UNSTABLE HEAVY PARTICLES IN COSMIC RADIATION

C. C. Butler*)

INTRODUCTION

While engaged in a detailed study of the properties of penetrating shower particles, Rochester and Butler\(^{2}\) in 1947 discovered in the gas of a Wilson chamber two remarkable “forks,” shown in photographs I and II (see the inserts at the end of the issue). These cases were explained by the spontaneous decay of neutral and charged particles with minimum masses equal to \(1000 m_e\). The discovery by Rochester and Butler was subsequently confirmed by a number of investigators\(^{2, 3, 6, 13, 17, 22, 23}\).

Professor Blackett proposed the term “\(V\)-shaped tracks”**) to designate the phenomena shown in photographs I and II. If the hypothesis were confirmed that these tracks arise from the decay of some unknown unstable particles, then these particles could be called \(V\)-particles. This name will apparently remain in use until additional information is obtained on the properties of the new particles. The new decay processes were studied mainly in the Wilson chamber. One \(V\)-shaped track was observed in photographic emulsion\(^{15}\). In photographic emulsion there was also found a case of decay of a charged \(V\)-particle at rest\(^{20}\).

In the course of the last several years the photographic-emulsion technique has been widely used to investigate all types of nuclear interactions. In 1949 the decay of a slow particle, heavier than a meson, into three charged particles was discovered\(^{7}\). Later\(^{14}\) two more examples of the same process were found. These unstable particles, called \(\tau\)-mesons, are apparently very rare. The present article considers only the decay processes of heavy particles.

The first evidence for the existence of particles with a mass intermediate between the masses of the \(\pi\)-meson and the proton was obtained by various—

*) C. C. Butler, Progress in Cosmic Ray Physics. Amsterdam, 1952, p. 65.

**) For brevity we shall also use the expression “fork.”

by personal methods. Leprince-Ringuet and Lheritier^18 observed, in a Wilson chamber placed in a magnetic field, the collision of a fast cosmic-ray particle with an electron. The dynamics of the collision made it possible to determine the mass of the fast particle, which turned out to be close to \(1000\,m_e\). Numerous measurements of the range and momentum of cosmic-radiation particles at an altitude of \(3250\) m were carried out by Alikhanian et al.^1. They came to the conclusion that many types of charged mesons exist, which they called “varitrons.” Finally, some researchers, for example^10,19,25, observed in photographic emulsions several unusual stars. These stars arose when nuclei captured particles whose mass was less than the proton mass but greater than the \(\pi\)-meson mass. It proved possible to determine a lower limit for the value of the mass of these particles. These measurements, however, being neither precise nor very convincing, give for the lower limit of the mass a value of about \(700\,m_e\).

In Part I the properties and mode of decay of neutral \(V\)-particles are considered in detail. In Part II the results are given of a similar analysis of the known data on the decay of \(\tau\)-mesons and charged \(V\)-particles.

Part I

DECAY OF NEUTRAL \(V\)-PARTICLES

1. The first \(V\)-shaped track

The \(V\)-shaped track discovered by Rochester and Butler^31 is a typical example of many similar tracks found subsequently. A description of this first case, shown in photograph I, may serve as an introduction to the consideration of the remaining work. The \(V\)-shaped track is formed by tracks (1) and (2), the angle between which is \(67^\circ\). Both tracks show minimum ionization, and therefore it must be assumed that they were formed by singly charged particles. A careful examination of the stereoscopic photographs shows that the tracks converge at one point; moreover, they begin at a point situated in the well-illuminated part of the Wilson chamber, where the presence of a uniform condensation background indicates exceptionally good conditions for the formation of tracks. The case under consideration is a “two-pronged fork,” the vertex of which lies in the gas of the chamber; no tracks of recoil nuclei or tracks of other particles emerging from the vertex can be observed. In these experiments, carried out at sea level, very few cases completely similar to such a “fork” were found, and the vertices of these “forks” proved to lie in a lead plate \(3\)–\(4\) cm thick, placed along the diameter of the chamber. If such “forks” arise as the result of some collision process, then in the plate they should appear hundreds of times more often than in the gas. Rochester and Butler pri-

came to the conclusion that such “forks” cannot arise in collision processes, but are formed as the result of a spontaneous process whose probability depends on the distance traversed, but not on the amount of matter. This \(V\)-shaped track was observed in a magnetic field of 3500 gauss. The momentum of the positively charged particle (track 1) is approximately \(0.2—0.3\ \mathrm{Bev}/c\), and, since the ionization is indistinguishable from minimum, it seems improbable that the particle could have been a proton. The length of the track of the negatively charged particle is too small for reliable measurements of the momentum to be made. However, if the neutral particle decays into only two particles, both charged, and if it is assumed that the direction of motion of the neutral particle coincides with the main direction of the main shower, then one can estimate the interval in which the momentum of the negatively charged particle lies. It is equal to \(0.7—1.0\ \mathrm{Bev}/c\). If it is assumed that the secondary particles are \(\pi\)-mesons (this assumption will be considered in detail in §§ 5.2 and 6.2), then for the mass of the neutral \(V\)-particle one obtains a value lying within the limits \((1000—1200)\, \(m_e\).

The work was continued at sea level\(^{4,8}\), but no new cases of such decay could be detected.

2. Investigations of \(V\)-shaped Tracks

In the summer of 1949 intensive investigations of the properties of \(V\)-shaped tracks began. In particular, Anderson and his collaborators\(^{32}\) carried out their investigations at sea level and at an altitude of \(3200\ \mathrm{m}\). The apparatus of Rochester and Butler was installed in the observatory on the Pic du Midi (2867 \(m\)) near Bagnères-de-Bigorre in the French Pyrenees (for a report on the first six months of work see \(^{4}\)). In what follows we shall call this group of investigators the Pic du Midi group. Investigations with the aid of a Wilson chamber were also begun by Fretter\(^{13}\) and Leighton et al.\(^{17}\).

2.1. Experimental arrangements used for the detection of \(V\)-shaped tracks

Anderson’s group\(^{32}\) worked with a Wilson chamber 30 \(cm\) in diameter, in which a lead plate 2 \(cm\) thick was placed. A magnetic field of 6500 gauss was produced by means of a small magnet. The air gap in the magnetic circuit was sufficient for the chamber, controlled by a Geiger-counter arrangement, to fit into it. After expansion the chamber fell freely, and the photographing was carried out when the chamber was outside the magnet coils. Unfortunately, the distortions of the tracks in the chamber were considerable. They were caused, apparently, by convection currents arising during the relatively long time of free fall of the chamber before photographing, and led

to the fact that pulses exceeding \(0.2\ \mathrm{Bev}/c\) were no longer measurable. To select showers of penetrating particles, the authors used an arrangement of Geiger counters selecting sixfold coincidences; two rows of counters were placed under the chamber and one row above it. Expansion of the chamber took place when, in the upper row, at least three counters operated, in the middle row, located directly under the chamber, two, and in the lower row, one counter. The counters of the upper row were placed under a layer of lead \(20\ \mathrm{cm}\) thick, and between the middle and lower rows there was a layer of lead \(5\ \mathrm{cm}\) thick.

On the Pic du Midi the magnet and the Wilson chamber were placed in a stationary laboratory, and the working conditions were just as favorable as in a laboratory at sea level. With a field of \(7500\) gauss and a track length of not less than \(6\ \mathrm{cm}\), the maximum measured momentum was \(8\ \mathrm{Bev}/c\). The rows of counters included in the sixfold coincidences are shown schematically in Fig. 1. It is of interest to compare this installation with that described above. Both counter installations register, at an altitude of \(3000\ \mathrm{m}\), about seven coincidences per hour. At least half of the coincidences are caused by interactions of neutrons and high-energy protons leading to the formation of penetrating showers. Anderson’s group’s installation is more compact and, probably, more sensitive to showers whose energy is less than the energy of the showers photographed on the Pic du Midi. The average energy of the latter exceeds \(10\ \mathrm{Bev}\). The installation on the Pic du Midi apparently has certain advantages. Thus, for example, because on the Pic du Midi, in order to expand the chamber, it is necessary that at least three counters operate in the row located under the chamber (in the installation of Anderson et al. only one counter must operate), the photographs obtained there contain a larger number of tracks. In order to be registered by the chamber, the interaction of fast neutrons with matter must occur in the upper \(15\)-cm layer of lead, whereas fast protons, in addition to this layer, can interact with the lead located directly above the chamber and in the chamber itself. Therefore showers of fast particles can arise in the immediate vicinity of the top of the chamber. This

Fig. 1. Schematic diagram of the installation operating on the Pic du Midi.

may prove to be a great advantage if the neutral \(V\)-particles have a short lifetime. In the Anderson group’s apparatus, showers should arise above the chamber, and most of them are formed at a distance not less than \(20\ \mathrm{cm}\) from the top of the chamber. Estabery et al.\(^{3}\) have recently installed, in the gap of an electromagnet, a chamber \(50\ \mathrm{cm}\) in diameter (on Jungfraujoch, \(3200\ \mathrm{m}\)). During preliminary experiments they observed several \(V\)-shaped tracks.

Thompson et al.\(^{23}\) have begun measurements at sea level, using a chamber \(30\ \mathrm{cm}\) in diameter placed in a magnetic field.

They succeeded in measuring the momenta for several \(V\)-shaped tracks. Fretter worked at sea level with a large chamber in which seven plates, each \(6\ \mathrm{mm}\) thick, were placed at distances of \(5\ \mathrm{cm}\) from one another. He used an apparatus that selected threefold coincidences between one counter located above the chamber and two others situated below it and separated from each other by a thin layer of lead. Bridge and Annis\(^{6}\) also used a large chamber with many plates. They worked without a magnetic field at an altitude of \(3000\ \mathrm{m}\). The triggering system was an apparatus intended for the registration of penetrating showers (the apparatus was of the same type as in \(^{24}\)). Part of the time this apparatus was located directly above the chamber; the rest of the time it was moved to a distance of \(150\ \mathrm{cm}\) above it. Most of the observed \(V\)-shaped tracks were found in secondary nuclear interactions in the lead plates. Such a counter arrangement was used in the study of penetrating showers, and there is no reason to suppose that it proved especially effective for observing \(V\)-shaped tracks.

2.2. Statistical data. Table I (see p. 394) lists the data available to the author (as of April 1, 1951) obtained by four groups of investigators. Fretter and the Pic du Midi group found, on the average, one \(V\)-shaped track arising from the decay of a neutral particle for every 25 high-energy interactions occurring in lead plates. In addition, the latter group found approximately one \(V\)-shaped track from a neutral particle for every 100 penetrating showers born above the chamber.

Table II (see p. 394) gives a more detailed analysis of the results obtained at Pic du Midi. The counting rate, corrected for the chamber recovery time, is \(7.2 \pm 0.1\) coincidences per hour. In using Table II it should be borne in mind that in series \(A\) and \(C\) a shower was regarded as penetrating if it contained two or more penetrating particles, or one penetrating particle and two or more strongly ionizing particles.

S. S. BUTLER

Table I

Statistical data

Height / Group	Anderson et al.: sea level	Anderson et al.: 3200 m	Fretter: sea level	Pic du Midi: 2867 m	Bridge and Ennis: 3200 m
Approximate number of photographs	3000	8000	17 000	10 000	10 000
Approximate number of penetrating showers	5000		0	5 000	—
Number of interactions in the lead plate	—		600	200	—
Total number of V-shaped tracks from neutral particles	6	24	24	53	4
Number of V-shaped tracks originating above the chamber	25		0	44	—
Number of V-shaped tracks in lead plates	5		24	9	4

Table II

Analysis of the data of the group at Pic du Midi, obtained from July 15, 1950, to March 1, 1951.

Series	Thickness of the lead plate (in cm)	Number of photographs	Operating time (hours)*)	Number of penetrating showers	Number of penetrating particles
A	2.0	5539	727	615	1844
B	0	2390	370	—	—
C	0.7	2213	316	467	1540
		10 142	1413	1082	3384

*) Excluding chamber recovery time.

In series C the thickness of the lead plate was 7 mm, so that the penetrating power of the particles indicated in the last row is not very great. It is possible in this case that some electrons were taken as penetrating particles. During series A and C, approximately 200 nuclear interactions of all types were recorded. Nine of them were accompanied by V-shaped tracks.

2.3. Place of origin of V-shaped tracks from neutral particles.

Almost all the V-shaped tracks observed by Fretter are directed with their apex toward thin lead plates, where high-energy nuclear interactions occurred. These interactions are a characteristic example of interactions caused by protons and neutrons with energies exceeding 5 Bev. The nine V-shaped tracks from neutral particles recorded at the Pic du Midi possess the same property. The occurrence of neutral particles which, in their decay, produce V-shaped tracks is shown in photographs III, IV, V (see the plates at the end of the issue).

3. Nature of the secondary particles

In most cases it was not possible, using the usual Wilson-chamber technique, to make an unambiguous determination of the nature of both secondary particles. These particles always have unit charge, sometimes produce strong ionization, and sometimes are able to pass through a lead plate without multiplying and without producing an interaction.

3.1. Strongly ionizing secondary particles.

All the investigators named above2, 6, 13, 22, 23 reported that among the secondary particles there are strongly ionizing particles. If one can measure the momentum of a particle and at the same time estimate its ionizing power, then the particles can be identified with considerable reliability. However, there have still been no cases in which it has been possible simultaneously to determine the mass of both secondary particles arising in the decay. Anderson et al.22 discovered one slow particle with a mass between \(100\,m_e\) and \(350\,m_e\). In five other cases they found that the mass of one secondary particle must be less than the mass of the proton. In one case both tracks were formed by strongly ionizing particles, but the mass of these particles could not be measured, probably because of the large distortions existing in the chamber. This case is shown in photograph VI (see the plate at the end of the issue). Fretter, as well as Bridge and Annis, found several examples of strongly ionizing secondary particles, but it was impossible to determine their mass. Thompson et al. found two slow protons at sea level. The group at the Pic du Midi discovered nine strongly ionizing particles, among which were protons and \(\pi\)- and \(\mu\)-mesons. Five of these particles could be identified with considerable reliability as protons. One such case is shown in photograph VII (see the plate at the end of the issue). Estimates of the momenta and ionizing power of these particles are given in Table III.

Four tracks of negatively charged particles with momentum less than \(0.1\) Bev/\(c\) show strong ionization and apparently belong to \(\pi\)- or \(\mu\)-mesons. One example is shown in photograph—

Table III

Changes in momentum and ionization for five proton tracks

Quantity	Detail	Case No. 33	43	47	56	13
Momenta (in BeV/c)	Positive track (1)	0.24	0.48	0.35	0.45	0.5
Momenta (in BeV/c)	Negative track (2)	0.25	0.19	0.14	0.16	0.12
Estimate of the ionizing power of the track (minimum ionization taken as unity)		8—15	3—4	4—6	3—4	3—4
Calculated ionization for a proton possessing the measured momentum (minimum ionization taken as unity)		9	3.0	5.0	3.5	3

photograph VIII (see the insert at the end of the issue). Not a single case was found in which the secondary particle could be identified with certainty as a positively charged $\pi$-meson.

3.2. Penetrating power of secondary particles. Anderson’s group, as well as the Pic du Midi group, found fifteen secondary particles penetrating through a lead plate 2 cm thick without interaction or radiation collisions. In addition, one secondary particle caused a disintegration in one of the lead plates, one particle apparently underwent sudden absorption, and two were scattered through large angles. These four cases of interaction are associated with fifteen traversals of the lead plate, whence it follows that the interaction length for secondary particles is equal to 7.5 cm of lead. The geometrical cross section in lead corresponds to an interaction length equal to 15 cm. As can be seen, the result obtained experimentally for the secondary particles does not differ greatly from this value. Thus, both negatively and positively charged secondary particles apparently undergo strong nuclear interaction, and therefore it is unlikely that they were electrons or $\mu$-mesons. A V-shaped track with two penetrating secondary particles is shown in photograph IX (see the insert at the end of the issue). In measurement series C at Pic du Midi, a lead plate 0.7 cm thick was placed in the chamber. Above this plate one V-shaped track was recorded, in which the negatively charged secondary particle produced minimum ionization above the plate and strong ionization below it. Measurements of the ionizing power and momentum agree with the assumption that the particle was either a $\pi$- or a $\mu$-meson. Another V-shaped

trace, produced above a thin lead plate, is shown in photograph X (see the inset at the end of the issue). Trace (2), belonging to a negatively charged secondary particle, has a short length above the plate. The ionization along this trace is probably above minimum. Under the plate this secondary particle produces strong ionization and is deflected in the chamber gas by \(23^\circ\).

The results of measurements relating to this negatively charged particle are collected in Table IV, from which it follows that this particle is apparently a \(\pi\)-meson.

Table IV

Measurement of the decay of a \(\pi\)-meson occurring in flight

	Trace (2)	Trace (3)
Momentum (in \(Mev/c\))	78 (\(\pm 5\%\))	61 (\(\pm 5\%\))
Estimate of ionizing power (minimum ionization taken as unity)	3—4	3—4
Calculated ionizing power for \(\pi\)-mesons	2.8	4.0
Calculated ionizing power for \(\mu\)-mesons	2.0	2.8

It is almost beyond doubt that this case is a \(\pi \to \mu\) decay. Scattering of the \(\pi\)-meson by a nucleus is a considerably less probable possibility. The decay angle is close to the maximum value corresponding to the momentum of the \(\pi\)-meson (see § 11.3).

3.3. Differential momentum spectrum of secondary particles. For twenty-six \(V\)-shaped traces obtained at Pic du Midi, it proved possible to make accurate measurements of the momentum of both secondary particles. The results are given in Table V in the form of a differential momentum spectrum

Table V

Differential momentum spectrum of secondary particles

Momentum category	1	2	3	4	5
Momentum interval \((Bev/c)\)	0—0.1	0.1—0.5	0.5—1.0	1.0—1.5	1.5
Positively charged particles	0	10	7	2	7
Negatively charged particles	1	16	4	0	5

of momenta for positively and negatively charged secondary particles.

It follows from Table V that, in general, the momenta of negatively charged particles are smaller than those of positively charged particles. Sixteen negatively charged particles that entered the second

category of momenta, produce minimal ionization, and therefore their mass cannot be close to the proton mass. For the same reason, three positively charged particles of category 2 and one of category 3 cannot be protons (the momentum of this particle is close to \(0.5\ \mathrm{Bev}/c\)). Two of these positively charged particles were found in pairs with negatively charged particles having masses smaller than the proton mass. Three other positively charged particles proved to be lighter than the proton. The corresponding tracks of the negatively charged particles were not measured. Thus, seven positively charged particles lighter than protons were found, but for none of them was it possible to determine the mass value accurately.

4. Possible explanations of V-shaped tracks

4.1.

In argon or oxygen filling the chamber, cosmic rays can produce interactions of electromagnetic and nuclear character. The formation in the gas of at least ten electron pairs with energies of several \(\mathrm{Mev}\) was observed, whereas the majority of V-shaped tracks have a total energy close to \(1\ \mathrm{Bev}\). Photons of such energy should produce electron pairs diverging at an angle considerably smaller than one degree. This angle is much smaller than any that has ever been observed in the experiments under consideration. Moreover, since many of the secondary particles proved to be protons and mesons, the observed V-shaped tracks cannot be explained by the formation of electron pairs. Neutrons and high-energy photons can produce nuclear interactions in the gas. The effective cross section for the formation of stars by fast neutrons is close to the geometrical value, but the cross section for analogous processes caused by photons is considerably smaller and may be neglected. The group on the Pic du Midi observed 23 V-shaped tracks during the period when there was a lead plate \(2\ \mathrm{cm}\) thick in the chamber. If all these events arose as a result of interaction between neutrons incident on the apparatus and atoms of the gas, then, assuming the cross section equal to the geometrical one, we find that about 10,000 such events should have occurred in the lead plate (i.e. 400 times more than was actually observed). In practice not all such “forks” are observable, since some of the “prongs” are absorbed in the lead.

However, half of the V-shaped tracks have high energy and should be visible in the chamber even if the tracks arose in the upper part of the lead plate. In reality, very few two-pronged stars of high energy emerge from the lead plate. During the same period in which 23 V-shaped tracks were observed, about 200 nuclear interactions of all types occurred in the plate. Relying on data \({}^{4}\), it may be assumed that in the pla-

...there arise in the plate about 200 more interactions that are not visible in the chamber, and thus in the plate there arise in all about 400 nuclear interactions. It follows from this that it is not possible to explain the \(V\)-shaped tracks in the gas by nuclear interactions. The number of stars in the gas resembling in appearance the \(V\)-shaped tracks from the decay of neutral particles can be calculated if one knows an estimate of the intensity of the neutron flux. In doing this it is necessary to take into account only interactions with neutrons of high energy, since all such stars must contain a meson, while the effective cross section for the production of a meson by neutrons is considerably smaller than the geometrical value until the neutron energy begins to exceed approximately \(1\ \mathrm{Bev}\).

It may be assumed that the flux of neutrons with momenta exceeding \(1\ \mathrm{Bev}/c\) is equal to the flux of protons with the same momenta. It has been found\(^4\) that at sea level the number of fast protons lies between 25 and 50% of the number of penetrating particles. Thus the number of fast neutrons can be determined from the flux of penetrating particles, whose spectrum was measured by the authors of the present work. The number of fast protons crossing the Wilson chamber in all penetrating showers (with a 2-cm lead plate present) lies between 300 and 500: they can create in the gas about 0.2 stars. Thus, the 23 \(V\)-shaped tracks cannot be stars produced by neutrons. Further convincing arguments can be adduced in support of this conclusion. Indicative is the absence of tracks of particles evaporated from the nucleus and of recoil nuclei. Despite the relatively small dimensions and the transparency of argon nuclei for fast neutrons, only a small fraction of the stars that arise will not have tracks of evaporated particles and visible tracks of recoil nuclei. If the \(V\)-shaped tracks had been produced by neutrons, one would expect the presence of a comparable number of analogous stars produced by high-energy ionizing particles. In fact, however, the group of Pic du Midi found only two such stars produced by ionizing particles. The first of them is shown in photograph XI and described in the caption. This \(V\)-shaped track cannot be regarded as a simple elastic collision. It is caused by an interaction proceeding probably according to the following scheme:

\[ \mathrm{p}^{+}+\mathrm{p}^{+}\longrightarrow \mathrm{p}^{+}+\mathrm{n}^{\circ}+\pi^{+}, \tag{1} \]

from which it follows that both secondary particles have positive charge and one of them is a proton. The presence of a large clump of ionization at the initial point of the interaction almost certainly indicates a recoil nucleus. On the second \(V\)-shaped “fork” there is visible the track of a negatively charged meson and a long track of a recoil nucleus; this interaction may have been caused by a fast \(\pi\)-meso-

Thus, by comparing \(Y\)-shaped tracks with all \(V\)-shaped tracks arising from the decay of neutral particles, we may conclude that two or three of the latter could have been caused by neutrons.

In the case of a \(V\)-shaped decay track of a neutral particle near a very large star, observed in a photographic emulsion\({}^{15}\), one secondary particle was identified as a proton, while the other particle, at the same momentum, produced minimum ionization and was either a \(\pi\)-meson, a \(\mu\)-meson, or an electron. At the apex of the fork there is a noticeably large grain, but the authors consider it insufficiently large for it to be attributed to a recoil nucleus.

The authors arrive at the conclusion that their case can be explained only by the decay of a neutral particle of mass \((2370 \pm 60)\,m_e\) into a proton and a \(\pi\)-meson. The large star does not lie in the plane of the “fork,” and therefore, if the neutral particle decays into only two particles, it did not originate in the star. Before accepting the explanation given by the authors, it is necessary to carry out a detailed analysis of all two-prong stars, which are found in photographic emulsions in far greater numbers than in Wilson-chamber experiments. This case may, for example, be interpreted as the result of a glancing collision of a neutron with a silver or bromine nucleus, proceeding according to the following scheme:

\[ \mathrm{n}^{\circ} + \mathrm{n}^{\circ} \to \mathrm{p}^{+} + \mathrm{n}^{\circ} + \pi . \tag{2} \]

4.2. Single scattering of particles through large angles in the gas of a Wilson chamber. Up to the present time, a considerably larger number of \(V\)-shaped tracks arising from the decay of neutral particles has been found than from the decay of charged particles. Such a result would be very unexpected if all these cases arose from scattering through large angles. Indeed, in that case one would expect predominantly scattering through small angles, i.e. the formation of spurious cases of \(V\)-shaped tracks arising from the decay of a charged particle (see photograph II). A second objection to such an explanation is the absence of recoil tracks. Thus, for example, an argon nucleus with a momentum of \(50\ \mathrm{MeV}/c\) can produce a noticeable clump of ionization upon recoil. The Pic du Midi group found only one such clump at the apex of a \(V\)-shaped track; thus only this one case can be explained by scattering through a large angle. If the \(V\)-shaped tracks of neutral particles could be explained by scattering, then recoil tracks should appear in all cases. Thus it is necessary to conclude that the only explanation for the majority of \(V\)-shaped tracks is that these tracks are caused by spontaneous decay processes\({}^{2,21,22}\).

5. Presumed decay processes

The nature of the two secondary particles arising in the decay of a \(V\)-particle has already been considered. It makes sense to consider possible decay schemes only if one assumes that these particles are the only secondary particles.

5.1. Number of secondary particles.

Among the neutral \(V\)-particles observed by Anderson’s group \(^{22}\), nineteen arose simultaneously with other particles; in twelve cases it proved possible to use the tracks of these latter particles to find the points at which the primary nuclear interaction occurred. Most of these points are located at distances of at least 15 cm from the top of the chamber, and, owing to secondary interactions and multiple Coulomb scattering of shower particles in lead, the position of the points cannot be determined with great accuracy. These investigators found that in all twelve cases, within the limits of experimental error, the point of the primary interaction lies in the plane of the “fork.” Such a result, the degree of persuasiveness of which is difficult to assess, nevertheless confirms that, apparently, two particles take part in the decay processes.

The Pic du Midi group finds that in those cases where neutral \(V\)-particles are formed in the upper layer of matter, the position of their point of origin cannot be determined exactly. Nine of the \(V\)-shaped tracks they found, arising from the decay of a neutral particle, were produced in interactions in a lead plate, and two of them contain tracks of secondary particles sufficiently long to allow the position of the plane of the “forks” to be determined with great accuracy. To within the errors of the experiment, the points at which the primary interaction occurred lie in these planes. Both decay points are located near the lead plate, so that the planes of the “forks” pass very close to the points at which the primary interaction occurred. In addition, the direction in which both neutral particles move makes with the direction of the secondary particles just such angles as should be expected from the momenta of the secondary particles, assuming that they are the only decay products. Fretter discovered two \(V\)-shaped tracks, and the neutral particles that formed these tracks do not emerge from the points where the nuclear interaction observed in the chamber occurred. These particles could have arisen outside the chamber or in secondary interactions that did not produce distinguishable tracks. Otherwise it is necessary to assume that one or several neutral particles may arise in the decay. At present it is difficult to assess the degree of persuasiveness of these measurements of the orientation of \(V\)-shaped tracks relative to the point of origin of the particles. Several cases examined in detail

the decay are consistent with the assumption of two secondary particles, but in order to draw final conclusions more data are needed.

5.2. Possible decay schemes into two particles.

The secondary particles were identified with protons and with negatively charged mesons, apparently \(\pi\)-mesons. Accordingly, for many of the observed cases the following decay scheme may be proposed:

\[ V^0_1 \to p^+ + \pi^- . \tag{3} \]

In 4.3 some \(V\)-shaped tracks were shown which were formed by secondary particles lighter than protons. For these cases the simplest decay scheme into two particles has the form

\[ V^0_2 \to \pi^+ + \pi^- , \tag{4} \]

and in this scheme the \(\pi\)-mesons may be replaced by \(\mu\)-mesons. (This does not contradict direct observations.) If the decay scheme is accepted, then the particle masses can be determined on the basis of the laws of conservation of energy and momentum, provided that the momenta of the secondary particles and the angle of divergence in the laboratory coordinate system are known. If we use the notation shown in Fig. 2 and measure mass and energy in the same units, the necessary equalities have the form

Fig. 2.

\[ \sqrt{M^2+p^2}=\sqrt{m_1^2+p_1^2}+\sqrt{m_2^2+p_2^2} \tag{5} \]

and

\[ p^2=p_1^2+p_2^2+2p_1p_2\cos\Phi . \]

Using both equalities (5), we obtain:

\[ M^2=m_1^2+m_2^2+2p_1p_2 \left[ \left\{1+\left(\frac{m_1}{p_1}\right)^2\right\}^{1/2} \left\{1+\left(\frac{m_2}{p_2}\right)^2\right\}^{1/2} -\cos\Phi \right]. \tag{6} \]

Investigation of equality (6) leads to the following conclusions:

a) If either \(\dfrac{m_1}{p_1}\), or \(\dfrac{m_2}{p_2}\gg 1\), then the term \(\cos\Phi\) has little effect on the magnitude \(M\).

b) The term \(\cos\Phi\) is meaningful only in the case when \(\dfrac{m_1}{p_1}\) or \(\dfrac{m_2}{p_2} \ll 1\). This occurs for very large values of \(p_1\) and \(p_2\). In this case the opening angle \(\Phi\) usually takes values less than \(15^\circ\), and if it is measured with an accuracy of up to one degree, then the main error is again determined by the errors in measuring \(p_1\) and \(p_2\).

c) As a rule, the most significant error arises from the term \(2p_1p_2\). If the conclusions drawn in § 5.1 are incorrect and in each decay three secondary particles arise, then equalities (5) can be generalized in the following way:

\[ \sqrt{M^2+p^2}=\sqrt{m_1^2+p_1^2}+\sqrt{m_2^2+p_2^2}+\sqrt{m_3^2+p_3^2}, \tag{7} \]

\[ \mathbf{p}=\mathbf{p}_1+\mathbf{p}_2+\mathbf{p}_3, \]

where the last equality is the law of conservation of momentum in vector form. If three particles arise in the decay, but it was interpreted as a decay into two particles, then, as comparison of equalities (6) and (7) shows, the calculated value of the mass will be less than the true one. For twenty-five neutral \(V\)-particles discovered by the Pic du Midi group, and for the neutral particle discovered by Butler at sea level, the values \(p_1p_2\) and \(\Phi\) can be measured. Not all these measurements possess comparable accuracy, since in many cases the tracks are too short. For tracks whose length is not less than 6 cm, the maximum measurable momentum is approximately \(8\ \text{BeV}/c\). In thirteen cases the length of the tracks of both secondary particles exceeds 6 cm. The differential momentum spectrum, calculated for twenty-six neutral particles on the basis of equality (5), is given in Table VI. These very limited data do not make it possible to notice anything unusual.

Table VI

Differential momentum spectrum of neutral \(V\)-particles

Momenta \((\text{BeV}/c)\) . . .	0.1–0.5	0.5–1.0	1.0–1.5	1.5–2.0	\(>2.0\)
Number of \(V^0\)-particles . . .	3	8	3	5	7

6. Determinations of masses.

Twenty-six of the most carefully measured \(V\)-shaped tracks must be distributed between two possible decay schemes. Below a method will be described for such a separation of the data obtained at Pic du Midi.

6.1. Decay of \(V_1^0\)-particles into protons and \(\pi\)-mesons.

In four measured “forks” the presence of protons was detected.

These cases can be interpreted only from the point of view of the decay scheme (3); the mass determinations for these cases are given in Table VII.

Table VII

Masses of four \(V_1^0\)-particles, among whose decay products protons were found

(1) No. of event	(2) Approximate track length (cm)	(3) Measured momentum (\(B\rho/c\))	(4) Ratio \(p_+/p_-\)	(5) Angle \(\Phi\) (degrees)	(6) Mass, according to equality scheme (3) (in units of \(m_e\))
33	9 4	\(+0.242\) \(0.254\)	0.95	27	\(2277 \pm 40\)
43	6 10	\(+0.480\) \(-0.192\)	2.5	50.5	\(2218 \pm 10\)
47	6 18	\(+0.350\) \(-0.142\)	2.5	87.5	\(2228 \pm 10\)
56	18 14	\(+0.450\) \(-0.162\)	2.8	44	\(2181 \pm 10\)

For the measured values of the momenta given in column (3), the standard deviation is equal to 10%, except for the negatively charged particle in event No. 33, for which the standard deviation reaches 20% of the indicated momentum value. In these particular cases the possible sources of significant errors are uncertainties in the value of the magnetic field and in measurements of the curvature of the track. In processing the data, corrections for the nonuniformity of the magnetic field were introduced, and the angle of divergence was determined with these corrections taken into account. All the measured momenta are very small, and the errors arising from distortions in the chamber are small. The standard deviations for the obtained mass values are indicated in column (6). The mean mass value is equal to \((2226 \pm 10)\,m_e\).

Thompson et al.\(^{33}\) measured a \(V\)-shaped track very similar to the tracks considered in Table VII. The positively charged particle ionized strongly, and the mass found for the \(V\)-particle proved to be \((2165 \pm 20)\,m_e\). Of the remaining nineteen “forks” discovered on the Pic du Midi, in eight the tracks of the secondary particles are longer than 6 cm and can be carefully measured: some of them belong to particles with high energy, and in this case distortions introduced by the chamber are the principal source of errors. The angles of divergence were determined from stereoscopic photogra-

phism. In this case angles smaller than \(10^\circ\) were measured with an error of 10%, and larger angles in many cases with an accuracy of up to 5%. Each of the eight positively charged secondary particles could have been a proton: in most cases the negatively charged particles had a smaller momentum than the positively charged ones. Not all mass values obtained for these cases are in good agreement with the results given in Table VII. Four \(V\)-shaped tracks give an average mass value equal to \(2200\,m_e\), but the other four give a substantially larger value, approximately \(2700\,m_e\). These tracks were produced by \(V\)-particles of high energy; the data for these tracks are given in Table VIII. In two

Table VIII

Masses of four \(V\)-particles apparently decaying into two \(\pi\)-mesons

(1) No. of case	(2) Approximate length of track (cm)	(3) Measurements of momentum (Bev/c)	(4) Ratio \(p_+/p_-\)	(5) Opening angle of the fork (degrees)	(6) Mass (according to scheme (3)) \((m_e)\)	(7) Mass (according to scheme (4)) \((m_e)\)
5 (photograph IX)	6	\(+2.6\)	0.9	6	2800	796
5 (photograph IX)	7	\(-3.0\)	0.9	6	2800	796
38	10	\(+1.4\)	2.0	20	2400	872
38	15	\(-0.7\)	2.0	20	2400	872
53 (photograph XII)	10	\(+1.5\)	0.9	12	2690	841
53 (photograph XII)	16	\(-1.6\)	0.9	12	2690	841
69	9	\(+2.2\)	1.2	5.5	2560	673
69	9	\(-1.9\)	1.2	5.5	2560	673

cases the tracks of secondary particles have a large length, and the corresponding masses are determined with standard deviations of \(\pm 50\,m_e\). Although these results are not yet sufficiently convincing, nevertheless the mass values in column (6) of Table VIII differ so strongly from the values given in column (6) of Table VII that it is necessary to assume either the existence of different \(V\)-particles decaying according to the same scheme, or the presence of different decay schemes. All the remaining fourteen \(V\)-shaped tracks contain at least one track of a secondary particle shorter than 6 cm; such short tracks cannot always be measured accurately. Five of these cases do not fit decay scheme (3), since the positively charged particles are not protons. Six cases give a mass lying within the range \((2150—2350)\,m_e\), and three

case, a mass of about \(2700\,m_e\) (if scheme (3) is used in determining the mass). Thus, twenty-one \(V\)-shaped tracks arising from the decay of neutral particles can be explained on the basis of scheme (3). In fourteen cases the mass of the neutral particles lies within the range \((2180—2350)\,m_e\); in the remaining seven cases the value of the mass is close to \(2700\,m_e\). The mass histogram for the twenty-one cases is shown in Fig. 3. As was to be expected on the basis of the scheme of the decay process, the mass distribution around \(2200\,m_e\) is asymmetric. The best value of the mass,

Fig. 3.

obtained from fifteen cases, each of which was included with a weight corresponding to the accuracy of that particular mass measurement, lies near \(2210\,m_e\).

6.2. Decay of neutral \(V_2^0\)-particles into two \(\pi\)-mesons. Evidence for the decay of neutral \(V\)-particles into two \(\pi\)-mesons has already been given. Thus one may interpret five measured \(V\)-shaped tracks: in these cases the positively charged particles are not protons and, moreover, in two cases (Nos. 63 and 66) the negatively charged particles proved to be lighter than protons. In several cases listed in Table IX, the lengths of the tracks of the secondary particles are too small for an accurate measurement of momentum. The result obtained from photograph 66 is the best, although even in this case the momentum of the negatively charged particle was measured inaccurately. The negatively charged particle in photograph 63 passed near the edge of the chamber and its momentum could not be measured accurately. In photograph 65 it was not possible to measure the opening angle accurately; this was hindered by the presence in the photograph of tracks of other shower particles. In photograph I the momentum of the negatively charged particle also cannot be measured accurately; the value of the momentum given in the table was obtained from consideration of the geometry of the track and of the main shower. In this case a significant error is possible, which

Table IX

Masses of four \(V_2^0\)-particles apparently decaying into two \(\pi\)-mesons

(1) No. of event	(2) Approximate track length (cm)	(3) Measured momentum \((B\rho/c)\)	(4) Ratio \((p_+/p_-)\)	(5) Opening angle (degrees)	(6) Mass (scheme 4) (in units of \(m_e\))
66 (photograph V)	6	\(+0.26\)	2	77	700
66 (photograph V)	3	\(-\sim 0.13\)	2	77	700
63	4	\(+0.30\)	0.6	46	820
63	7	\(-\sim 0.5\)	0.6	46	820
65 (photograph X)	5	\(+0.32\)	0.5	\(\sim 10\)	\(\sim 610\)
65 (photograph X)	5	\(-0.66\)	0.5	\(\sim 10\)	\(\sim 610\)
1	5	\(+0.35\)	0.7	14	\(\sim 600\)
1	5	\(-\sim 0.5\)	0.7	14	\(\sim 600\)
Event of photograph 1	5	\(+0.20\)	0.3	67	\(\sim 1120\)
Event of photograph 1	4	\(-0.85\)	0.3	67	\(\sim 1120\)

can explain the high value of the mass. The five cases cited do not allow one to draw a definite conclusion; all of them have tracks of positively charged secondary particles that can be measured accurately, but some momenta of negatively charged particles have been measured inaccurately. Nevertheless, these cases are evidence for the existence of neutral \(V\)-particles with a mass of about \(800 m_e\). If neutral \(V\)-particles decay only into two secondary particles, then the cases found by the group at Pic du Midi are best explained by the existence of two types of neutral particles. The mass of particles of the first type has still not been determined with sufficient accuracy, but, according to the available data, the best value is \(2210 m_e\). The mass of particles of the second type probably lies within the limits \((700—800)m_e\). Many of the \(V\)-shaped tracks have secondary particles that produce minimal ionization; such cases satisfy both scheme (3) and scheme (4). Thus, it becomes necessary to find some additional arguments that would help in distributing the available data between the two schemes. Extremely valuable additional information can be obtained from studying the dynamics of these two decay schemes.

7. Dynamics of decay schemes into two secondary particles. The existing data show that the decay of neutral \(V\)-particles takes place according to two different schemes, if it is true

the assumption that only two secondary particles arise in the decay. Below, the dynamics of these schemes will be considered. Special attention will be paid to such phenomena in \(V\)-shaped tracks, which are the most probable in the laboratory coordinate system.

7.1. Dynamics of the decay scheme: \(V_1^0 \to \mathrm{p}^+ + \pi^-\). If a neutral \(V\)-particle decays into a proton (mass \(m_1\)) and a meson (mass \(m_2\)), then in the center-of-inertia system these secondary particles are emitted in opposite directions, as shown in Fig. 2. In such a coordinate system the pairs of secondary particles are emitted in random directions. It is easy to show that the fraction of all cases for which \(\vartheta\) lies between \(\vartheta_1\) and \(\vartheta_2\) is given by the expression \(\frac{1}{2}(\cos \vartheta_1 - \cos \vartheta_2)\).

Thus, for example, half of all observed cases must have values of \(\vartheta\) lying between \(60^\circ\) and \(120^\circ\). The most probable value of \(\vartheta\) is \(\frac{\pi}{2}\), i.e., the direction that in the center-of-inertia system makes a right angle with the direction of motion of the \(V\)-particle is the most probable direction of emission of the secondary particles. In the center-of-inertia system (in this coordinate system the \(V\)-particle is at rest), the momenta of both secondary particles are given by the expression

\[ p=\frac{1}{2M}\left\{[M^2-(m_1-m_2)^2][M^2-(m_1+m_2)^2]\right\}^{1/2}, \tag{8} \]

where \(M\) is the mass of the \(V\)-particle, expressed in units of energy. To determine the properties of the particles in the laboratory coordinate system, it is necessary to apply the Lorentz transformation to the particle velocities in the center-of-inertia system. This transformation leaves unchanged the components of momentum perpendicular to the direction of motion of the \(V\)-particle, and changes only the components directed along the motion. Besides this method one may use a geometrical method based on Lorentz transformations\(^5\). The transformed momenta of the two secondary particles depend on the energy of the particles in the center-of-inertia system. If the masses of the particles differ sharply, as is the case for the proton and the \(\pi\)-meson, then in the general case the two transformed momenta will differ greatly in magnitude. In the laboratory coordinate system the proton will have a considerably greater momentum than the \(\pi\)-meson. This excess of the momenta of positively charged particles over the momenta of negatively charged particles must be strongly pronounced, except in cases of very large or very small energy. If one measures the momenta for a certain number of tracks, then the momentum distribution of the secondary particles of each type should differ strongly. The Bristol group found that the differential momentum spectrum for positively charg—

of the secondary particles differs strongly from the corresponding spectrum of negatively charged particles; namely, positively charged particles have considerably larger momenta than particles of the opposite sign (see 3.3). As an example, let us consider Table VII, from which it is seen that the three particles identified as protons have considerably larger momenta than the corresponding negatively charged particles. This is also true for all cases leading to mass values in the interval \((2180—2350)\, \(m_e\), but it is not fulfilled in three cases for which the mass values are close to \(2700 m_e\) (if the mass is calculated according to scheme (3), see Table VIII). For these three cases the mean value of the ratio \(p_+/p_-\) is close to unity. Such a result should be expected if the particles have equal or nearly equal masses, and this is an indication that the decay of these three particles is apparently not in agreement with the scheme described by expression (3). This conclusion will be confirmed by other arguments considered in this paragraph. Given a larger amount of data, the study of the ratio \(p_+/p_-\) will be a very valuable means of dividing the available data between the two decay schemes.

In the center-of-mass system both secondary particles have equal momenta, and therefore the velocity of the meson is considerably greater than the velocity of the proton. If the velocity of the unstable \(V\)-particle is greater than the velocity of one of the secondary particles in the center-of-mass system, then in this case the direction of motion of the secondary particle in the laboratory coordinate system always forms an acute angle with the direction of the \(V\)-particle, which means that the secondary particle is always emitted forward. Suppose, for example, that the velocity of the \(V\)-particle exceeds the velocity of the meson in the center-of-mass system of the secondary particles. In this case both secondary particles are emitted forward at a small angle. If the velocity of the \(V\)-particle is greater than the velocity of the proton but less than the velocity of the meson in the center-of-mass system, then the proton is always emitted forward, but the meson in the laboratory coordinate system may move in the opposite direction. In this system both secondary particles may move backward if the velocity of the \(V\)-particle is less than the velocity of either of the secondary particles in the center-of-mass system. These properties of the decay scheme can be investigated in more detail if one calculates the dependence of \(\Phi\) on \(\vartheta\) for given values of \(p\) and \(M\). From the family of curves shown in Fig. 4, calculated for the mass \(2210 m_e\), it follows that for \(p\) greater than \(1.0\ \mathrm{Bev}/c\) the value of \(\Phi\) is bounded. For \(p\) less than \(0.16\ \mathrm{Bev}/c\), \(\Phi\) takes values greater than some minimum. Between these two critical values of the momentum of the \(V\)-particle, all values of \(\Phi\) between \(0^\circ\) and \(180^\circ\) are possible. In this momentum region the proton is always emitted forward in the laboratory system, but the meson may be emitted in the opposite direction. The probability distribution for obtaining a given \(\Phi\) at

at a given value of the momentum of the \(V\)-particle can be compiled from the curves in Fig. 4. Three typical differential probability distributions for \(\Phi\) are shown in Fig. 5; they were compiled for

Fig. 4. Angular correlations for the scheme \(V_1^0 \to p^+ + \pi^-\).

Fig. 5.

ten-degree intervals. If the values of \(\Phi\) are restricted, then most probably the angle between the directions of motion of the particles will be close to \(\Phi_{\max}\). From Fig. 5 it is seen, for example, that if \(M = 2210\,m_e\) and \(p = 1.5\ \text{Bev}/c\), then \(\Phi_{\max} = 46^\circ\), and 58% of all “forks”

will have \(\Phi\) lying between \(30^\circ\) and \(46^\circ\). For \(p=0.9\) Bev/\(c\), all values of \(\Phi\) are possible, but 95% of all “forks” will have \(\Phi\) less than \(90^\circ\). It is of interest to develop a method which would make it possible to determine what the distribution of the angles \(\Phi\) is for all cases giving a mass value close to \(2210\,m_e\). For this mass value, found from experiment, \(\Phi_{\max}\) and \(\Phi_{\min}\) can be calculated as functions of \(p\). The curves obtained in this way are shown in Fig. 6. In addition,

Fig. 6.

one can calculate the dependence of \(\Phi\) on \(p\) for a fixed value of \(\vartheta\), representing the emission angle in the center-of-inertia system (see Fig. 2). The dashed lines in Fig. 6 are drawn for values of \(\vartheta\) equal to \(60^\circ\) and \(120^\circ\), and, as was shown above, half of the observed “forks” should lie between these lines. Fig. 6 contains the data of fourteen cases for which the mass values lie in the interval \((2180—2350)\,m_e\). For each case the interval of values of \(p\), equal to twice the standard deviation from the given mean value, is indicated. The “forks” are distributed approximately in the most probable region of the \(p-\Phi\) diagram. About half of them fall between the dashed lines. Consequently, they form a family of cases that can be explained by the decay of \(V\)-particles of mass \(2210\,m_e\) into protons and \(\pi\)-mesons. When a larger

a larger number of data, the distribution of the values of \(\Phi\) can be determined experimentally and compared with the theoretical distribution calculated for the mean value of the mass. It is now necessary to find out how the cases of the assumed decay, according to the same particle scheme, for which the computed value of the mass is close to \(2700\,m_e\), fit onto the \(p\)—\(\Phi\) diagram. For these few cases the dependence of momentum on angle is plotted in Fig. 7; the dashed curve indicates the dependence of \(p\) on \(\Phi\) for \(\vartheta\) equal to \(60^\circ\). Three quarters of all the “forks” with masses close to \(2700\,m_e\) should lie between the solid and dashed curves. In fact

Fig. 7.

six of the seven cases fall to the left of the dashed curve, i.e., in a relatively unlikely region of the \(p\)—\(\Phi\) diagram. This proves that in the present case the assumed decay scheme is not fulfilled. All the values of \(p_+/p_-\) are close to unity and, probably, these cases are more correctly explained by the decay of neutral \(V\)-particles into two mesons.

7.2. Dynamics of the decay scheme \(V_2^0 \to \pi^+ + \pi^-\). The emission of two mesons in the center-of-inertia system occurs as described in 7.1, but because of the symmetrical form of the decay process the dynamics of this case is greatly simplified. For example, the momentum distributions of positively and negatively charged secondary particles in the laboratory coordinate system turn out to be identical, and the mean value of the ratio \(p_+/p_-\) is equal to unity. The family of \(p\)—\(\vartheta\) curves shown in Fig. 8 was calculated for

mass \(1000\,m_e\); it is symmetric with respect to \(\theta=\dfrac{\pi}{2}\). These curves make it possible to find the main dynamical properties of the decay scheme. The dependence of \(\Phi_{\max}\) and \(\Phi_{\min}\) on \(p\) is given in Fig. 9; it can be seen that the intermediate region of Fig. 9, in which all values of \(\Phi\) are possible, is unattainable for the symmetric decay scheme. The most probable values of \(\Phi\) in the “forks” under consideration lie close to the curves of Fig. 9. In 6.1 it was pointed out that the masses of seven \(V\)-particles prove to be too large if it is assumed that

Fig. 8. Angular relations for the scheme

\[ V_2^0 \to \pi^+ + \pi^- . \]

their decay proceeds according to the first scheme. These decays may be regarded as proceeding according to the second scheme; they are plotted in Fig. 9. In addition, five \(V\)-shaped tracks can be interpreted only within the framework of the second scheme. This possibility was considered in 6.2 (Table IX), and the corresponding values of \(p-\Phi\) are also plotted in Fig. 9. Of the eleven cases indicated in Fig. 9, ten are situated close to the curve, and it may tentatively be assumed that these cases are explained by the decay of \(V\)-particles with a mass of about \(1000\,m_e\). One point falls in the forbidden region. In this case the calculated value of the mass is \(700\,m_e\), which is substantially less than \(1000\,m_e\). A detailed consideration of the dynamics of the two proposed decay schemes has made it possible to distribute all the available data between these two schemes.

Thus, there is convincing evidence for the decay of \(V\)-particles into protons and mesons, and the fourteen events found by the Pic du Midi group fit well into this scheme. The best value of the mass is \(2210\,m_e\). In addition, twelve

Fig. 9.

events can be explained by the decay of \(V\)-particles into two \(\pi\)-mesons. So far no event has been found in which both secondary particles could be identified as \(\pi\)-mesons.

8. Mean lifetime of neutral \(V\)-particles

The Anderson group \(^{23}\) made an estimate of the lifetime of neutral \(V\)-particles. For this purpose, the distribution of decay points along the line of flight of the particles was constructed, and corrections were introduced for the change in path length arising from the geometrical conditions of the cylindrical chamber, and for relativistic time dilation in each event. They had very limited data, since the initial point of the particle track could be determined for only nineteen events. The correctness of the geometrical corrections is difficult to assess, and the insufficient accuracy of the momentum measurements does not allow the relativistic corrections to be considered

accurate. The mean lifetime estimated by this method is \((3 \pm 2)\cdot 10^{-10}\) sec. The same method can be applied to the data obtained by the group on Pic du Midi. This result is in agreement with the broad range of values found in \(^{32}\). A reliable value of the mean lifetime can be obtained from those cases in which the nuclear interaction occurred in the chamber itself. In these cases the point of origin of the \(V\)-particle is determined exactly, and the geometrical corrections are of no great importance. Using fifteen tracks, Fretter found that the mean lifetime lies within the limits \((1.0—2.0)\times 10^{-10}\) sec. Assuming that the decay occurs according to the second scheme, he made an approximate determination of the correction associated with the relativistic time dilation for the geometrical conditions of each track. These lifetime values are very approximate, since the investigators were not able to assign their cases to definite decay schemes. If the results given in Section 7 are correct, they indicate rather the existence of two different \(V\)-particles with different values of mass and lifetime than the existence of a single neutral particle with two different decay schemes.

9. Conclusions

In a Wilson chamber it has been possible to observe more than one hundred “forks” arising from the decay of neutral \(V\)-particles. One such case was found in a photographic emulsion. Rochester and Butler reported the discovery of a \(V\)-shaped decay track of a neutral particle in 1947, at about the same time as Lattes, Occhialini, and Powell discovered the \(\pi\)-meson. However, during the last four years the properties of the \(\pi\)-meson have been successfully studied and are now known in considerable detail. There are at least three reasons explaining why the study of \(V\)-particles is proceeding so slowly. First, these particles occur much more rarely than \(\pi\)-mesons. It may be assumed \(^{32}\) that \(V\)-particles constitute about three percent of the ionizing particles in penetrating showers. Second, \(V\)-particles in quantities suitable for study are found only in Wilson chambers operating under difficult conditions at high altitudes. Finally, the lifetime of these particles is neither too small nor too large. This greatly complicates the study of the decay processes. If the lifetime were of the order of \(10^{-12}\) sec or less, the decay process of \(V\)-particles could conveniently be observed in photographic emulsions; on the other hand, if the lifetime were considerably greater than \(10^{-9}\) sec, the particles would often decay after almost coming to rest. The frequency of observation of all known decay processes increases when the particle approaches the state of rest.

On the basis of an analysis of the properties of neutral \(V\)-particles known as of April 1, 1951, the following conclusions may be drawn.

1. No more than 10% of \(V\)-shaped tracks can be explained by the presence of processes different from the spontaneous decay of particles hitherto unknown.

2. Not all secondary particles can be identified. Protons and negatively charged mesons, probably \(\pi\)-mesons, have been observed. Evidence has been found for the existence of positively charged secondary particles lighter than protons, but the existence of positively charged mesons could not be established with certainty.

3. Preliminary investigations agree with the assumption that in the decay processes only two charged secondary particles arise. Serious difficulties arise in attempts to relate the orientation of the “forks” to the place of origin of the neutral particle. Here additional and more accurate measurements are necessary.

4. To explain all the “forks” found it is necessary to admit at least two decay schemes:

\[ V_1^0 \to p^+ + \pi^- \qquad (\text{scheme (3)}), \]

\[ V_2^0 \to \pi^+ + \pi^- \qquad (\text{scheme (4)}). \]

One may expect the presence of the scheme

\[ V_1^0 \to p^- + \pi^+, \]

which is symmetric with respect to the first decay scheme.

Among the secondary particles five slow protons have been found, but not a single negatively charged proton has been observed. This may be an argument in favor of the supposition that the production of positively and negatively charged particles are not symmetric processes.

1. The Pic du Midi group subjected twenty-six neutral \(V\)-particles to detailed study. An analysis was made which showed that fourteen “forks” correspond to the first decay scheme. The mean value of the mass is \(2210\,m_e\). The remaining twelve cases, apparently, can be explained by decay proceeding according to the second scheme, and give a mass value close to \(800\,m_e\). Thus there is rigorous evidence for the existence of at least two different neutral \(V\)-particles.

2. The fact that a well-agreeing series of mass values exists is an argument in favor of the occurrence of only two charged secondary particles. If in each decay a third, neutral, secondary particle arises, then the calculated mass values will be underestimated. The number of cases forming two families of close mass values is very small. This does not make it possible to carry out a proper statistical analysis in order to find out whether the mass values obtained agree with one mean valu—

by them, or else they represent a distribution over some interval of values, as should be expected if the decay into three particles is interpreted as a decay into two particles. In order for such an analysis to be carried out reliably, a large number of very accurately measured cases will be required.

7. The first measurements of the lifetime of neutral \(V\)-particles gave values between \(10^{-10}\) and \(5\cdot 10^{-10}\) sec. Two different neutral \(V\)-particles may have different lifetimes.

In conclusion, it is useful to consider possible directions for the development of the problem under discussion. A detailed consideration of the properties of \(V\)-particles that follow from the nature of \(V\)-shaped tracks depends on the assumption of decay into two particles. Obviously, it is necessary to examine the grounds for this assumption and to outline further experiments. It is necessary to take into account the consequences following from the assumption of the possible decay of a particle into three secondary particles. The theoretical treatment of a process of this type is very complicated and cannot be carried out in detail without recourse to theory. Two types of \(V\)-shaped tracks have been observed. If there exist only two secondary particles, then both types of \(V\)-shaped tracks can be explained by two different decay schemes. These two schemes can be extended so as to apply them to a single \(V\)-particle decaying in two ways, namely:

\[ V^{0}\to p^{+}+\pi^{-}+\pi^{0} \]

and

\[ V^{0}\to \pi^{+}+\pi^{-}+n^{0}. \]

If these schemes actually exist, then in principle it is possible to detect neutrons and \(\pi^{0}\)-mesons by interactions whose vertex is directed toward the lead plate.

It is also necessary to obtain a substantially larger number of “forks” with long tracks of secondary particles, which can be measured with considerable accuracy. In this way it will be possible to obtain additional data on the nature of the secondary particles. Although the existence of neutral \(V\)-particles has been established, many of their properties are known only approximately.

Part II

DECAY OF HEAVY CHARGED PARTICLES

10. Decay of \(\tau\)-Mesons

During the first experiments with photographic plates sensitive to electrons, carried out on Jungfraujoch, a very unusual phenomenon was discovered,\(^7\) shown in photograph XIII (see the insert at the end of the issue). In the picture two stars are visible, connected by a \(\pi\) track. The probability that these two centers are

• unrelated events is extremely small, and therefore it may be disregarded.

The length of the track \(k\) in the emulsion exceeds \(3000\,\mu\), and the grain density increases continuously in the direction toward \(A\). Near \(A\) the track is indistinguishable from the track of a singly charged particle at the end of its range. It is therefore natural to think that particle \(k\) caused event \(A\), while particle \(\pi\) caused event \(B\). The mass of particle \(k\) can be determined from measurements of the dependence of the grain density on the residual range. In processing the plates, careful attention was paid to uniform development and to ensuring that the degree of regression was insignificant. For several proton tracks found on the same plate, a curve was constructed for the dependence of the mean number of grains (in an interval of \(10\,\mu\)) on the particle range. An analogous curve was constructed for particle \(k\). The mass of this particle was determined by comparing the grain-density curve obtained for it with the mean curve for protons. The authors found that the mean value of the mass for the particle is equal to \((1030 \pm 160)\,m_e\). From measurements of small-angle scattering for particle \(k\), a mass of \((1800 \pm 400)\,m_e\) was obtained. The more reliable value should be considered the value of the particle mass obtained by the grain-density method. The track \(\pi\) is characteristic of a \(\pi\)-meson captured at \(B\). The lengths of the two remaining secondary tracks, \(a\) and \(b\), belonging to singly charged particles, are respectively \(2000\,\mu\) and \(116\,\mu\). Within the limits of statistical fluctuations both these tracks exhibit the same ionization, 2.2 times the minimum. The energies and momenta of these two particles were obtained from observations of grain density and scattering, under various assumptions about their masses. For example, it was assumed that these particles are protons or \(\pi\)-mesons. The length of their tracks and the ionization measurements indicate that these particles cannot be electrons, if it is true that the increase in ionization for high-energy electrons ceases before the ionization value 2.2 times the minimum is reached. There are two possible interpretations of event \(A\), produced by particle \(k\): either particle \(k\) was captured by a nucleus, or it decayed spontaneously. A particle with a mass approximately equal to \(1000\,m_e\), at the end of its range, could have been captured by a nucleus, as a result of which two high-energy protons and a \(\pi\)-meson were emitted. The energies of the secondary particles would be approximately the same as those already obtained under the assumption that particles \(a\) and \(b\) are protons. It is obvious, however, that the liberation of such a large amount of energy should lead to the evaporation of the nucleons remaining in the nucleus. In that case a powerful many-pronged star should have been observed. Since such a phenomenon is not observed, the tracks \(a\) and \(b\) were apparently produced not by protons, but by \(\pi\)- or \(\mu\)-mesons. If the tracks \(a\) and \(b\) were produced by \(\pi\)-mesons, then the kinetic energy of the latter should have been equal to ...

27 MeV, and for μ-mesons 37 MeV. These values are small and cannot be reconciled with the absorption of 500 MeV of energy by a nucleus, which should occur upon the capture of particle \(k\) with a mass approximately equal to \(1000\,m_e\). Another explanation may also be considered, namely that tracks \(a\) and \(b\) are tracks of secondary particles produced in the spontaneous decay of particle \(k\). After introducing a correction for shrinkage of the emulsion, the authors determined the relative directions of the three particles and concluded that they are coplanar. The direction of any one of these three tracks makes an angle of less than \(4^\circ\) with the plane of the other two tracks. The errors in determining the angles are due to the fact that the \(\pi\)-meson track is very short in comparison with tracks \(a\) and \(b\). These measurements support the assumption that particle \(k\), having almost come to rest, decayed into particles \(a\), \(b\), and \(\pi\).

The particle \(\pi\) was almost certainly a \(\pi\)-meson. From observation of its range it was found that its energy was 1.04 MeV. Having determined the directions of motion of the three secondary particles and the energy of the \(\pi\)-meson, it was possible to find the momenta of the particles, which proved to be \((98 \pm 5)\,\text{MeV}/c\) and \((104 \pm 5)\,\text{MeV}/c\), respectively. Since, in addition, the grain densities are known, particles \(a\) and \(b\) can be identified. It turned out that these particles are either \(\pi\)- or \(\mu\)-mesons. The mass of particle \(k\) can be calculated for the two most probable decay schemes, namely:

\[ \begin{aligned} &k \to \pi + \pi + \pi \\ \text{and}\qquad &k \to \pi + \mu + \mu . \end{aligned} \tag{9} \]

These schemes are the most probable because the observed grain density agrees best with the assumption that particles \(a\) and \(b\) belong to one and the same type. The values of the masses obtained are, respectively, \(985\,m_e\) and \(869\,m_e\). Finally, one may consider the assumption that particle \(k\) is not connected with events \(A\) and \(B\). The mass value obtained for particle \(k\) does not exclude, as an extreme fluctuation, the possibility that it was a proton which stopped in the emulsion very close to \(A\) and was not connected with particles \(a\) and \(b\). Then, however, tracks \(a\), \(b\), and \(\pi\) are very difficult to explain, since stars of this type are not observed in emulsions. The authors, alternately assuming one or several of the observed tracks to be unrelated to the others, considered a number of possible explanations of event \(A\), but were unable to find a satisfactory scheme explaining the phenomenon. They came to the conclusion that the only reasonable explanation of the entire phenomenon is the assumption that particle \(k\) was an unstable particle with a mass of about \(1000\,m_e\), which produced events \(A\) and \(B\). Charged particles of this type are now called \(\tau\)-mesons.

After this discovery, a considerable amount of photographic emulsion sensitive to fast particles was studied, but it proved possible

to discover only two more phenomena of the same type[^14]. The first of the decay phenomena was found in an emulsion sensitive to electrons, exposed for 85 days under 3 m of ice. In this case the strongly ionizing particle ended its range at a center analogous to the center A in the case described above. The multiple scattering of this particle increased in the direction toward the star, and measurements of grain density indicated that the particle, denoted by the letter k, had almost stopped before it produced the star. The star consisted of three tracks, 1300 μ, 420 μ, and 30 μ long, respectively. The phenomenon was observed in a plate exposed for a long interval of time. The author showed that the plate had been uniformly developed; moreover, he took into account the effect of regression. For protons and μ-mesons stopped in the emulsion, measurements of the grain density were made and curves of grain density versus range were constructed. The corresponding curve for a π-meson was obtained by interpolation between these two curves. The curve of grain density versus range for the k-particle always lay above the curve for π-mesons. If the particle π was a meson, then it must have passed through the emulsion just at the end of the exposure.

The only well-known capture process that could explain the star is the capture of a π-meson. If it is assumed that the particle k was a π-meson, then the energy released in the nucleus was only 150 MeV. Further, if it is assumed that the secondary particles were protons, then the ionization measurements show that their total energy must have been of the order of 500 MeV. Therefore the phenomenon could not have been produced by a slow π-meson. The star could have been caused by the capture of a π-meson if one or both of the secondary particles were electrons. Direct formation of electrons in stars was not observed and, thus, this explanation is unlikely. The value of the product of momentum by velocity for the secondary particle with the longer track is 25 MeV. This particle is probably a π-meson. The tracks of the other two secondary particles are too short for reliable scattering measurements to be made. However, for the shorter track the scattering is considerably less than for the long one. It is evident that if a π-meson is captured by a nucleus, the energy released is insufficient even for the creation of a μ-meson and for imparting kinetic energy to the two other particles. In this connection the author came to the conclusion that this phenomenon cannot be interpreted as the capture of a π-meson by a nucleus.

After introducing the correction for shrinkage of the emulsion, the spatial arrangement of the three secondary tracks was carefully studied. The normal to the plane containing any two tracks was perpendicular to the plane containing the third track to within 2°. Thus, all three tracks were coplanar, as in the experi-

in the case described above. This is evidence that the \(k\)-particle decayed spontaneously into only three singly charged particles. The author assumed that the secondary particle with the longest track was a \(\pi\)-meson. Using the data obtained in the study of scattering, he calculated that the energy of this particle should have been equal to \(13\,M_{\text{ev}}\). If one assumes that the other two particles were also \(\pi\)-mesons, then, using the conservation laws of momentum and energy, it could be calculated that the mass of the \(\tau\)-meson is equal to \(1040\,m_e\). If the track \(k\) was produced by a particle of such mass, then the effect of regression was evidently very large, since the ionization exceeded only slightly the mean ionization from \(\pi\)-mesons in the same plate. In the second event of the same type, observed by the author, the tracks of the secondary particles were very short, so that no conclusions could be drawn from it, except that the secondary particles were approximately coplanar. The interpretation of the events described is supported by a large amount of similar evidence, and the existence of decay into three mesons seems very convincing. This conclusion is of special interest in connection with works \(^{11}\) and \(^{13}\), in which it was shown that no more than \(2\%\) of all strongly ionizing particles arising in stars can be \(\tau\)-mesons, provided only that their lifetime is not too short.

11. Decay of Charged \(V\)-Particles

11.1. The First \(V\)-Shaped Track of a Charged Particle

The first \(V\)-shaped track of a charged particle was discovered \(^{9}\) in a small Wilson chamber, without a magnetic field, installed at an altitude of \(2000\ \text{m}\). This phenomenon, however, was not subjected to detailed discussion. The angle of deflection was approximately \(10^\circ\), and the phenomenon could quite well have been a \(V\)-decay (see 11.3), since the particle was probably strongly ionizing. Photograph II shows a \(V\)-shaped track produced by a charged particle, discovered and examined in detail by Rochester and Butler \(^{21}\). The primary track (1) runs in the principal direction of the shower. This track is short and cannot be measured. The particle in the gas of the chamber underwent an apparent deflection of \(19^\circ\). The secondary charged particle, which passed without noticeable scattering through a lead plate \(3.4\ \text{cm}\) thick, was positively charged and had a measured momentum equal to \((0.77 \pm 0.10)\,B_{\text{ev}}/c\). At the vertex of the “fork” there is no noticeable cluster of ionization that could have been due to recoil. Therefore the “fork” could hardly have been due to scattering or to a nuclear interaction in the gas. The authors interpreted this phenomenon as the decay of a positively charged particle into one charged particle and one or several neutral particles. Assuming the existence of only two secondary particles, they found that the minimum mass of the unstable particle is equal to \((980 \pm 150)\,m_e\).

11.2. Statistical data on V-shaped tracks produced by charged particles

Among their 11,000 photographs, Anderson et al. ^32 discovered four V-shaped tracks produced by charged particles. Three of these unstable particles arose in nuclear interactions in a lead plate \(2\ \text{cm}\) thick, placed in the Wilson chamber. The angles between the primary and secondary tracks were \(7^\circ\), \(15^\circ\), \(34^\circ\), and \(40^\circ\), respectively. These cases are not characteristic of tracks produced by unstable particles; probably all the particles were moving at minimum ionization. The Pic-du-Midi group discovered eleven cases of decay of charged particles, three of which originated in lead plates. The ionization along the tracks of two unstable particles considerably exceeded the minimum. Fretter discovered four V-shaped tracks of charged particles that arose in lead plates. Four analogous tracks were found in their chamber with a large number of plates by Bridge and Annis. The primary tracks in two of these cases belonged to strongly ionizing particles. In addition, Bridge and Annis observed seven strongly ionizing particles whose range ended in one of the lead plates. In each of these cases a track with minimum ionization emerged from the lead plate. O’Ceallaigh ^30, studying \(\mu\)-decay, found in a photographic emulsion a V-shaped track of a charged particle. The grain density in the secondary track had the minimum value for the emulsion used.

11.3. Explanation of V-shaped tracks produced by charged particles

Anderson and collaborators did not report the results of momentum measurements for the four V-shaped tracks of charged particles observed by them. However, they concluded that the observed phenomena can be explained only as the decay of charged particles. One of the secondary particles penetrated a lead plate \(2\ \text{cm}\) thick and, probably, its mass was greater than the electron mass. There are at least three possible explanations of the V-shaped tracks of charged particles discovered at Pic du Midi, different from that proposed by Rochester and Butler. The observed phenomena may be caused, first, by nuclear interactions, second, by scattering, and third, by the well-known processes of decay of \(\pi\)- and \(\mu\)-mesons. The first explanation seems unlikely, since in all cases there are no tracks of recoil nuclei. Moreover, not a single phenomenon similar to a V-shaped track from a charged particle was observed together with tracks of evaporated particles. It seems unlikely that 11 high-energy stars would be observed in the chamber gas without being accompanied by at least one track of an evaporated particle. By analogy with how this was done in 4.1, one can estimate the expected number of high-energy nuclear reactions in the gas associated with the observed penetrating showers. Probab-

the probability of detecting such an interaction or star is small. In fact, however, two such stars were found, but they are different from the \(V\)-shaped tracks of charged particles: in each of them tracks of the recoil nucleus are visible (see 4.1).

The observed phenomena can hardly be attributed to nuclear scattering, since recoil tracks are absent. For many of the detected cases it is easy to show that recoil in the chamber would have been noticeable if these phenomena had been caused by scattering. If they were in fact explained by scattering, then in the lead plate there should have occurred 400 times as many scattering events. During the period when a lead plate 2 cm thick was in the chamber, three \(V\)-shaped tracks of charged particles were found. Thus, according to what was set forth above, 1200 particles should have undergone large-angle scattering in the plate. In reality, however, 120 cases of deflections greater than \(5^\circ\) were found in the lead plate. The momenta of not all these particles were measured. Particles with momentum less than \(0.3\ \mathrm{Bev}/c\) could have undergone multiple Coulomb scattering. Thus the observed number of examples of anomalous scattering cannot exceed 60. This number is substantially smaller than the number predicted on the basis of the assumption that the \(V\)-shaped tracks of charged particles arise as a result of large-angle scattering.

Finally, it is necessary to consider the probability that a small part of the observed events can be explained by the well-known decay processes of \(\pi\)- and \(\mu\)-mesons. \(\pi\)-mesons constitute a considerable fraction of the fast particles in penetrating showers, and one may expect that in the gas of the chamber they should decay. An approximate estimate of the number of decays can be made on the basis of the known flux of \(\pi\)-mesons, their lifetime, and reasonable assumptions about their spectrum. The result obtained is that about thirty \(\pi \to \mu\) decays should be expected. Many of these events, however, will be high-energy cases, for which the apparent angle of deflection is very small. The dynamics of the decay scheme is as follows:

\[ \pi \to \mu + \nu, \tag{10} \]

where \(\nu\) is the neutrino. This decay scheme is relatively simple, and it can easily be shown that for a \(\pi\)-meson of given momentum there exists a maximum value of the angle \(\vartheta\) between the directions of the \(\pi\)- and \(\mu\)-mesons. The value of \(\vartheta\) is determined from the relation

\[ \sin \vartheta_{\max}=0.04/p, \tag{11} \]

where \(p\) (in \(\mathrm{Bev}/c\)) is the momentum of the \(\pi\)-meson.

It can also be shown that the most probable values of \(\vartheta\) for a meson with a given \(p\) lie very close to the corresponding value \(\vartheta_{\max}\). If the momenta are known, then the values of \(\vartheta_{\max}\) for each observed charged particle that formed a \(V\)-shaped track can be calculated and compared with the actual values.

If it turns out that the observed value is substantially greater than the computed maximum value, then it is obvious that the observed decay cannot be explained by means of this scheme. This method, apparently, is the only reliable means of separating the decay of charged \(V\)-particles and \(\pi\)-mesons; however, it is inevitable that some \(V\)-shaped tracks produced by charged particles will in this case be interpreted as the decay of \(\pi\)-mesons.

In a Wilson chamber triggered mainly by penetrating showers, the decay of \(\mu\)-mesons should be observed very rarely, since they can be produced only in the decay of \(\pi\)-mesons. Broad air showers triggered the chamber from time to time, and thus several \(\mu\)-mesons passed through it.

The four \(V\)-shaped tracks of charged particles discovered on the Pic du Midi can be explained by the decay of \(\pi\)-mesons, and one case by the decay of a \(\mu\)-meson. In five cases that could not be explained with the aid of well-known decay processes, measurements were made of one, and sometimes of both, tracks. These cases were interpreted as the decay of charged \(V\)-particles. Anderson’s group discovered two \(V\)-shaped tracks of charged particles with deflection angles smaller than \(20^\circ\). These “forks” could have been caused by the decay of \(\pi\)-mesons, if only the unstable particles did not possess a large energy. In two decay cases discovered by Bridge and Annis, secondary particles were observed that could have been electrons. The authors believe that these phenomena may be examples of \(\beta\)-decay or of the decay of \(\mu\)-mesons. Both of these explanations seem improbable.

11.4. The nature of the secondary particles arising in the decay of charged \(V\)-particles. In the Wilson chamber, no phenomenon analogous to that described in Section 10 has so far been found. In all examples of the decay of a charged particle discovered up to the present time in chambers, only one ionizing secondary particle was observed. No investigator has reported the existence of a strongly ionizing secondary particle formed in the decay of a \(V\)-particle in a magnetic field. One of the secondary particles observed in such a decay penetrated through \(3.4\ \mathrm{cm}\) of lead, and another through \(2\ \mathrm{cm}\) of lead; in both cases no appreciable scattering and no electromagnetic or nuclear reactions were detected. Bridge and Annis obtained an interesting \(V\)-shaped track of a charged particle, which is shown in photograph XIV. The secondary particle produces ionization approximately twice the minimum, and the direction of its motion makes an angle of \(90^\circ\) with the direction of the \(V\)-particle, which itself is strongly ionizing. The secondary particle then apparently underwent scattering through a large angle in an aluminum plate located above the decay point. After penetrating through four plates, this particle came to rest. On the basis of the observed values of the range,

scattering and ionization, the authors came to the conclusion that this particle must have been a meson, and probably a \(\pi\)-meson, since it underwent nuclear scattering in the aluminum plate. However, it is impossible to establish unambiguously the nature of this particle before it interacted with the material of the plate. It is quite probable that the interaction in the plate had a more complicated character than that assumed by the authors; for example, the \(\pi\)-meson could have been created in the aluminum plate. The group at the Pic du Midi measured both tracks for five cases of decay of \(V\)-particles. The results of the measurements are given in Table X. The same table also gives the measurement results for the case of photograph 11.

Table X

Measurements of six charged \(V\)-particles

Event No.	Sign	Measured momentum of the primary particle \((\mathrm{BeV}/c)\)	Measured momentum of the secondary particle \((\mathrm{BeV}/c)\)	Angle of deflection (degrees)
Photograph 11	\(+\)	too short a track	0.77	19
1	\(-\)	1.1	0.15	24
17	\(-\)	too short a track	0.13	100
40	\(-\)	1.4	0.71	11
54	\(+\)	1.0	too short a track	10
61	\(-\)	0.2	0.15	70

Many tracks are very short and are located near the edges of the chamber; accordingly, the momentum measurements in these cases are not very accurate. The negatively charged secondary particles in cases 1 and 17 had minimum ionization and such a momentum that, undoubtedly, their mass is less than the proton mass. However, they could have been mesons or electrons. If all the cases of decay of charged particles belong to one and the same type, then it is natural to think that the charged secondary particles are \(\pi\)-mesons.

At present there is no possibility of obtaining any substantial information about the nature and number of neutral particles that arise in the decay of charged \(V\)-particles. For simplicity, in analyzing the data we shall assume that one neutral particle participates in the process under consideration. This assumption can be discarded when additional information is obtained about the actual decay process. The most probable particles participating in the process are neutrons, \(\pi^0\)-mesons, and neutrinos. The first two particles, in principle,

may be identified by their interactions or by the interactions of their secondary particles in lead plates. The existence of the neutrino cannot be detected by such direct methods. There is, however, some evidence that a neutral particle may be a neutral \(V\)-particle (see 11.5).

11.5. Mass of a charged \(V\)-particle. The mass of a charged \(V\)-particle can be determined in two ways. First, the mass can be calculated from the magnitude of the momentum and the ionization, if the latter appreciably exceeds the minimum. Secondly, the mass can be calculated from the magnitudes of the momenta of the \(V\)-particle and its secondary particle, the angle of emission of the latter, and the accepted decay scheme.

Fig. 10

O’Ceallaigh\(^{20}\) observed the decay of a charged \(V\)-particle in a photographic emulsion. Before stopping and decaying, the unstable particle left a track \(4200\,\mu\) long, and on decay produced one charged particle possessing minimum ionization. The mass of the slow particle can be determined from measurements of the dependence of the grain density on the range. It was found to be \((1380 \pm 180)\,m_e\). The mass can also be obtained from measurements of the scattering of the particle through small angles as a function of its residual range. The value obtained in this way is \((1260 \pm 290)\,m_e\). At Pic du Midi, in a magnetic field, two slow \(V\)-particles were observed (cases 17 and 61). Unfortunately, both tracks are too short for reliable measurements of the momentum to be made. Bridge and Annis also observed two strongly ionizing particles; however, in both cases there was no magnetic field, and therefore it is difficult to determine the mass values. Figure 10 shows the decay of a charged particle into two secondary ones. The mass of the charged particle can be calculated with the aid of the following formulas:

\[ \left. \begin{aligned} \sqrt{M^{2}+p^{2}} &= \sqrt{m_{1}^{2}+p_{1}^{2}}+\sqrt{m_{2}^{2}+p_{2}^{2}},\\ p_{2}^{2} &= p^{2}+p_{1}^{2}-2pp_{1}\cos\theta \end{aligned} \right\} \tag{12} \]

which can be combined to obtain an expression for \(M\). The chief sources of error lie in the measurements of the momenta. The first case described, observed at Pic du Midi, still remains unique (No. 1 of Table X) and is the only source of our information about the nature of the neutral particle arising in the decay of a charged \(V\)-particle. This photograph was the first photograph of the decay process obtained at Pic du Midi and, unfortunately, cannot be repro-

introduced because of the indistinctness of the tracks. A negatively charged particle penetrated a lead plate of thickness \(2\ \mathrm{cm}\) and decayed in the chamber gas. Following this, the decay of a neutral particle occurred at a distance of \(1\ \mathrm{cm}\) below the first decay. The Pic du Midi group concluded that these two decay phenomena are directly connected. The decay point of the charged \(V\)-particle lies, to within the experimental errors, in the plane of the second “fork.” The simplest explanation of the double decay is the assumption that the neutral \(V\)-particle was formed in the decay of the charged particle. The measurements of the momenta of the secondary particles formed in the decay of the neutral \(V\)-particle are very inaccurate, since the tracks are short and poorly defined. The data given in Table IX of Section 6.2 indicate that, apparently, decay according to scheme (4) took place. The scheme according to which the decay of the negatively charged particle occurs apparently has the form

\[ V^- \to \pi^- + V_2^0, \tag{13} \]

where, within the existing errors of measurement, the \(\pi\)-meson may be replaced by a \(\mu\)-meson. The mass of the neutral \(V_2^0\)-particle is of the order of \(800\,m_e\). It is possible that the particle under consideration could have had a mass of \(2200\,m_e\) (the decay scheme according to equation (3)). From the dynamics of the observed decay it is clear that the momentum of the neutral particle was considerably greater than the momentum of the charged secondary particle. From the existence of an asymmetry in the momenta it follows that the mass of the neutral particle was considerably greater than the mass of the charged particle, since otherwise the observed distribution of the momentum of the \(V\)-particle between the two secondary particles would have been improbable.

Another, but considerably less plausible, explanation is the assumption that the incident particle, owing to interactions in the lead, created two unstable particles moving in the same direction as the primary particle, without producing any other visible particles. The two \(V\)-particles then decayed in the chamber gas under the plate. The neutral particles formed in the decay of the charged particle are most probably \(\pi^0\)-mesons, neutrons, and neutrinos. The various possible explanations of the double decay are given in Table XI. Approximate values of the masses are given in row 4. The second case (No. 40 of Table X), which may be analyzed from the point of view of the five schemes given in Table XI, is shown in photograph XV. It is analogous in every respect, except for the sign, to the case observed by Rochester and Butler. The mass values are given in row 5.

The third event (No. 17 of Table X) is shown in photograph XVI. A strongly ionizing particle, formed as a result of a nuclear interaction in the lead plate, decays

Table XI

	(1)	(2)	(3)	(4)	(5)
1. Scheme No.	(1)	(2)	(3)	(4)	(5)
2. Nature of the charged secondary particle	$\pi$	$\pi$	$\pi$	$\pi$	$\pi$
3. Nature of the neutral secondary particle	$V^0$ $(800\,m_e)$	$V^0$ $(2200\,m_e)$	$n^0$	$\pi^0$	$\gamma$
4. Mass for case No. 1 $(m_e)$	1160	2460	2140	820	790
5. Mass for case No. 2 $(m_e)$	1280	2900	2530	750	660
6. Interval of masses for case 17 $(m_e)$ — minimum mass	1310	2630	2320	900	800
6. Interval of masses for case 17 $(m_e)$ — maximum mass	1440	2740	2420	1060	960
7. Minimum mass for the case of photograph 11 $(m_e)$	1530	2910	2580	1120	1050

at a distance of 2 cm below the plate. The point of decay is not clearly visible because of the tracks of other particles. However, under stereoscopic examination the decay point can be discerned. The length of the track of the primary particle is small and cannot be measured, but it is evident that the specific ionization exceeds the minimum value by a factor of four. The track of the negative secondary particle makes an angle of $100^\circ$ with the direction of the primary particle. The momentum of the secondary particle could be measured, and it turned out to be $0.18\,\mathrm{Bev}/c$. If one assumes that the particle decayed at the instant of stopping and adopts some decay scheme, then the minimum mass of the charged particle can be determined. The maximum value of the mass of the charged particle for the adopted decay scheme can be calculated if the decaying particle is assigned the maximum momentum consistent with the specific ionization observed for it. The minimum and maximum mass values are given in line 6 of Table XI. If one tries to explain this case as a $\pi$—$\mu$ decay, then for the mass of the $\pi$-meson an absurdly high value of $630\,m_e$ is obtained.

The $V$-shaped track discovered by O’Ceallaigh is very similar to the case in the Wilson chamber shown in photograph XVI. The decay occurred at the instant of stopping. Assuming that the charged secondary particle was a meson, the author found that its momentum was $0.28\,\mathrm{Bev}/c$. This value substantially exceeds the value obtained by the group on Pic du Midi. If the $V$-particle decayed into a charged and a neutral $\pi$-meson, then its mass should have been equal to $1260\,m_e$. However, if the neutral particle was a neutral $V$-particle with mass $800\,m_e$, then the mass of the primary particle should have been equal to $1320\,m_e$. These values are greater than the values obtained by the group on Pic du Midi for an analogous event; however, they are incompatible with the magnitude of the mass found from the analysis of the track of the $V$-particle before stopping. O’Ceallaigh

could not identify the secondary charged particle, which could have been either an electron or a meson.

The \(V\)-shaped track of a positively charged particle, observed by Rochester and Butler, cannot be analyzed in detail, since the momentum of the incident primary particle is unknown. It is possible, however, to assume any of the five decay schemes given in Table XI and to use the momentum of the secondary particle to calculate the minimum possible value of the mass. These minimum values are given in row 7 of Table XI.

The various schemes give mass values that agree sufficiently well with one another. However, with the small number of fully analyzed events it is impossible to conclude which of the schemes agrees best with the available data. The scheme

\[ V^{\pm}\to \pi^{\pm}+\pi^{0} \]

gives several mass values that agree well with the only direct determination of the mass made up to the present time.

11.6. Mean lifetime of resting charged \(V\)-particles. From the small number of phenomena investigated up to the present time it is impossible to determine the lifetime of the charged \(V\)-particle. Anderson and co-workers believe that this lifetime may be considerably shorter than the lifetime obtained for neutral \(V\)-particles. They found twenty-five neutral \(V\)-particles born above the chamber, and five emerging from the lead plate. At the same time, one charged particle emerged from the lead above the chamber and three from the lead plate located in the chamber. These data indicate that the greater part of the charged \(V\)-particles may have decayed, owing to their short lifetime, before they reached the chamber. The number of events is small, and the conclusion obtained may be incorrect if one or two \(V\)-shaped tracks of charged particles can be explained by the decay of \(\pi\)-mesons rather than of \(V\)-particles. It is unlikely that the lifetime of charged \(V\)-particles was less than \(10^{-10}\) sec, since the decay of slow \(V\)-particles was observed also by the group of Pic du Midi and by Bridge and Ennis. Indeed, the lifetime may be quite long, if the event shown in photograph XVI resembles the negatively charged \(\tau\)-meson observed by Butler et al.\(^8\) These investigators found three slow \(\tau\)-mesons with a total track length of about 20 cm which did not decay in the chamber. Bridge and Ennis found seven cases in which a particle entered the chamber from the counters and, evidently, stopped in one of the plates. In each case, from the bottom of the corresponding plate there emerged the track of one secondary particle, with minimum ionization. One of the secondary particles traveled approximately 3 cm

lead without multiplication. Bridge and Annis came to the conclusion that this secondary particle could not have been an electron and, consequently, they could not interpret this phenomenon as the decay of a \(\mu\)-meson. In their opinion, some other cases likewise could not have been \(\mu \to e\) decays, which led them to the conclusion that several of the cases considered were examples of the decay of slow \(V\)-particles. If these conclusions are correct, then the mean lifetime of the charged \(V\)-particle cannot be much shorter than \(10^{-9}\) sec.

12. Conclusions

Convincing evidence has been obtained for the existence of unstable charged particles heavier than \(\pi\)-mesons. At present it is not clear how many such particles there are. In the coming years a large amount of research must be carried out in order to determine their properties. The principal conclusions may be formulated as follows:

1. In photographic emulsions three cases of the decay of charged particles were found, in each case into three \(\pi\)-mesons. In two of these cases the mass of the unstable particle was close to \(1000\,m_e\). In a photographic emulsion one case was observed of the decay of a charged particle into a singly charged secondary particle. The mass obtained as a result of studying the track of the unstable particle proved to be equal to \((1260 \pm 290)\,m_e\). This value is greater than that obtained from analogous measurements for \(\tau\)-mesons.

2. In Wilson chambers approximately thirty \(V\)-shaped tracks of charged particles were observed. In each of these cases one charged secondary particle was found. It was shown that in order to distinguish the phenomena described from the comparatively common decays of \(\pi\)-mesons in penetrating showers, it is necessary to measure the momenta. The group on the Pic du Midi discovered seven examples of the decay of charged particles heavier than \(\pi\)-mesons.

3. The decay of several strongly ionizing particles in the gas of a Wilson chamber was discovered. However, up to April 1951 only two cases had been observed in a magnetic field, and in both cases the tracks were too short for measurement of the momenta.

4. The masses of several charged particles were calculated for various decay schemes. In choosing the decay schemes, data on the nature of the secondary particles are used as a guide. In one case the secondary particle was probably a \(\pi\)-meson. In another case there is reason to think that the neutral secondary particle was a \(V\)-particle, apparently belonging to a type of particles with a mass of the order of \(800\,m_e\). If charged \(V\)-particles decay according to the scheme

\[ V^\pm \to \pi^\pm + V_2^0, \]

then their masses lie within the range \((1200\text{--}1500)\,m_e\). These values are substantially greater than those obtained for the \(\tau\)-meson. On the other hand, if both secondary particles formed in the decay of the charged particle are \(\pi\)-mesons, then the mass of the \(V^\pm\)-particle must be of the order of \(1000\,m_e\).

References

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Photograph I (see §§ 1 and 9.2). Decay of a neutral \(V\)-particle produced in the cascade chamber. The momentum of the positively charged particle (1) is \((0.2—0.3)\ \mathrm{BeV}/c\). Track (2) cannot be measured. The opening angle of the secondary particles is \(67^\circ\). If it is assumed that the direction of motion of the neutral \(V\)-particle coincides with the direction of the main shower and that only two secondary particles arise in the decay, then the momentum of (2) lies within the limits \((0.7—1.0)\ \mathrm{BeV}/c\). The positively charged particle is not a proton, and therefore the “fork” may be explained by the following decay scheme:

\[ V_2^{0} \to \pi^{+} + \pi^{-}, \]

where the mass of the neutral \(V\)-particle is close to \(1100\,m_e\).

Photograph II (see § 11.1). Decay of a positively charged \(V\)-particle produced above the chamber. Track (1) of the incoming particle undergoes an apparent deflection of \(19^\circ\) in the gas. The positively charged secondary particle proves capable of passing through a lead plate \(3.4\ \mathrm{cm}\) thick. Track (1) cannot be measured; track (2) gives a value of \(0.77\ \mathrm{BeV}/c\) for the momentum below the plate. The \(V\)-shaped track arose from the decay in flight of a positively charged \(V\)-particle into a charged particle, apparently a \(\tau\)-meson, and into one or several neutral particles. Since the momentum of the \(V\)-particle could not be measured, the value of its mass cannot be calculated. By considering various decay schemes, one can calculate a minimum mass for each of them. The mass values for a number of possible schemes are given in Table XI, § 11.5.

Photograph III (see § 2). Birth of a neutral \(V\)-particle. A charged particle created an interaction of great energy in the third lead plate. The \(V\)-shaped track is located between the third and fourth plates. The length of the path of the neutral \(V\)-particle is apparently less than \(2\ \mathrm{cm}\). Both secondary particles produce minimal ionization. The straight particle passes through at least two plates and is strongly scattered in the fourth plate.

Photograph IV (see § 2.3). The birth of a neutral \(V\)-particle outside the plates, the decay products of which evidently possessed a high energy. Between the fourth and fifth plates a \(V\)-shaped trace is visible, formed by two particles, of which one produces strong ionization. The ionization from the other particle is minimal. The slow particle is absorbed in the fifth plate. A thin secondary track passes through all the plates, experiencing a noticeable scattering in the sixth. From the bending of the \(V\)-shaped trace relative to the point of origin of the \(V\)-particle it may be concluded that the momentum of the slow particle is greater than the momentum of the secondary particle. It is very likely that the slow particle is a proton, and the other secondary particle is a meson.

Photograph V (see §§ 2.3 and 6.2). A neutral \(V\)-particle, scattered backward on a 7-mm lead plate, produced a nuclear interaction of very high energy. In addition to a large number of fast particles, probably protons and mesons, several slow particles are visible beneath the plate. This interaction is secondary with respect to an interaction of considerably higher energy that occurred above the chamber. Tracks (1) and (2) form a \(V\)-shaped track whose direction is almost opposite to the direction of the shower. The angle of divergence is \(77^\circ\). The momentum of the positively charged particle (1) is \(0.27\) BeV/\(c\), and that of the negatively charged particle (2) is approximately \(0.13\) BeV/\(c\); the latter is apparently a negatively charged \(\pi\)-meson. The positively charged particle is lighter than a proton; the decay may be described by the scheme

\[ V_2^0 \to \pi^+ + \pi^-, \]

where the mass of the neutral \(V\)-particle is close to \(700\,m_e\) (see Table IX, § 6.2).

Photograph VI (see § 3.1). A \(V\)-shaped track from the decay of a neutral \(V\)-particle, with two slow secondary particles. The \(V\)-shaped track is formed by tracks (1) and (2), the angle between them being \(120^\circ\). Because of distortions, precise measurements of the momenta are impossible, and only some general conclusions can be drawn. If the direction of motion of the neutral \(V\)-particle coincides with the direction of motion of the two fast particles crossing the top of the chamber, then in this case the momentum of particle (1) is several times greater than the momentum of particle (2), unless other particles are produced in the decay. Track (2) apparently belongs to a slow meson, and track (1) to a slow proton, but a more precise identification of the tracks cannot be made.

Photograph VII (see §§ 3.1 and 6.1). Decay of a neutral \(V\)-particle into a proton and a meson. The \(V\)-shaped track is formed by tracks (1) and (2), the angle between which is \(50.5^\circ\). The ionization along track (1) is equal to \((3\text{–}4)\) times the minimum ionization. The momentum of particle (1) is \(0.48\,\mathrm{Bev}/c\). From a considerable reliability this particle must be recognized as a proton. The negatively charged particle has a momentum of \(0.19\,\mathrm{Bev}/c\), and is probably a \(\pi\)-meson. The \(V\)-shaped track can be explained by the following decay scheme:

\[ V_1^0 \longrightarrow p^+ + \pi^-, \]

where the mass of the neutral \(V\)-particle is \(2220\,m_e\) (see Table VII, § 6.1).

Photograph VIII (see § 3.1). A secondary particle arising in the decay of a neutral \(V\)-particle is a negatively charged \(\pi\)-meson. The negatively charged particle (1) has a momentum of \(82\,\mathrm{Mev}/c\). \((\pm 5\%)\) and an ionization \(2.5\text{–}3.5\) times greater than the minimum. A \(\pi\)-meson with such a momentum should possess triple ionization. The track of the positively charged particle is directed toward the piston of the chamber and therefore quickly leaves the field of view. The angle between the directions of motion of the secondary particles is \(27^\circ\).

Photograph IX (see § 3.2). Decay of a neutral \(V\)-particle in a hydrogen propane chamber. The \(V\)-shaped track is formed by tracks (1) and (2), the angle between which is close to \(6^\circ\). Measurement of the momenta is possible only under the assumption that the positively charged particle (1) has momentum \(2.6\ \mathrm{Bev}/c\), and the negatively charged particle (2) has momentum \(3.0\ \mathrm{Bev}/c\). When the charged particles pass through a lead plate \(2\ \mathrm{cm}\) thick, no interactions occur. This indicates that the secondary particles are electrons. The \(V\)-shaped track under consideration can be successfully interpreted by the following decay scheme:

\[ V_2^0 \to \pi^+ + \pi^-, \]

where the mass of the neutral \(V\)-particle is equal to \(796\,m_e\) (see Table VIII § 6.1 and also §§ 7.1 and 7.2).

Photograph X (see § 3.2). Decay of a neutral \(V\)-particle in which one secondary particle is a \(\pi\)-meson. A neutral \(V\)-particle, immediately above the plate, decayed into particles (1) and (2). Track (1) belongs to a positively charged particle. Its momentum cannot be measured accurately, but it is probably greater than \(1\ \mathrm{BeV}/c\). Track (2), of a negatively charged particle, has a very short length above the plate. The ionization along this track is somewhat greater than minimum. Beneath the \(7\)-mm plate this secondary particle becomes strongly ionizing and is deflected in the gas by \(23^\circ\). Measurements relating to this particle and to the secondary particle (3) associated with it are given in Table IV, § 3.2. Track (2) belongs to a \(\pi\)-meson decaying in flight into a \(\mu\)-meson—track (3). The photograph is evidence for the existence of \(\pi\)-mesons among the secondary particles arising in the decay of neutral \(V\)-particles. The positively charged secondary particle is probably a proton, whence it follows that the decay of the \(V\)-particle proceeds according to the following scheme:

\[ V_1^0 \longrightarrow p^+ + \pi^- . \]

In the photograph a second \(V\)-shaped track is visible, formed by tracks (4) and (5), the angle between which is approximately \(10^\circ\). The momenta of the positively (4) and negatively (5) charged particles were measured and are respectively \(0.32\ \mathrm{BeV}/c\) and \(0.56\ \mathrm{BeV}/c\). Both secondary particles are lighter than the proton, and therefore such a decay proceeds according to the scheme

\[ V_2^0 \longrightarrow \pi^+ + \pi^- , \]

where the calculated value of the mass of the neutral \(V_2^0\)-particle is equal to \(510\,m_e\) (see Table IX, § 6.2).

Photograph XI (see § 4.1). Nuclear interaction in gas. The interaction occurred beneath the plate and was caused by particle (1). Between the tracks (2) and (3) produced in this process, a cluster of ionization is visible, apparently produced by a recoil nucleus. Track (1) cannot be measured, since it is partly obscured by the track of a low-energy α-particle. The measured momentum of the positively charged particle (2) is \(0.35\ \mathrm{BeV}/c\), and the ionization along track (2) exceeds the minimum by a factor of 4–5; apparently particle (2) is a proton. The measured momentum of the positively charged particle (3) is \(0.65\ \mathrm{BeV}/c\), and the track of this particle is inclined at an angle close to \(7^\circ\) to the plane of tracks (1) and (2). In the direction forming a right angle with the direction of the primary particle (1), the law of conservation of momentum is not satisfied. Therefore this event cannot be simply elastic scattering.

Photograph XII (see § 5.1). A high-energy V-shaped track with a small opening angle. The fork is formed by two high-energy tracks, (1) and (2), diverging at an angle of \(12^\circ\). The measured momenta of the positively (1) and negatively (2) charged particles are, respectively, \(1.5\ \mathrm{BeV}/c\) and \(1.6\ \mathrm{BeV}/c\). A detailed consideration of the dynamics of decay processes leads to the conclusion that in the present case there probably occurs a decay proceeding according to the scheme:

\[ V_2^0 \longrightarrow \pi^+ + \pi^-, \]

where the mass of \(V_2^0\) is equal to \(840\,m_e\) (see Table VIII, § 5.1).

Photograph XIII (see § 10). Decay of a slow $\tau$-meson. Particle $k$ stops at point $A$ and creates particles $a$, $b$, and a slow $\pi$-meson; after this, at point $B$, capture of the $\pi$-meson occurs. The mass of particle $k$ can be found from the measured range density of the stars from the path. It is equal to $(1030 \pm 160)m_e$. The arguments considered in detail above,^7 showing that at point $A$ there was no nuclear capture of particle $k$ accompanied by the emission of particles $a$, $b$, etc., and careful measurements show that the traces of these secondary particles lie in one plane and that the given case can be interpreted only as the spontaneous decay of particle $k$. The traces $a$ and $b$ apparently belong to mesons whose mass can be measured from the grain density of the trace and from the magnitude of the scattering.

Photograph XIV (see § 11.4). Decay of a slow $V$-particle. A slow charged particle decays between plates 4 and 5. The chamber contains, alternately, 8 aluminum and lead plates. The secondary particle produces ionization twice the minimum value, and its direction of motion makes an angle of $90^\circ$ with the direction of motion of the $V$-particle. The secondary particle then enters the aluminum plate located above the decay point. The authors suppose that there it is scattered through a large angle, after which it moves downward and comes to rest after passing through four plates. From the observed values of range, scattering, and ionization, they conclude that this particle is a meson; and since the particle undergoes nuclear scattering, it is probably a $\pi$-meson.

Photograph XV (see § 11.5). Decay of a negatively charged \(V\)-particle of high energy. This case is analogous, with the exception of the sign of the \(V\)-particle, to the case discovered by Rochester and Butler in 1947. The momentum of the primary particle cannot be measured exactly, but, judging by the curvature, it is greater than \(1.4\ \mathrm{Bev}/c\). The momentum of the secondary particle is \(0.7\ \mathrm{Bev}/c\); the angle between the directions of both particles is \(11^\circ\). If one makes the assumption that the secondary neutral particle is a proton, then the mass of the \(V\)-particle can be calculated. The values obtained are given in Table XI, § 11.5. If, for example, the neutral secondary particle is a \(\pi\)-meson, then the mass of the \(V\)-particle is \(750\,m_e\). If the neutral secondary particle has a mass of \(400\,m_e\), then the mass of the \(V\)-particle is \(1280\,m_e\).

Photograph XVI (see § 11.5). Decay of a slowly moving negatively charged \(V\)-particle. In a nuclear interaction of high energy that occurred in a lead plate, a slow \(V\)-particle arose, decaying at a distance of 2 cm beneath the plate. Because of the short length of the primary track, it cannot be assumed with certainty, but it is nevertheless evident that the ionization exceeds the minimum by a factor of four. The track of the negatively charged particle (2) forms an angle of \(100^\circ\) with the direction of the primary particle. The measured momentum of particle (2) is \(0.18 \pm 0.02\) Bev/\(c\). The minimum and maximum values of the mass of the negatively charged \(V\)-particle can be calculated: they are given in Table XI, § 11.5. If, for example, the neutral secondary particle is a \(\pi\)-meson, then the mass of the \(V\)-particle lies between \(900\,m_e\) and \(1080\,m_e\); if the neutral particle is a \(V\)-particle with mass \(800\,m_e\), then the mass of the \(V\)-particle lies between \(1310\,m_e\) and \(1440\,m_e\).