shower particles diverge, then the energy \(\gamma_p\) of the primary particle, expressed in proton masses, is given by the approximate expression

\[ \gamma_p = 2/\eta^2 . \]

Fig. 3. Relation between the mean value of the total energy of the “shower” particles and the number of “shower” particles \(n_s\), for three intervals of values of \(N_h\).

Table I gives data characterizing several measured cases of this type. In those cases where the energy of the primary particle \(E_p > 50\) Bev, all tracks of secondary particles for which \(g^{**}\) could be determined with a probable error of less than 3%, and \(\alpha\) with an error of less than 20%, were measured. The mean value of the probable error in the measurement of \(\alpha\) for all measured tracks was equal to 13%. With these restrictions, only 16% of all shower particles connected with the cases considered proved suitable for measurements. It should be noted that the mean value of \(E_p\) for all such showers is \(\sim 500\) Bev.

The results of the measurements are given in Fig. 4; the curves drawn in this figure have the same meaning as the curves in Fig. 2. Fig. 4

Table I

includes the results of all cases for which the energy of the primary particle proved to be greater than 50 BeV. The mass distribution,

Fig. 4. Measurements of “stars” with \(E_p > 50\) BeV, \(\langle E_p\rangle \sim 300\) BeV, for all values of \(N_h\).

obtained on the basis of these data, is shown in Fig. 7,b. In constructing it, all points for which \(g^*\) lies

Nuclear Interactions of High Energy

between 1.05 and 2.0. A remarkable property of the distribution obtained is that almost all the secondary particles selected in this way are heavy mesons with an average mass value close to \(1300\,m_e\). We shall call these particles \(K\)-mesons, since the value obtained for the mass agrees well with the mass of \(K\)-mesons that stop in the emulsion[^15]. It should be noted that the results shown in Figs. 2, 4, 5, and 6 were obtained in measurements carried out by completely identical methods in plates from the same pouring. The only difference between the measurements lay in the types of stars with which the tracks under consideration were associated. This excludes the possibility that systematic errors could have affected the result obtained.

Fig. 5. Measurements of “stars” with \(E_p>50\) BeV, \(\langle E_p\rangle\sim 500\) BeV, for \(N_h<5\).

Although the mass measurements made are not sufficiently accurate for a complete identification of the particles, we assumed that the slower particles in the jets are \(K\)-mesons. This enabled us to estimate the expected frequency of observation of the stopping of such particles in nuclear emulsions. The result obtained is in agreement with observations[^11].

It is possible that among these heavy mesons there are particles of other types as well. However, the scatter of the mass values obtained is consistent with the assumption that the particles are of a single type. It follows from the results obtained that if \(\tau\)-particles do occur in phenomena of the type considered, such cases are rare. The fraction of protons among the particles considered is estimated at \(10\%\).

Figure 5 shows analogous results obtained for jets with \(N_h<5\) and \(E_p>50\) BeV. In their main features they coincide

with the data of Fig. 4 and have been included in the consideration because a significant part of the detailed analysis carried out by us below is based on consideration of cases of this type. The results shown in Fig. 6 for stars with \(N_h \leq 3\) and \(10 < E_p < 50\) Bev indicate that for this energy interval of the primary particles the fraction of emerging \(K\)-particles is small. Measurements made on one track from this series of stars show the existence of a particle to which a mass \((520 \pm 70)m_e\) should be assigned. Since there is

Fig. 6. Measurements of “stars” with \(E_p = 10—50\) Bev, \(\langle E_p\rangle \sim 30\) Bev.

the possibility of unusually large statistical fluctuations of the quantities \(\alpha\) and \(g^*\), it cannot be asserted with certainty that the particle under consideration is not a \(\pi\)-meson. However, the probability that this particle is a \(\pi\)-meson is less than 10%. Let us note that in these particular measurements no sources of systematic errors can be indicated. This follows from the fact that the same star contains secondary particles that are a \(\pi\)-meson, a proton, and a \(K\)-meson. The mass spectrum constructed from the data of Fig. 6 is shown in Fig. 7c.

On the basis of Figs. 4, 5, and 6 one can estimate the relative number of \(K\)- and \(\pi\)-mesons among the secondary particles. In interpreting the number obtained, however, one must exercise a certain caution, connected with the fact that particles of both types have different values of \(p\beta\). Therefore the measurement method itself may create a difference in the number of \(\pi\)- and \(K\)-particles. In practice, the influence of this circumstance can be checked by considering only such

tracks which form, with the direction of the primary particle, angles \(\vartheta\) greater than the mean value of the angle \(\eta\). We assume that these tracks belong to those particles which, in the center-of-inertia system of the interacting nucleons, were emitted in the opposite direction. These cases are represented among the data plotted in Fig. 5 by black circles. A simple analysis of the observations shows,

Fig. 7. Mass spectrum of secondary particles arising in “stars” of various types.

that

Table II

that the angular distribution for all measured tracks (the angles were measured from the direction of motion of the primary particles) does not differ from the distribution for all tracks with $\theta > \eta$.

For the relative number of $K$-mesons and protons, on the one hand, and $\pi$-mesons, on the other, we obtain, according to Fig. 5:

\[ \frac{N_K+N_p}{N_\pi}=\frac{9}{18}=0.5\pm0.2. \]

For large values of $g^*$ the conditions we used for counting grains become inconvenient, and therefore our analysis is restricted to values $g^*<2.0$. Among 500 tracks of secondary particles observed in showers with $N_h \leq 5$, however, only one measurable track was found for which $g^*>2.0$.

3. FREQUENCY OF PRODUCTION OF NEUTRAL $\pi$-MESONS. RATIO BETWEEN THE NUMBER OF NEUTRAL AND CHARGED $\pi$-MESONS

Additional information on particles produced by protons of very high energy can be obtained from consideration of electron pairs associated with such interactions. Most of these pairs are formed as a result of the “materialization” of $\gamma$-radiation arising from the decay of $\pi^0$-particles[^4]. Knowing the mean path length of a $\gamma$-quantum in the emulsion before its conversion into two electrons, and measuring the number of electron pairs and the total length of the tracks of all shower particles associated with the same stars, one can determine the relative number of charged and neutral $\pi^0$-particles:

\[ R=\frac{N_{\pi^0}}{N_\pi}. \]

In the case of high-energy disintegrations in which the production of $K$-particles becomes appreciable, one should, however, expect a decrease in the ratio of the number of electron pairs to the number of shower particles, since the latter now contain a certain number of $K$-particles. This argument assumes, of course, the absence of $\gamma$-rays produced by any process other than the decay of $\pi^0$-particles. Such radiation might arise, for example, in the decay of short-lived heavy neutral mesons, or it might be formed directly in the collision of two protons. If such sources of $\gamma$-radiation are absent, then the observed change in the value of $R$ makes it possible to estimate the fraction of $K$-mesons among the shower particles.

In order to use such observations for estimating the number of $K$-mesons, it is necessary to know the value of $R$ for stars of low energy, i.e. for such stars in which $K$-mesons are not produced, or are produced very rarely. Carlson et al.[^4] obtained for the value of $R$ the value $0.45 \pm 0.15$, but in later experiments carried out by other methods different results were obtained. This prompted us to determine anew

...to determine the value \(R\), using for this purpose the method described earlier. To this end, stars with \(n_s > 6\) and with a length of the tracks of secondary particles greater than 1 mm were selected. The sector of the plate located near each star on the side opposite to that from which the primary particle arrives was investigated. For these measurements a special microscope stage was constructed. It allowed the plate to be rotated about the beginning of the star as about a center. The selected portion of the plate was examined in the direction from the center of the star, over a length from 1 to 2 mm. The actual values of the length depended on the magnitude of the inclination of the secondary tracks in the emulsion. The volume of emulsion investigated in this way contained the tracks of more than 80% of all shower particles. This method made it possible at once to separate electron pairs “associated” with the star from “unassociated” ones, since the bisector of the angle between the components of the pair was determined immediately. If the tracks of the pair components were of sufficient length, scattering measurements were made.

It was assumed that a pair is associated with the star and suitable for measurements if the bisector of the pair passed at a distance of several microns from the center of the star and if the total energy of the pair \(E_T\) exceeded 100 MeV. The mean value of the kinetic energy of neutral \(\pi\)-mesons producing \(\gamma\)-quanta with an energy of 100 MeV is 70 MeV, and this energy value is minimal for a \(\pi\)-meson if it is classified as a shower particle. In all, 19 pairs satisfying the stated conditions were observed. They were obtained by examining 140 stars; moreover, the total length of the tracks of shower particles on the surface investigated was equal to 100 cm. The value of \(R\) can be determined from these data as follows:

(a) The contribution made by protons to the total track length of shower particles was estimated on the basis of the data of Camerini et al. (Fig. 5 of paper\(^3\)). We considered stars with \(n_s = 9\). For such stars the fraction of protons among the shower particles is 16%, whence it follows that the total path length of mesons in the emulsion is 84 cm.

(b) It is assumed that the angular distribution of neutral \(\pi\)-mesons is identical with the distribution for shower particles. It should be noted that, owing to the fact that the directions of motion of the two photons arising in the decay of a neutral meson make a certain angle with one another, it is not possible directly to compare the total path length of the photons with the total path length of charged \(\pi\)-mesons. The approximate value of the corresponding correction is equal to 2%, and it may be introduced.

(c) It should be taken into account that the mean path length of a photon before its conversion into a pair depends on the photon energy. It was calculated that on the average this quantity is equal to 4.45 cm.

R. R. Daniel, J. H. Davies, D. H. Malvey and D. H. Perkins

(d) Assuming that the true ratio \(R_t\) of the number of neutral to the number of charged \(\pi\)-mesons is constant, it can be shown that for \(n_s \ne 0\)

\[ R_t = R_0 \frac{n_s p(n_s)}{(n_s+1)p(n_s+1)}, \]

where \(p(n_s)\) is the number of stars with \(n_s\), and \(R_0\) is the observed ratio.

From the observed distribution of the values of \(n_s\) for the stars studied, an approximate value of the correction factor was calculated; it proved to be equal to 1.1.

In a separate plate each photon usually traverses a distance small in comparison with the mean conversion length. Thus, the path length of photons in the investigated area of the emulsion is found to be \(19 \times 4.45 \times 1.02 \times 1.10 = 90\) cm. Assuming that all quanta arise as a result of the process \(\pi^0 \to 2\gamma\), we obtain that the equivalent path length of neutral mesons for decay is 47 cm. Comparing this length with the total path length of charged \(\pi\)-mesons (84 cm), we obtain \(R = 0.56 \pm 0.12\). This result is in good agreement with Saldwin’s experiments carried out with a Wilson chamber.

It should be noted that the result obtained refers to stars of a definite type, for which \(n_s > 6\). This group of stars is produced by primary protons whose energy \(E_p\) is greater than 10 Bev: the mean value \(\langle n_s\rangle = 9\) corresponds to the mean value \(\langle E_p\rangle = 25\) Bev. In the preceding paper it was concluded that at \(n_s = 10\) multiple meson production predominates. In this case, for \(R\) one should expect values equal to 0.5. However, at small values of \(n_s\), when single mesons are formed, it follows from considerations of charge independence that \(R = 0.75\).

If, further, cases of the \(0_p\) type are included in the consideration, then the resulting value of \(R\) increases. These arguments show that the existing discrepancy between the results of different experiments may be explained, at least in part, by a different distribution of the quantity \(n_s\) in the stars used for observation.

The second decay scheme of the neutral meson

In addition to the 19 electron pairs discussed above, it was possible to observe 11 pairs whose components form small angles with one another. These pairs arise at distances of less than \(5\ \mu\) from the center of the star, and measurements of \(\bar{\alpha}\) and \(g^{**}\) show that they are formed by electrons. Fig. 8 shows the corresponding distribution \(f(r)\) for all the electron pairs considered, as a function of the distance \(r\) of the point of formation of the pair from the center of the star. This distribution includes pairs for which \(r < 1\) mm. Owing to the fact that some of the particles and quanta leave the emulsion, a significant

more likely to observe pairs for which the value of \(r\) is small than pairs with large values of \(r\). Simple geometrical considerations make it possible to estimate this “loss” effect. The results shown in Fig. 8 are given with the corresponding approximate corrections.

Let us suppose that all electron pairs arise as a result of the decay of short-lived \(\pi^0\)-mesons into photons. In this case the corrected distribution for the small values considered here must be independent of \(r\): \(f(r)\,dr = k\cdot dr\). However, the results

Fig. 8. Frequency of occurrence of “associated” electron pairs as a function of the distance of the point of formation of the pair from the star.

shown in Fig. 8 indicate that a considerable fraction of the pairs arises at points situated very close to the center of the star. Most of these pairs cannot be explained by conversion of photons arising from the decay of \(\pi^0\)-mesons formed in stars. It is also difficult to suppose that these pairs are the result of the following process: in the collision of primary protons with nuclei, bremsstrahlung arises, whose \(\gamma\)-quanta convert in the field of the same nucleus, forming an electron pair. The occurrence of these pairs can be readily explained if one admits that there exists a second decay scheme of the neutral meson:

\[ \pi^0 \to \gamma + \beta^+ + \beta^- . \]

The existence of such a process was assumed earlier\(^5\). If this hypothesis is correct, then the result obtained makes it possible to estimate the ratio of the decay constants corresponding to the two decay schemes.

Thus, we find that per 1200 shower particles the number of \(\pi^0\)-mesons is equal to \(0.56 \times 1200 \times 0.84 = 565\), while the number of pairs formed in the immediate vicinity of the star is equal to 11. Hence it follows that

\[ \delta = \frac{11}{565} = 0.020 \pm 0.006 . \]

It should be noted that decisive evidence against the assumption that the close pairs arose as a result of gamma-ray conversion on the “parent” nuclei could be obtained if it were found that there is a noticeable increase in the number of pairs formed at points near the center of the star as a function of the distance from it. At present the statistical accuracy of the data obtained for high-energy cases is insufficient for such a test. Calculations show\(^6\) that many of the pairs formed in the assumed decay

\[ \pi^0 \to \gamma + \beta^+ + \beta^- , \]

must diverge at larger angles than pairs of approximately the same energy arising in the conversion of \(\gamma\)-rays. Among the secondary particles emitted in nuclear explosions, several single electrons were indeed observed. It is possible that in these cases a second electron existed, but was emitted in such a direction that its track could not be detected. Therefore it has so far proved impossible to obtain from experiment the true distribution of angles between the tracks of both electrons arising as a result of the second assumed mode of decay of the \(\pi^0\)-meson, and to compare it with the predictions of the theory. Some electron pairs may have remained unnoticed because their energy was too large. If, however, the energy spectrum of the electron pairs does not depend on the mode of decay of the \(\pi^0\)-mesons as a result of which these pairs are formed, then it may be asserted that about 90% of all pairs whose component angles are less than \(3^\circ\) are recorded.

If the angular distribution of electron pairs formed directly agrees with Dalitz’s calculations\(^6\), then the median of the corresponding distribution of angles between the components of the pairs under our experimental conditions is equal to \(\sim 3^\circ\). It follows from our results, therefore, that \(\delta > 0.04\).

Because of the existence of the second mode of decay of \(\pi^0\)-mesons, the mean value of the photon path length, determined by the method described in the preceding paragraph, proves to be overestimated. This effect, however, is very small. It does not exceed 1% and may be neglected. We note that all 19 pairs formed at distances exceeding \(18\,\mu\) from the “parent” star were assumed to have arisen as a result of photon conversion.

Relative number of mesons of different types

Using the method described above, we investigated the presence of electron pairs in the region of the emulsion located near high-energy “jets.” In doing so, owing to the fact that all tracks in the “jets” as a rule diverge at small angles, the search for pairs

it was possible to carry out at a considerably greater distance than was possible in low-energy stars. In all, 23 pairs were found. The total length of the tracks of the corresponding shower particles, distributed among 33 “jets,” was equal to 101 cm. In all cases the energy of the primary particles exceeded 50 Bev, and the total number of shower particles associated with the stars under consideration was 740. In these “jets” some pairs arising in the decay \(\pi^0 \to \gamma + \beta^+ + \beta^-\) cannot be immediately identified, owing to the relativistic expansion of the time scale for neutral \(\pi\)-mesons (mean energy about 500 Bev). Assuming that the probability of direct decay into a pair is 2%, we obtain for the sought ratio of neutral mesons to the total number of shower particles the value

\[ \frac{N_{\pi^0}}{N_{\pi^\pm}+N_{K^\pm}+N_p} = \frac{23}{(2 \times 101)/3.75+(740 \times 0.02)} = 0.33 \pm 0.07 . \]

In obtaining this result, we assumed that the mean path length for the conversion of high-energy photons formed in jets is 3.75 cm, and that the effect of the angular divergence between each pair of photons may be neglected. It was estimated that the contribution of protons to the total track length of the shower particles amounts to 10%. It is also necessary to introduce corrections for the production of photons in other processes. The fraction of photons produced in bremsstrahlung of the primary protons and in the decay of mesons can be estimated on the basis of Omi’s theory\({}^{16}\). If the energies are very large \((E_p > 1000\ \text{Bev})\) and if the particles produced in nuclear collisions have spin greater than zero, then a considerable part of the primary energy may be released in the form of photons. For mesons with zero spin, the total addition to the photon flux produced by bremsstrahlung is, apparently, only 5%. Let us assume that the mean lifetime of the neutral \(\pi\)-meson is \(10^{-14}\) sec or less. Then the correction connected with the finite path length of \(\pi^0\)-mesons, which should be introduced into the value of \(N_{\pi^0}/n_s\), will be less than 2%, and, taking it into account, we obtain:

\[ \frac{N_{\pi^0}}{N_{\pi^\pm}+N_{K^\pm}} = 0.35 \pm 0.07 . \]

Assuming that the quantity \(R\) remains constant for disintegrations of all types and is equal to \(0.56 \pm 0.12\) (the value obtained for low-energy stars), we find that

\[ 1+\frac{N_{K^\pm}}{N_{\pi^\pm}}=1.6 \pm 0.5;\qquad \frac{N_{K^\pm}}{N_{\pi^\pm}}=0.6 \pm 0.5 . \]

This value is in agreement with the value obtained by direct mass measurement. Despite the large statistical errors, these results are an additional confirmation of the fact that, if the primary energies exceed 50 Bev, the production of heavy mesons assumes the same significance as the production of \(\pi\)-mesons.

An important feature of this second method is that, in contrast to the direct determination of the mass of shower particles, which is usually carried out only for tracks lying outside the mean value of the angle, in the search for electron pairs the whole region of the central cone of the shower is used. It is therefore desirable to carry out more extensive measurements in order to obtain results having greater statistical weight. We note that, if photons in fact exist which arise not in the decay of \(\pi^0\)-particles but, for example, in the bremsstrahlung of primary protons, then, when the method under consideration is used, the quantity \(N_{\pi^0}/N_{\pi\pm}\) will be overestimated, and the number of \(K\)-particles will be underestimated. The total energy of pairs of particles arising in showers traveling at a small angle often proves too large for the particles to be identifiable by measuring \(a\) and \(g^*\). However, in all such cases the observed value of the grain density was close to \(g_0\), and along the tracks phenomena were found which are explicable by the presence of bremsstrahlung and cases of the production of “tridents.” It follows from this that these particles are electrons. We find additional confirmation of this point of view in the fact that, at the point of formation of such a pair of tracks, the track of a slow recoil electron is often observed (see the photographs). Such recoil electrons are not formed in the conversion of a neutral meson into charged particles. They are characteristic of processes of pair production by photons in the field of a nucleus, in which ionization of the atom occurs.

4. SECONDARY INTERACTIONS OF SHOWER PARTICLES

If the heavy mesons found among the particles of a “shower” are mesons of the nuclear forces and are formed directly in high-energy nuclear collisions, their effective cross section for nuclear interactions should be of the order of the geometrical cross section. To check this assumption we measured the total length of the tracks of shower particles arising in all the observed events produced by protons with energy \(>50\) Bev. It turned out that, for a total track length equal to 129.3 cm, 5 nuclear interactions were found. (It was shown that among these five tracks one track belonged to a \(\pi\)-meson.) If it is assumed that the effective cross sections of nuclear interactions of all secondary particles in the showers are equal to the geometrical cross section, then for the mean length

NUCLEAR INTERACTIONS AT HIGH ENERGY

one should expect a value of the path length in the emulsion equal to 25 cm. Our result is thus consistent with the assumption that heavy mesons, like π-particles, have an effective nuclear-interaction cross section close to the geometrical one, and are produced directly in nuclear interactions. For final conclusions, however, it is desirable to increase the statistical weight of the observations. Among the shower particles composing the jets, we observed two cases of apparent deflection through large angles, equal to \(7^\circ\) and \(25^\circ\), respectively. Also noted was a secondary particle with energy \(8.8 \pm 1.5\) Bev, emitted to the side from one of the jets. After this particle has traveled a path of \(1.5\) cm, the scattering suddenly increases, and the new value of \(\alpha\) corresponds to an energy equal to \(2.7 \pm 0.5\) Bev. This phenomenon may be interpreted as the formation of an electron of bremsstrahlung radiation. However, the direct production of electrons in showers occurs rarely, and they are usually produced in pairs. Therefore it seems reasonable to explain this phenomenon by the decay of a heavy meson into an electron. Since a large decrease of energy occurs here, this case cannot be a \(\pi \to \mu\) decay.

It was shown earlier that in phenomena of the type \(N_h \leqslant 5\) and \(E_p > 50\) Bev the ratio \(N_K/N_\pi \sim 0.5\). It follows from this that, of the total length of the tracks of all shower particles in phenomena of this class, the share due to \(K\)-mesons is 43 cm. In the laboratory system the mean value of \(\gamma\) for \(K\)-mesons is 7. If the three cases described above are regarded as the process of \(K \to \mu\) decay, then one can roughly estimate the true lifetime of the \(K\)-meson, which turns out to be \(10^{-10}\) sec. In searching for electron pairs, we tried to find, in the jets under consideration, evidence for the decay of \(V_2^0\) particles, but without success. If one assumes that \(V_2^0\)-particles and \(K\)-mesons are formed in equal quantities, it follows that the path length of \(V_2^0\)-particles in the investigated volume of emulsion is 43 cm. Further assuming that the mean value of \(\gamma\) for these particles is equal to the value of \(\gamma\) for \(K\)-mesons, we obtain for the lifetime of \(V_2^0\)-particles an upper limit equal to \(2 \times 10^{-10}\) sec. This result does not contradict the data obtained by the Wilson chamber method. It may be supposed that, with time, the total path length of particles identified with \(K\)-mesons will become sufficiently large to allow an accurate determination of the mean path length over which the interaction occurs.

The interaction of the identified secondary particles is of interest in connection with the possible existence of negatively charged protons. The total energy released in the star arising from the annihilation of such a particle with a proton must exceed the kinetic energy of the “parent” star by 2 Bev. Under favorable observational conditions such cases may be detected.

5. ANGULAR CORRELATION BETWEEN SECONDARY PARTICLES IN JETS

A study of the angular distribution of particles emitted in high-energy disintegrations, carried out by Cosyns[^5], indicated the presence of a correlation in the directions of emission of pairs, and sometimes also triads, of particles. Recently[^7] it was shown that in stars formed by primary particles with energy less than \(10\) Bev, about \(10\%\) of the secondary particles occur in close pairs. Such an angular correlation cannot be explained by accidental coincidence. In those cases where both particles of the pair are \(\pi\)-mesons, they also have close values of the energy. Our explanation of phenomena of this type is that they are produced by the decay of neutral mesons \((\pi^0)\) with a very short lifetime. The energy released in their decay is approximately \(2\) Mev. Bearing these results in mind, we made a comparison of the expected and observed number of pairs among shower particles in jets. For this purpose it was convenient to use the angular distribution obtained from observations of tracks formed in all events, measuring for each track the ratio of the angles \(\vartheta'=\vartheta/\eta\). Having the distribution obtained in this way, one can calculate for each star the expected number of pairs due to random coincidences. Table III gives the expected and observed numbers of pairs for various values of \(\delta\vartheta'\) and various intervals of \(\vartheta'\). From these data it follows that any non-random associations of tracks are rare.

Table III

Expected and observed numbers of pairs for various values of the angle between the components of a pair, \(\delta\vartheta'\), and of the angle between the direction of the pair and the direction of the primary particle, \(\vartheta'\)

In the case of the smallest value of \(\delta\vartheta'\) we observed 15 pairs. The expected number of pairs in this case is 8. The difference exceeds the standard deviation by only a factor of two, but if it is regarded as significant, then the presence of such a difference means a correlation among approximately \(3\%\) of the shower particles. On the basis of the available numbers of \(K\)-mesons and protons, this means that among the shower particles there are about \(4.5\%\) correlated \(\pi\)-mesons. The mean angle of divergence for \(\delta\vartheta' < 0.1^\circ\) is \(0.7^\circ\). This angle has the correct order of magnitude if the observed effect is attributed to the decay of a \(\zeta^0\)-meson, in which energy of approximately \(3\ \mathrm{MeV}\) is released.

At present the number of pairs with sufficiently long tracks, allowing measurements of \(\bar{\alpha}\) and \(g^*\) to be made, is too small for it to be possible to ascertain the presence of an energy correlation among the particles forming the pair.

6. LIFETIME OF THE NEUTRAL MESON

Dalitz\(^6\) pointed out that the study of pairs arising in the process of direct decay of a neutral \(\pi\)-meson into electrons according to the scheme

\[ \pi^0 \to \gamma + \beta^+ + \beta^-, \]

makes it possible, in principle, to determine the mean lifetime of the neutral meson. This method is less complicated than the method based on photon conversion. Whereas in practice it is possible to distinguish between pairs arising in the two decay schemes, an exact determination of the points of formation for all pairs arising in direct decay is not easy. The lifetime for such a decay is so small that such pairs usually arise very close to the center of the corresponding disintegration, and if the kinetic energy of the \(\pi\)-meson is less than \(300\ \mathrm{MeV}\), reliable measurements cannot be made.

However, at high energies the relativistic broadening of the time scale of the moving particle can considerably increase the length of the path traversed by it before decay. It then proves possible to measure the distribution of the values \(r/p\), where \(p=\beta/\sqrt{1-\beta^2}\). The determination of the value \(p\) for a given neutral meson is made from its energy, determined on the basis of the assumption that the photon and the electron pair receive, in the decay, approximately equal parts of the total energy of the decaying \(\pi^0\)-meson.

The energy of the pairs in most cases was determined by measuring scattering. In those cases where this was impossible, the lower limit of the energy was established from the angle between the tracks of the electrons of the pair.

The probability of observing a pair at a distance \(r\) from the star is

\[ \left\{ \frac{(2-\delta)\exp\!\left[-\frac{r}{L}\right] -\exp\!\left[-\frac{r}{pc\tau}\right]} {L-pc\tau} + \frac{\delta}{pc\tau}\exp\!\left(-\frac{r}{pc\tau}\right) \right\}\,dr, \]

where \(L\) is the mean conversion length. This expression can be

Fig. 9. Frequency of occurrence of “associated” electron pairs as a function of \(\frac{r}{p}\); \(r\) is the distance of the point of pair formation from the star, and

\[ p=\frac{\beta}{(1-\beta^2)}. \]

The curves shown were calculated for different values of the lifetime of the \(\pi^0\)-meson.

normalized with respect to the total number of \(\pi^0\)-particles, \(N_0\). Introducing the notation \(x=(r/p)\), we can write:

\[ N(x)\,dx = \]

\[ = N_0 \left\{ \frac{(2-\delta)\exp\!\left[-\frac{xp}{L}\right] -\exp\!\left[-\frac{x}{c\tau}\right]} {L-pc\tau} + \frac{\delta}{pc\tau}\exp\!\left(-\frac{x}{c\tau}\right) \right\}p\,dx. \]

Since \(L\) is large and \(\delta\) is small, it follows that

\[ N(x)\,dx \simeq \]

\[ \simeq N_0\left\{\frac{2\langle p\rangle}{L}\left(1-\exp\left[-\frac{x}{c\tau}\right]\right) +\frac{\delta}{c\tau}\exp\left(-\frac{x}{c\tau}\right)\right\}dx, \]

where \(\langle p\rangle\) is the mean value of \(p\). The dependence obtained for \(L=4\) cm is presented in the graphs of Fig. 9; in constructing them we used the observed value \(\delta=0.02\) and values of \(\tau\) equal to \(5\cdot 10^{-15}\), \(1\cdot 10^{-14}\), and \(5\cdot 10^{-14}\) sec. These graphs can be compared with the distribution obtained experimentally after the corresponding geometrical corrections, taking into account the “loss” of pairs in the emulsion, have been introduced into the latter. These corrections for “loss” increase with increasing \(r\), and therefore the distribution \((r/p)\) is given only up to \(70\mu\).

The best agreement between the experimental data and the calculated curves is obtained for \(\tau\) equal to \(10^{-14}\) sec. Although these results do not allow us to exclude a shorter lifetime, nevertheless it seems reasonable to assume that the observed small increase in the number of pairs for small values of \(r/p\) has physical meaning.

The value \(10^{-14}\) is in agreement with the value obtained by Kaplon, Peters, and Ritson.

7. CONCLUSION

Our main conclusions may be formulated as follows:

1. In nuclear interactions produced by primary protons with energy greater than 50 Bev, the formation of heavy mesons, provisionally identified with \(K\)-particles, begins to compete seriously with the formation of \(\pi\)-mesons.

2. We have no evidence that the formation of heavy charged mesons, different from \(K\)- and \(\pi\)-mesons, played an important role even at the highest energies studied (1000 Bev). In the cases studied, the energy of the colliding nucleons in the center-of-inertia system, expressed in proton masses, lies within the limits from 10 to 70. It follows from this that the formation of strongly interacting particles whose mass is comparable with the mass of nucleons, or even greater than it, is energetically possible. However, such particles have not been detected.

3. Between the data on the number of \(K\)-particles formed in disintegrations, obtained by direct mass measurement, and the data derived from observation of the frequency of occurrence of associated electron pairs, there is rough agreement.

1. The mean lifetime of the \(\pi^0\)-meson was found to be \(10^{-14}\) sec, which is in agreement with the data of Kaplan, Peters, and Ritson.

2. The probability of direct decay of the \(\pi^0\)-meson, according to the scheme \(\pi^0 \to \gamma + \beta^+ + \beta^-\), does not exceed 4%.

3. The lifetime of the \(K\)-meson is equal to \(\sim 10^{-10}\) sec.

CITED LITERATURE

1. Camerini, Fowler, Lock and Muirhead, Phil. Mag. 41, 413 (1950).

2. Camerini, Davies, Franzinetti, Lock, Fowler, Muirhead, Perkins and Yekutieli, Phil. Mag. 42, 1241 (1951).

3. Camerini, Davies, Franzinetti, Lock, Perkins and Yekutieli, Phil. Mag. 42, 1261 (1951).

4. Carlson, Hooper and King, Phil. Mag. 41, 701 (1950).

5. Cosyns, Nuovo Cim. 6 (Supp. No. 3) 397 (1949); Report of Harwell Conference, 19 (1950).

6. Dalitz, Proc. Phys. Soc. A, 64, 667 (1951).

7. Danysz, Lock and Yekutieli, Nature, Lond., 169, 364 (1952).

8. Fowler, Phil. Mag. 41, 169 (1950).

9. Fowler, Menon, Powell, Rochat, Phil. Mag. 42, 1040 (1951).

10. Heitler and Janossy, Proc. Phys. Soc. A, 62, 364, 669 (1949); Helv. Phys. Acta, 23, 417 (1950).

11. Menon, Bristol Conference on \(V\)-particles and heavy mesons, 1951.

12. McDiarmid, Phys. Rev. 84, 851 (1951).

13. Morrish, Phil. Mag. 43, 533 (1952).

14. Occhialini, Report of Como Conference (1949).

15. O’Ceallaigh, Phil. Mag. 42, 1032 (1951).

16. Oehme, Zeits. f. Phys. 129, 573 (1951).

17. Voyvodic and Pickup, Phys. Rev. 85, 91 (1952).

“Jet” produced by a primary particle with energy greater than \(1000\ \text{Bev}\). One of the secondary particles in case (c) forms a second shower of type \((7+13p)\). The designation \(x \to y p\) indicates that the star contains \(y\) shower particles and \(x\) strongly ionizing particles.

For the article by R. R. Daniel et al.

Top labels in the figure:

\(0+7p\)
\(E_p \sim 200\) BeV

\(1+16p\)
\(E_p \sim 200\) BeV

\(5+26p\)
\(E_p \sim 850\) BeV

Scale: \(50\mu\)

In the figure:

“associated” electron pair

\(\pi\) \(K\)

a) b) c)

\(\pi\) \(K\)

Decay in flight
\((K \to \mu?)\)

Three “jets,” constituting evidence for the production of heavy \((K)\) mesons. In the events (a) and (b) the masses of these particles were determined from measurements of Coulomb scattering and grain density. In case (c) the Coulomb scattering of one of the secondary particles increases by approximately a factor of 3 after it passes through 12 mm of emulsion. We suppose that this is a case of decay of a heavy meson in flight \((K \to \mu?)\).

To the article by R. R. Daniel et al.

A “jet” produced by a primary particle with energy greater than 300 BeV. In the photograph an electron pair is visible, with total energy about 5 MeV, produced by conversion of a $\gamma$ quantum arising from the decay of a neutral $\pi$ meson. The initial grain density in the track left by the electron pair is approximately twice the grain density in the neighboring tracks of shower particles. One of the electrons produces a second electron pair (formation of a “trident”).

Visible labels in the figure:

• $2 + 36p$
  $E_p \sim 300$ BeV
• 50 $\mu$
• To the star: 1.5 mm
• “Bound” pair of two slow electrons $e_1$ and $e_2$
• 2.8 mm
• Formation of a “trident” on one branch of the pair

To the article by R. R. Daniel et al.

Two examples of “jets” produced by primary $\alpha$-particles of high energy.

For the article by R. R. Daniel et al.