HEAVY UNSTABLE PARTICLES

(hyperons and $K$-mesons)

A. O. Weisenberg

CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

I. Experimental Methods

I. 1. Photographic-emulsion chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
I. 2. Exposure of photographic emulsions . . . . . . . . . . . . . . . . . . . . . . . . . . 367
I. 3. Methods for identifying particles in emulsion . . . . . . . . . . . . . . . . . . . 369
I. 4. Wilson chambers and spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . 381

II. Methods of Analysis of Observations

II. 1. Analysis of the dynamical conditions of decay . . . . . . . . . . . . . . . . . 395
II. 2. Determination of the mean lifetime from time of flight . . . . . . . . . . 400

III. Neutral Particles

III. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
III. 2. $V_1^0$-particles; neutral hyperons $\Lambda^0$ . . . . . . . . . . . . . . . . . . 403
III. 3. $V_2^0$-mesons; $\vartheta^0$-mesons . . . . . . . . . . . . . . . . . . . . . . . . 410
IV. Charged hyperons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
V. Charged $K$-mesons. VI. Charged $V^{\pm}$-particles. VII. Generation of hyperons and $K$-mesons and their interaction with nuclei. Bibliography.

INTRODUCTION

The study of heavy unstable particles, which began in 1947–1948, achieved especially great success during the last three years. In these years it proved possible to refine considerably the preliminary data obtained in 1947–1951 on the properties of heavy unstable particles and to obtain reliable data on new particles. Such successes became possible for the following reasons. First, there was

further refinement of measurements with Wilson chambers, accompanied, as material accumulated, by an increase in its statistical accuracy. Secondly, many laboratories mastered the method of the nuclear-emulsion chamber, which made it possible to examine large volumes of nuclear emulsion and to trace particle tracks over distances of centimeters. Thirdly, in 1953 the Brookhaven Cosmotron began operating, producing a proton beam with an energy of 2.2 and then 3 Bev. With the aid of fast protons at the Cosmotron it proved possible to obtain a beam of π-mesons with an energy of 1.37 Bev. These beams made it possible to generate in the laboratory all the heavy unstable particles known from cosmic-ray investigations. Thus, in 1953 cosmic radiation ceased to be the sole source of heavy unstable particles, just as in 1948 it had ceased to be the sole source of π-mesons.

Finally, of great importance in obtaining new data on the nature of unstable heavy particles was the fact that investigations of their properties were carried out by many groups of researchers, who used—especially in measurements with emulsions—similar and coordinated methods of measurement. This made it possible to combine the results obtained and increased their reliability and accuracy.

The present review includes, first of all, data on heavy unstable particles discussed at the Conference in Bagnères-de-Bigorre (June 1953) and at the Padua Conference (April 1954). These data have been supplemented by the results of the most important investigations carried out later. The discussion of the principal works has been brought up to April 1955.

In accordance with established terminology, the following phenomenological designations of particles and decays are used in the review: a \(V\)-particle is a neutral (\(V^0\)) or charged (\(V^\pm\)) particle which decays in flight in a Wilson chamber or in an emulsion. Examples of decays of \(V\)-particles (\(V\)-decays) are given in Figs. 18, 33, 36, 60, 61, and others. An \(S\)-particle is a charged particle coming to rest in a plate located in a Wilson chamber or in an emulsion. Examples of decays of \(S\)-particles (\(S\)-decays) are given in Figs. 19 and 46. Depending on their rest mass, charged and neutral heavy unstable particles are divided into hyperons (particles with a mass greater than the mass of the neutron) and \(K\)-particles (particles with a mass intermediate between the masses of the π-meson and the neutron). Further details concerning the classification and designations are given in the text.

The review consists of four parts. In the first part, the existing experimental methods for observing heavy unstable particles and the methods of analyzing data are considered in general terms (Chapters I and II). The second part of the review is devoted to charged and neutral

ny hyperons (Chapters III and IV), the third to \(K\)-particles (Chapters V and VI); in the last part (Chapter VII) data are considered on the nuclear interaction of heavy unstable particles and on the conditions of their production in high-energy nuclear interactions.

I. EXPERIMENTAL METHODS

I.1. Photographic Emulsion Chamber

The appearance in 1948 of electron-sensitive emulsions was of decisive importance for the application of the photographic method to the study of heavy unstable particles. In emulsions of the old type it was possible to investigate only the decay of \(\pi\)-mesons. The new emulsions made it possible to begin the study of decays in which relativistic secondary particles are produced (\(\mu \to e\)-decay, decay of \(K\)-mesons).

After 1948 the most important improvement in the emulsion method of observing heavy unstable particles, and in general rare phenomena in cosmic radiation, was the photographic emulsion chamber. It is a block consisting of a large number of emulsions without backing, stacked one upon another. Such a chamber, like ordinary single-layer emulsions, is exposed in the stratosphere by means of pilot balloons and is lowered by parachute. After detection the chamber is dismantled, each emulsion layer is processed as an ordinary emulsion layer and examined under a microscope. In this way a trajectory emerging from a given layer can be followed in the next layer, and so on, from layer to layer. The photographic emulsion chamber method made large blocks of emulsion available for examination and thereby made it possible to trace particle trajectories over distances of centimeters. Such an improvement in observation methods had several important consequences. Whereas previously, in single photographic emulsions, it was generally possible to observe only the end of the range of a heavy unstable particle, and the fast secondary particles arising in its decay almost always left the emulsion without being stopped in it, in an emulsion chamber it is often possible to observe the star in which the heavy unstable particle arose, the entire path of this particle in the emulsion up to complete stopping, and the secondary particles arising in its decay. The increase in the length of the tracks examined greatly increased the statistical accuracy of determining the mass of heavy particles stopping in the emulsion by the known range–scattering or range–grain-density methods. In those cases where the energies of the secondary particles arising in the decay are not too large, they also stop in the emulsion chamber, which greatly facilitates their identification. Thus, for example, \(\pi\)-mesons and the sign of their charge can be identified by \(\pi \to \mu \to e\)-decay or by characteristic \(\sigma\)-stars, \(\mu\)-mesons by \(\mu \to e\)-decay, etc. The sign-

measurement of the range of known particles makes it possible to determine their energy with great accuracy, limited, in the case of long tracks, by the accuracy with which the range–energy relation is known.

The possibilities of the new method are evident from two photographs of $\tau$-decay, shown in Figs. 1 and 2. In one of them (Fig. 1) are shown

Fig. 1. First decay of a $\tau$-meson in electron-sensitive emulsion (1949). $K$ — meson track; $\pi$, $a$, $b$ — tracks of three secondary particles.$^{1}$

the first decay of a $\tau$-meson in photoemulsion, observed by Brown, Camerini, Fowler, et al.$^{1}$ in 1949; the second photograph (Fig. 2) represents a typical picture of the decay of a $\tau$-meson observed in emulsion-

in a cloud chamber (Debenelletti, Garelli, et al.\(^2\) in 1954). The length of the track \(K\), belonging to the \(\tau\)-meson, is slightly more than \(3\ \mathrm{mm}\) in the first photograph, and the mass of the \(\tau\)-meson, measured from the grain density and range, is \(1080 \pm 160\ m_e\). Of the three \(\pi\)-mesons produced in the \(\tau\)-decay, both positively charged mesons leave the emulsion, leaving in it short tracks equal to \(2\ \mathrm{mm}\) and \(0.12\ \mathrm{mm}\), while the third, negatively charged \(\pi\)-meson, is captured by a nucleus of the emulsion at the end of its range and forms a star. The second photograph (Fig. 2), obtained with the aid of an emulsion chamber consisting of 40 layers of emulsion, gives

Fig. 2. Decay of a \(\tau\)-meson in an emulsion chamber (1954). Two secondary \(\pi\)-mesons undergo \(\pi \to \mu \to e\)-decay; the third forms a \(\sigma\)-star\(^2\).

an incomparably more complete picture of the production and decay of the \(\tau\)-meson and of the behavior of the secondary particles. In the figure one can see a star of the type \(21 + 7p\) \(^*)\), in which the \(\tau\)-meson was born. Its range in the emulsion chamber is \(17\ \mathrm{mm}\). Two secondary particles produced in the decay of the \(\tau\)-meson come to rest in the emulsion and, after stopping, give the characteristic \(\pi \to \mu \to e\)-decay, which makes it possible to identify them with certainty as positive \(\pi^+\)-mesons. The third particle, before coming to rest in the emulsion, forms a two-pronged \(\sigma\)-star, character-

\(^*)\) Notation of the Bristol group: 21 is the number of strongly ionizing particles (“black” and “gray” tracks), 7 is the number of shower particles; the star was produced by a proton \(p\).

needed for capture by the nucleus of a negatively charged $\pi^-$-meson. Knowing that the secondary particles are $\pi$-mesons and measuring their range, one can determine with great accuracy their kinetic energy $Q$, and consequently also the mass of the meson, equal to three pion masses plus the mass corresponding to the energy $Q$.

The advantages of the emulsion-chamber method that have been considered have led to the fact that at present investigations of heavy unstable particles with single emulsions are almost no longer carried out. Since prolonged exposure of emulsion chambers in the stratosphere and their recovery after descent is a technically difficult problem, in recent years several laboratories have combined their efforts and carried out joint expeditions in Italy (Sardinia) to raise emulsion chambers into the stratosphere. The first such expedition was carried out in May–July 1952^3, the second in June–August 1953^4. Some details of the technique of raising the emulsions are given below (see Section I, 2). The photoemulsion chambers used during the second Sardinian expedition consisted of 40 layers of Ilford G5 emulsion with a layer thickness of $600\,\mu$ and an area of $15 \times 10$ and $15 \times 15\ \mathrm{cm}^2$. The total volume of emulsion in such chambers was equal to 0.36 or 0.54 liters. Between the emulsion layers a layer of thin cigarette paper of thickness $15\ \mathrm{mg}/\mathrm{cm}^2$ was inserted. To facilitate the tracing of particle trajectories from one layer to another, the relative position of the layers was fixed by means of a narrow beam of X-rays^5. A similar method of fixing the relative position of emulsion layers had already been used by W. W. Alpers in the first emulsion chambers made by him^6. Large emulsion chambers were made by the Bombay group of physicists. Their first chambers^7,8 had 24 emulsion layers, whereas the two most recent chambers contained 125 and 200 layers of thickness $600\,\mu$^9. The thickness of these chambers (7.5 and 12 cm of emulsion) was close to the linear dimensions of the emulsion surface ($15 \times 15\ \mathrm{cm}^2$). The volume of emulsion in these chambers was equal to 1.7 and 2.7 liters; the mean range of particles in them is 3.75 and 4.6 cm, instead of 1.15 cm in 24-layer chambers, or 1.8 cm in the chambers of the Sardinian expedition. As an illustration of the capabilities of these chambers, we note that Daniel and Pal^10 traced a $\tau$-meson emitted from a star through 90 emulsion layers; its range in this case was 8.7 cm. In 1954, in the Bristol laboratory, chambers were made consisting of 80–90 emulsion layers^11. In the same laboratory a photoemulsion chamber is being made^12 whose volume is $36 \times 26 \times 15\ \mathrm{cm}^3 = 14$ liters, which is 5 times greater than the volume of the large chamber of the Bombay physicists^9. This chamber contains 250 emulsion layers each $0.6\ \mathrm{mm}$ thick and weighs more than 50 kg. It is proposed to raise it into the stratosphere with the aid of a polyethylene cylindrical balloon 60 m long and 15 m in diameter, observation of which will be carried out by a radar installation.

The manufacture and processing of a nuclear-emulsion chamber and, in particular, the error-free tracing of a particle trajectory from layer to layer are associated with great difficulties, which increase very sharply as the number of layers increases*). Even carefully and tightly packed emulsion layers, when exposed, have a gap sometimes reaching up to 0.1 mm. Therefore the points where a track leaves one layer and enters the adjacent layer do not coincide, but are separated by an unknown distance, which is the greater the less steeply the track runs (i.e., the smaller the angle it makes with the plane of the emulsion). In addition, the distortion arising during processing of the emulsion makes it impossible to superpose simultaneously the entrance and exit points for all tracks. The Bombay group points out⁷ that tracks of relativistic particles in strongly irradiated emulsion can be traced through many layers if the entrance and exit points lie along the line of the track at a distance not exceeding 10–15 microns. In the first emulsion chambers of 24 layers it was possible to achieve relative adjustment of neighboring plates, when viewing them under a microscope, with an accuracy no better than 50 μ. This accuracy was sufficient only for error-free tracing of particles with ionization exceeding the minimum. It should be noted that, instead of fixing the relative position of the layers with a narrow beam of X-rays, as was done in the chambers of the Sardinian expedition, the Bombay group made use of the tracks of primary multiply charged particles available in emulsions exposed in the stratosphere. Chambers with 125 and 200 layers⁹ required a considerable improvement of the methods of relative adjustment of the emulsions and of trajectory tracing. Instead of a thin paper spacer, in these chambers a mesh of nylon threads 18 μ thick, spaced 1 cm apart, was placed between the emulsion layers. Before installation the threads were impregnated in a weak solution of α-active polonium (30 μcuries per 15 liters of water). The blackening from the α-particles \(P_{\alpha}\) emitted by the threads (range ∼25 μ) created a common coordinate grid on the two emulsion surfaces facing one another. The position of the lines of this grid could be determined with an accuracy up to 5 microns. The relative position of two adjacent emulsion layers on the microscope stage could be fixed, owing to the presence of the grid, with an accuracy up to 20 μ. This accuracy, as indicated above, is sufficient for tracing trajectories with minimum ionization.

I.2. Exposure of photoemulsions

The scheme of the lifting devices used in the second Sardinian expedition of 1953⁴ is shown in Fig. 3. The total weight of the lifting device (without the balloon) reached 35 kg, of which the share

*) See the review by A. A. Varfolomeev, UFN, vol. LVII (1955).

containers with photoemulsion chambers had a mass of about 10 kg. The expanding-type balloon, filled with hydrogen, was provided with a valve that released excess gas if the apparatus reached too great a height and there was a danger of rupture of the greatly expanded balloon. When altitude was lost, caused by leakage or diffusion of hydrogen from the balloons, a pressure-sensitive ballast device was actuated, ejecting sand. Radiosondes located below the ballast relays transmitted pressure signals during the flight. The altitude data thus obtained were supplemented by the results of ground observations with aerological theodolites and a telescope. A time relay located above the parachute, at the end of the flight, switched on the heating of a nichrome wire, which burned through the nylon cord fastening the parachute to the balloon. The pilot-balloon ascents were made from an airfield at the southern end of the island. Owing to its small size and the favorable direction of the winds, in most cases the emulsions fell into the sea and were kept on its surface by a float. In this way the containers with the photoemulsion were in the water at a relatively constant temperature, which is an extremely important factor in the whole irradiation technique: prolonged exposure of the emulsions on land under the sun would have led to their spoilage. On the float there was a transmitter whose signals were direction-finded by a ground station. After the direction of the search had been established, the float was located with the aid of a seaplane and a small vessel, connected with it by radio, which put out to sea in advance so as to arrive in the fall area in good time. Packets of slowly dissolving phosphorescent dye were attached to the float, making it possible to find the float at night. The duration of the balloon ascent to an altitude of 25–30 km was 1.5–2 hours; at this

Fig. 3. Diagram of lifting devices for exposure of photoemulsion chambers in the stratosphere.^4^

Labels in the figure:
safety valve; time relay; parachute; ballast; radiosonde; emulsions; emulsions; radio beacon; floats; container for emulsions; emulsions; packing.

at altitude the balloons remained for 5–9 hours. In all, 25 ascents were carried out, of which about half were completely successful. The exposed emulsion chambers were distributed among the laboratories that had collaborated in organizing the expedition. A large part of the data published in 1953–1955 was obtained in the investigation of the emulsion chambers of the Sardinian expedition of 1953.

I.3. Methods of identifying particles in emulsion

I.3.1. Characterization of existing methods

Here we shall briefly consider the modern methods for identifying particles from their tracks in photoemulsion. Identification of a particle consists in determining its charge \(Z\), mass \(m\), and kinetic energy \(E\). In principle, to determine these three quantities one must make in the photoemulsion three independent measurements of certain physical quantities that depend on \(Z\), \(m\), and \(E\). Since the ionization produced by a particle is proportional to the square of its charge, the tracks of singly charged particles in emulsion are readily distinguishable in appearance from the tracks of multiply charged particles; and for identifying singly charged particles in emulsion it is sufficient to measure not three quantities, but any pair of quantities depending on \(m\) and \(E\). Such quantities are, for example, the residual range of a particle stopping in the emulsion (\(R\)), the density of grains in the particle track (\(g\)), the mean length of the gaps between grains (\(\bar{l}\)) or their number \(G\), and also the mean angle of multiple scattering undergone by the particle in the emulsion (\(\bar{\alpha}\)).

For particles of low energy that stop in the emulsion, the parameter that can be measured very accurately is the residual range. As the second parameter one may take any of the quantities indicated above, or quantities connected with them by known relations.

Measurements of the number of developed grains, the lengths of the gaps, and especially of the mean scattering angle are extremely laborious tasks. Moreover, the accuracy of these measurements may be affected by subjective errors introduced by the observer. Therefore, in recent times several methods have been proposed for measuring ionization by photometric methods \(^{13-15}\). These methods have been used successfully to measure the masses of heavy unstable particles stopping in emulsion, when the second measured parameter is the residual range \(^{15}\).

For particles with high kinetic energy that do not stop in the emulsion, measurement of the residual range \(R\) is impossible. The mass of such particles is determined from the grain density and the mean scattering angle. Below are listed the existing methods of identifying particles in emulsion and the regions of their application.

Name of method	Notation	Field of application
Grain density—residual range . . . . . . . . . . .	\((g, R)\)	Strongly ionizing particles stopping in the emulsion
Mean gap length—residual range . . . . . .	\((\bar l, R)\)	Strongly ionizing particles stopping in the emulsion
Scattering—residual range	\((\bar \alpha, R)\)	Strongly ionizing particles stopping in the emulsion
Photoelectric measurement of ionization—residual range . . . . . . .	\((P, R)\)	Strongly ionizing particles stopping in the emulsion
Mean gap length—scattering . . . . . . .	\((\bar l, \bar \alpha)\)	Strongly ionizing particles that have not reached the end of their range in the emulsion
Grain density—scattering . .	\((g, \bar \alpha)\)	High-energy particles, for example shower particles, primary particles, stars produced, high-energy electrons, high-energy secondary particles arising in the decay of unstable particles.

Most of the methods for determining the mass of slow particles stopping in an emulsion require measurement of the grain density, gap length, or photoelectric measurement of the blackening density in the track. These quantities depend on the conditions of development, which is their substantial drawback. In contrast to these methods, the mass-measurement method \((\bar \alpha, R)\) does not depend on the conditions of development, which affect the results of measuring the scattering angle only to a very small degree.

1.3.2. Energy–range relation. The range of protons in emulsion for energies from 1 to 40 MeV was studied experimentally by Bradt et al.\(^{16}\), Lattes et al.\(^{17}\), Rotblat\(^{18}\), and other investigators. As a result of these measurements, between the proton energy (in MeV) and its range in emulsion (in \(\mu\)) there was...

the following empirical relation has been established:

\[ E=aR^n, \tag{1} \]

where \(a\) and \(n\) are constants that vary slowly with energy.

Knowing the energy–range relation for protons, it is easy to obtain it for any particles with known mass and charge. Indeed, theory gives the following dependence of the ionization losses \(\frac{dE}{dx}\) on the charge \(Z\) and the particle velocity \(\beta=\frac{v}{c}\):

\[ \frac{dE}{dx}=\frac{Z^2}{\beta^2} f(\beta,Z). \]

Integrating this expression, we obtain the range–energy relation in the form

\[ R=\frac{\mu}{Z^2}F(\beta)=\frac{\mu}{Z^2}\varphi\left(\frac{E}{\mu}\right) \]

(\(\mu\) is the mass of the particle expressed in proton masses), from which it follows that the quantity \(\frac{RZ^2}{\mu}\) depends only on the particle velocity. Substituting into the energy–range relation for the proton (1), instead of \(R\) the quantity \(\frac{RZ^2}{\mu}\), and instead of \(E\) the quantity \(\frac{E}{\mu}\), we obtain the energy–range relation for a particle with mass \(\mu\) and charge \(Z\):

\[ E=a\mu^{1-n}Z^{2n}R^n \]

or, for a singly charged particle:

\[ E=a\mu^{1-n}R^n . \tag{2} \]

Having treated their data by the method of least squares, Bradner et al.\(^{16}\) obtained the following values of the coefficients \(a\) and \(n\) for Ilford C2 emulsion in the proton energy interval \(17\text{–}33\) MeV:

\[ a=0.251, \]

\[ n=0.581. \]

In order to pass to the electron-sensitive Ilford G5 emulsion used in emulsion chambers, the range values for a given energy should be reduced by \(1\%\).\(^{19}\) Processing the most reliable of the existing measurements of proton ranges, Fay, Gottstein, and Hain\(^{19}\) obtained the following values of the coefficients \(a\) and \(n\) (\(R>700\,\mu\)) in Ilford G5 emulsion:

\[ a=(0.281\pm0.005), \]

\[ n=(0.568\pm0.003). \tag{3} \]

This relation is in agreement with the results of the theoretical-

...of Wigner’s calculations\({}^{20}\), which can be expressed by the following formula:

\[ E = 0.2806 \cdot R^{0.568}. \tag{4} \]

The data presented in (3) give an idea of the accuracy with which the range–energy relation is known for protons with energies up to \(40\) MeV (range \(6.2\) mm). However, with an accuracy determined by the coefficients (3), formula (4) can also be used for considerably larger ranges that fit within existing emulsion chambers. The most distant point in the range–energy relation for protons\({}^{21}\) is \(E = 342.5\) MeV, for which \(R = 92.68 \pm 0.25\) g/cm\(^3\) was obtained for an emulsion with density \(3.81 \pm 0.01\) g/cm\(^2\). Calculation of the energy for this range by formula (4) gives \(E = 320\) MeV, differing from the measured value by \(6\%\)*).

The accuracy of range measurements in emulsions is very high: for large ranges it exceeds the accuracy with which the range–energy relation is known. Thus, for example, ranges for tracks longer than \(0.5\) mm, inclined to the plane of the emulsion by no more than \(15^\circ\), can be measured with an accuracy of \(\sim 1\%\) or better. The relative error caused by straggling may be neglected for high energies: for example, the error in measuring the range caused by this reason changes from \(10\) to \(2\%\) when the proton energy changes from \(1\) to \(5\) MeV.

I.3.3. Identification of particles by grain density and range. From the range–energy relation (2), which has the form

\[ \frac{E}{\mu} = a \left( \frac{R}{\mu} \right)^n, \]

it follows that knowledge of the range is insufficient for determining the mass and energy of a particle. It is necessary to measure one more quantity, dependent on the mass and energy or on the velocity. Such a quantity is, for example, the specific energy loss, an expression for which can be obtained by differentiating the range–energy relation:

\[ \frac{dE}{dR} = an\mu^{1-n} R^{n-1} = an \left( \frac{R}{\mu} \right)^{n-1}. \tag{5} \]

The quantity \(\left( \dfrac{dE}{dR} \right)\) is determined from the grain density \(g\), associated with it and easily measurable, which is the number of grains falling on a section of track \(100\,\mu\) long. The value of the particle mass is obtained directly from (5):

\[ \mu = \left( \frac{dE}{dx} \right)^{\frac{1}{1-n}} (an)^{\frac{1}{n-1}} R. \tag{6} \]

*) More accurate data on the range–energy relation for protons in Ilford G5 emulsion are given in the Recommendations on Standardization in Photoemulsions\({}^{22}\).

From this expression it follows that if, in certain sections of the tracks of two particles, the grain densities are identical, then the particle masses are proportional to the residual ranges.

Knowing the mass of a particle and its range, one can also determine its kinetic energy from the range–energy relation.

The magnitude of the specific energy losses is determined by the grain density in the track, which is uniquely related to it. Fig. 4 gives the experimentally established[^23] dependence between the grain density \(g\) and the specific energy loss \(dE/dx\) for Ilford G5 emulsion. This graph begins with the minimum energy losses \(\left(dE/dx\right)_{\min}\) experienced in the emulsion by a relativistic particle with a velocity close to the speed of light. The minimum energy losses \(\left(dE/dx\right)_{\min}\) correspond to the minimum grain density \(g_{\min}\). It is seen from the graph that, in an electron-sensitive emulsion, the linear dependence between \(g\) and \(dE/dx\) is preserved starting from \(g_{\min}\) up to values of \(g\) equal to \((3 \div 4)g_{\min}\).

Fig. 4. Dependence of the grain density \(g\) on the energy losses \(\dfrac{dE}{dx}\) for Ilford G5 emulsion.[^23]

1.3.4. Methods for counting the number of grains. Counting the number of grains in a track is a simple problem if the grains are discrete and the fog is not too large. The second condition sets, for ordinary emulsions, a lower limit on the measurable quantity \(g \sim 20\) grains per 100 microns of emulsion, which corresponds to an average distance between grains of 5 microns.

As the ionizing power of the particle increases, the average distance between grains decreases, individual grains cease to be resolvable and merge into elongated clusters (blobs). So long as the number of such clusters is small compared with the number of grains \((g < 1.5—2g_{\min})\), the method of counting grains remains applicable, provided that the number of grains \(n\) in each cluster can be estimated. Under these conditions such an estimate can be made by a more or less arbitrary method, if the length of the cluster \(l\) has been measured and the mean grain diameter after development is known \((0.3—0.4\,\mu)\). Thus, for example, Fowler and Perkins[^24] assumed that \(n = 2.4l\). More often in these

under these conditions, however, another counting method is used, when each clump is counted as one grain (the “clump-counting” method). This method has the following advantages over direct grain counting:

1) faster counting,
2) reduction of subjective errors associated with the observer, and
3) for one and the same number of readings, the clump-counting method gives somewhat better statistical accuracy than the grain-counting method.

On a given segment of the particle track the number of clumps \(g_{\mathrm{cl}}\) is somewhat less than the number of grains \(g_{\mathrm{grains}}\). Between these quantities there exists the following, almost obvious, relation^[5] \(g_{\mathrm{cl}} = g_{\mathrm{grains}} \times e^{-\alpha g_{\mathrm{grains}}}\), from which it is seen that for grains of diameter \(\alpha = 0.3\) mm, with \(g_{\mathrm{grains}} \approx 40\) grains per 100 microns, grain counting and clump counting give numbers differing by \(\sim 12\%\).

1.3.5. Method of counting the number or length of gaps.

As a particle approaches the end of its range, its ionizing ability increases and the number of clumps increases. The track of a strongly ionizing particle in a sensitive emulsion consists of a sequence of such clumps separated by gaps. Under these conditions grain counting is impossible, and determining the number of grains on the basis of clump counting is also very difficult, since for large clumps the proportionality between \(n\) and \(l\) is violated. This leads to the fact that the method of direct counting of grains or clumps proves applicable only to “thin” tracks of weakly ionizing particles. Thus, for example, in identifying secondary particles arising in the decay of \(K\)-particles, which often possess high energy, the method of counting individual grains is, as a rule, used. If, however, a heavy particle stops in the emulsion, then its ionizing ability is large, and in these cases other methods of measuring ionizing ability are used, such as, for example, the method of counting the number and length of the gaps between clumps of grains, photoelectric methods of measuring ionization, or measurement of \(\dfrac{dE}{dx}\) from the number of \(\delta\)-particles visible in the track *).

Figure 5 shows a characteristic segment, visible in the field of view of a microscope, of the track of a particle consisting of grains and clumps of grains. The method of counting gaps is usually used for identifying particles that leave tracks of this kind. At present there exist several variants of this method^[26,27], in which either integral characteristics of the track are measured (the total number of gaps in the track, or the number of gaps whose length is greater than a specified value, or the total length of the gaps in the track), or

*) This last method has so far been little used; it is discussed in detail in work 28.

differential characteristics (the number of gaps per unit length in the track, or the length of gaps per unit length of track).

All variants of this method of mass measurement are based on the assumption that the ionizing power of a particle depends only on its velocity. Therefore, if the tracks of particles over some segment have identical differential characteristics, then the masses of these particles are proportional to their residual ranges, just as, for particles with identical grain density, the masses are proportional to the residual ranges.

Fig. 5. Appearance of the track of a strongly ionizing particle in an emulsion. The length of the gaps is equal to \(AB + CD + EF + \cdots\).

One variant of measuring mass by the integral method of counting gaps is used by a group of the Polytechnic School \(^{26,31}\). It requires measuring the total number of gaps in the track and is analogous to the Perkins method of measuring a particle’s mass by the total number of grains in the track. Experience shows that the relation between the total number of gaps \(G\) and the range for protons is described with sufficient accuracy by a relation analogous to the range–energy relation, namely

\[ G = aR^n, \]

where \(a\) and \(n\) are constants depending on the degree of development of the plate. Since the number of gaps per unit length

\[ \frac{dG}{dR} \]

depends only on the particle velocity, i.e.

\[ \frac{dG}{dR} = f\left(\frac{R}{\mu}\right), \]

it follows that for particles of another mass

\[ G = a\mu^{1-n}R^n, \]

where \(\mu\) is the particle mass in fractions of the proton mass. On a plot of \(\ln G,\ \ln R\) (see Fig. 6), this dependence for reference particles (for example, protons) and for the particle whose mass is being measured is represented by two parallel lines (the dashed lines show the limits of error—

Fig. 6. Determination of particle mass from the integral number of gaps. \(G\)—number of gaps in a track with residual range \(R\) \(^{26,31}\).

... in determining these lines). Intersecting these two straight lines with a line going at an angle of \(45^\circ\) to the coordinate axes (Perkins’ method), we obtain two points \((R_1, G_1)\) and \((R_\upsilon, G_\upsilon)\), for which

\[ \frac{R_0}{R_1}=\frac{G_0}{G_1}=\frac{t_0}{t}. \]

As an example of the resolving power of this method, we shall give the results of mass determinations for 40 protons with ranges from 4 to 10 mm and with an angle of inclination to the plane of the emulsion \(< \frac{10}{100}\). The distribution of masses shown in the histogram of Fig. 7 is characterized by a mean value of \(1840\,m_e\) and a root-mean-square deviation of \(\sim 200\,m_e\) 26, 31.

Fig. 7. Results of the mass measurement for 40 protons by the method “integral number of gaps—ranges” 26, 31.

Ritson 29 improved the method of counting gaps by making it automatic, in order to ensure speed and accuracy of observations. He attached a mechanical drive to the microscope stage, so that the track moved past the eyepiece crosshair with constant speed (100 μ in 4 minutes). The observer had two counters at his disposal, operated by a source of pulses. One counter worked continuously, the other only from a button, which was switched on for the whole time during which the crosshair passed through a gap. The ratio of the readings of the two counters directly gave the length of the gaps per unit length of track. Baroni and Castagnoli 29 used a variant of this method for counting the magnitude \(\bar l\).

1.3.6. Identification of particles by multiple scattering. Measurements of the mean angle of multiple Coulomb scattering experienced by a particle in an emulsion make it possible to determine the product \(p\beta\) of the particle momentum \(p\) by its velocity \(\beta\). Such measurements in emulsion usually consist in measuring the projection of the scattering angle onto the plane of the emulsion *). They can be carried out by several methods. In the angular method of measuring the scattering angle 23,32, the particle track is divided into equal parts (cells), usually of length \(t\), a multiple of 100 μ, and the angles between the tangents to sections of the track in neighboring cells are measured.

*) Mabboux-Stromberg developed another method of measuring scattering, in which the projection of the scattering angle onto a plane perpendicular to the plane of the emulsion is measured 30.

At present a second coordinate method for measuring scattering is used, proposed by Fowler \(^{23,33}\). It is also called the sagittal method. As in the angular method, the particle track is divided into equal cells of length \(t\) (Fig. 8), and the distance from the \(x\)-axis, determined by the direction of motion of the microscope stage, to the corresponding point of the track is measured.

Fig. 8. Coordinate method for measuring scattering.
\(t\) is the length of the cells into which the track is divided \(^{33}\).

The difference of two adjacent coordinates \(s_i = y_i - y_{i-1}\) determines the slope of the chord connecting the beginning and end of a cell. The second differences \(D_i = s_i - s_{i-1} = y_i - 2y_{i+1} + y_{i+2}\) are a measure of the angle between two adjacent chords. From the quantities \(D_1, D_2\), etc., the mean absolute value of the second difference is determined,

\[ \overline{D}=\frac{1}{n}\sum_i |D_i|, \]

which is related to the mean angle of deflection of the particle in the emulsion by the relation

\[ \overline{D}=\bar{\alpha}\cdot t. \]

The mean scattering angle of a singly charged particle is related as follows to the product of the momentum by the velocity \((p\beta)\) of the particle and to the cell length \(t\) into which the track is divided \(^{23,34}\):

\[ \alpha=\frac{K}{p\beta}\left(\frac{t}{100}\right)^{1/2}. \]

In this formula \(t\) is measured in microns, \(\alpha\) in degrees, \(p\beta\) in MeV, and \(K\) is a constant, slowly varying with the particle energy and lying in the range 22–28. The value of \(K\), calculated on the basis of Molière’s theory of scattering, is in agreement with experimental determinations of this parameter made for electrons and fast protons of known energy.

The quantity \(p\beta\) directly determines the kinetic energy of the particle in the regions of strongly nonrelativistic and strongly relativistic energies \(\left(p\beta=\frac{2E}{c}\right.\) in the first case and \(p\beta=\frac{E}{c}\) in the second case). Having determined, with the aid of ionization measurements, the quantity \(\beta\), or having measured the particle range and knowing \(p\beta\) from the scattering measurement, one can determine the mass and energy of the particle under investigation.

The method of measuring the mass and energy of a particle from scattering and residual range, which is of greater importance for elucidating the nature of heavy unstable particles stopping in the emulsion, is associated with difficulties caused by the rapid increase of

scattering as the particle approaches the end of its range. Until quite recently this made it necessary to divide the track into several sections and determine the mean scattering angle for each section (each being divided in turn into cells \(t\)). Dividing the track into sections reduced the statistical accuracy of measuring \(\bar{\alpha}\), while obtaining the mean value of the mass from the values \((a_i, R_i)\) in each section required the use of a complicated method of balancing the counts \({}^{35}\).

In 1953, simultaneously in several laboratories \({}^{36}\), an improved method was developed for determining particle masses from measurements of scattering and range; it was called the “constant-sagitta method” and was based on the following considerations. As the particle approaches the end of its range in the emulsion, its scattering increases. In order to keep the scattering per cell constant along the entire track, it is evidently necessary to divide the track into cells whose length increases monotonically with distance from the end of the range. The law according to which the cell length must vary in order that the mean scattering within a cell remain constant along the whole track is easy to find. If \(\bar{\alpha}\) is the mean scattering angle for a cell of length \(100\,\mu\), then for a cell of any length \(t\) (in \(100\,\mu\)) the mean scattering angle will be \(\bar{\alpha}_t=\bar{\alpha}t^{1/2}\), and since the mean value of the second difference \(\bar{D}=\bar{\alpha}_t\cdot t\), then \(\bar{D}=\bar{\alpha}\cdot t^{3/2}\). In the nonrelativistic case

\[ \bar{\alpha}=\frac{\bar{D}}{t^{3/2}}=\frac{K}{p\beta}=\frac{Kc}{2E}. \]

Substituting

\[ E=\frac{Kct^{3/2}}{2\bar{D}} \]

into the range–energy relation \(E=aM^{1-n}R^n\), we obtain:

\[ \frac{Kt^{3/2}}{2\bar{D}}=bR^nM^{1-n}, \tag{7} \]

where \(b\) is a constant.

In order that the second difference remain constant along the entire track, it is necessary to keep the quantity \(Kt^{3/2}R^{-n}\) constant. The condition \(Kt^{3/2}R^{-n}=\mathrm{const}\) determines the “scheme of division” of the track into cells of variable length. Within this scheme one may use various scales of division, determining the specific cell lengths. The optimum cell length is obtained as a compromise between the need to have a large number of cells in order to obtain statistically reliable results and the need to obtain a substantial ratio of the true scattering to the scattering caused by extraneous factors (the “signal-to-noise” ratio). Numerical tables of division schemes for protons, \(\pi\)- and \(\tau\)-mesons were calculated by Faem et al. \({}^{19}\). Having determined, by the constant-sagitta method, the mean value of the second difference for tracks of standard particles (for example, protons or \(\pi\)-mesons), one can, by measuring \(\bar{D}\) for the trajectory under study, directly obtain the mass of the particle.

Indeed, from (7) it follows that \(\overline D_0=C_0M_0^{n-1}\) and \(\overline D=C_0M^{n-1}\), whence

\[ \frac{M}{M_0}=\left(\frac{\overline D_0}{\overline D}\right)^{\frac{1}{1-n}} . \tag{8} \]

1.3.7. Accuracy of the measurement of \(p\beta\) by scattering. The accuracy of measuring the quantity \(p\beta\) by the scattering method, provided systematic errors are excluded, is limited by the level of “noise” for the second-difference quantity \(\overline D\). These noises are caused by the following two main reasons:

1. The developed grains are distributed asymmetrically along the particle trajectory; therefore the center of the developed grain does not coincide with the trajectory.

2. Random irregularities in the motion of the movable stage of the microscope.

The average error caused by the first reason, for relativistic particles in Ilford G5 emulsion, is \(\sim 0.07\,\mu\). The magnitude of the second error is an increasing function of the cell length, owing to which the overall noise level can be expressed by the relation \(\overline D_{NL}=kt^n\). In Cooke and Leitz microscopes specially intended for examining emulsions, \(n\sim 0.5\), and the average error caused by irregularities of the stage is \(\sim 0.03\,\mu\) for \(t=50\,\mu\) and reaches \(0.1\,\mu\) for \(t>500\,\mu\). Thus, at present \(\overline D_{NL}\sim |0.05-0.10|\,\mu\), whence for the upper limit of the measurable momentum \(|\overline D\sim \overline D_{NL}|\) we obtain:

\[ (p\beta)_{\max}\approx t^{2/3}\,M\text{eV}/c, \]

where \(t\) is expressed in \(\mu\). It follows from this formula, for example, that for a cell length of \(100\,\mu\) the maximum measurable value is \(p\beta\sim 10^9\,\text{eV}/c\).

The use of special “noiseless” microscopes, similar to the “Koriсa” microscope developed with the participation of Kozhies, and the application of special measurement methods that exclude noise make it possible to increase this limit considerably; for long tracks it may exceed \(10^{10}\,\text{eV}/c\) [36].

1.3.8. Ionization losses of relativistic particles in emulsion. It was indicated above that the only method for identifying a fast particle that is not stopped in the emulsion is the measurement of the mean multiple-scattering angle, which determines the value of \(p\beta\), and of the grain density, which determines the particle velocity \(v\). For resolving particles with different masses, it is therefore extremely important to determine experimentally, with the greatest possible accuracy, the dependence of the grain density on the quantity \(p\beta\), or on the energy or velocity of the fast particle. Such measurements have been carried out in recent years by many researchers.

mi \(^{27,37—39}\), who used the tracks of fast particles in photographic emulsions exposed in the stratosphere. From the magnitude of the scattering of these particles the value \(p\beta\) was determined, while counting the number of grains or clusters gave the value \(g\). Figures 9 and 10 give the results

[Figure 9: vertical axis: “Cluster density (number of clusters per 50 \(\mu\))”; horizontal axis: “\(p\beta\) in MeV/c”; in-figure labels: \(\pi\), \(p\), \(D\); “electron pairs 4500 clusters”; plotted points and dashed curves.]

Fig. 9. Dependence of the cluster density \(g\) on \(p\beta\) for relativistic particles in emulsion \(^{37}\).

of Shapiro and Stiller \(^{37}\), who measured long tracks that make possible an accurate determination of the value \(p\beta\). All these tracks were found in one Ilford G5 plate, exposed for 8 hours at an atmospheric depth of \(11\ \text{g}/\text{cm}^2\). In this work

[Figure 10: vertical axis: “Number of clusters per 100 \(\mu\)”; horizontal axis: \(\gamma = E/\mu\); legend: “Experiment,” “Theory”; plotted points and theoretical curve.]

Fig. 10. Dependence of the cluster density on the velocity for relativistic particles in emulsion
\[ \gamma = \frac{E}{mc^2}=\left(\frac{1}{\sqrt{1-\beta^2}}-1\right)^{37}. \]

43 tracks of secondary particles from high-energy nuclear disintegrations were measured, as well as eleven tracks of primary particles that had caused these disintegrations, and five tracks of high-energy electron–positron pairs. Figure 9 gives the dependence of the grain density on the value \(p\beta\), and Fig. 10, on the value
\[ \gamma=\frac{E}{mc^2}, \]
which is the kinetic energy of the particle expressed

in units of the rest energy \(mc^2\). In constructing the last curve, in order to increase the statistical accuracy the \(\gamma\)-axis was divided into intervals containing approximately the same number of particles. From consideration of these curves it follows that the grain density for all particles is indeed described, within the accuracy of the measurements, by a universal curve depending only on the parameter \(\gamma\), i.e., on the particle velocity. As \(\gamma\) increases, the grain density first decreases, approximately inversely proportional to \(\beta^2\), reaches a minimum \(g_{\min}\) at \(\beta \sim 0.96\), and then, in the interval \(10 < \gamma < 100\), slowly increases, reaching at \(\gamma \sim 100\) a constant value \(g_{\mathrm{pl}}\), which is maintained up to \(\gamma \sim 3000\). The magnitude of the saturation can be characterized by the ratio \(g_{\mathrm{pl}}/g_{\min}\). According to Shapiro and Stiller[^37],

\[ a = \frac{g_{\mathrm{pl}}}{g_{\min}} - 1 = 14 \pm 3\%. \]

According to Voyvodich and Pickup[^38], the quantity \(a\) is close to \(10\%\). At present, in determining the ionizing power of relativistic particles from the grain density, it is customary to specify the quantity \(g^*\), which is the ratio of the measured grain density to the grain density of relativistic particles “on the plateau” (“normalized” grain density).

The observed saturation of ionization losses at \(\gamma > 100\) is in agreement with the predictions of Fermi’s theory, which takes into account the influence of the polarization of the medium in which the particle moves, and with subsequent refinements of this theory[^23].

1.4. Wilson chambers and spectrometers.

1.4.1. Basic types of apparatus.

In this section the principal experimental apparatuses are considered in which a Wilson chamber is used to study the properties of heavy unstable particles. All these apparatuses are controlled by Geiger—Müller counters and may be divided into the following types:

1. Wilson chambers without plates, or with one or two plates of dense material, placed in a magnetic field (magnetic Wilson chambers).

2. Wilson chambers without a magnetic field, but with a large number of plates, making it possible to identify particles by ionization, by range in the plates, and also by multiple Coulomb and nuclear scattering in them (multiplate Wilson chambers).

3. Apparatuses permitting both magnetic analysis and analysis by means of a large number of plates.

Below we shall briefly consider the arrangements, parameters, and distinguishing features of the principal apparatuses, the regions of their application, and typical photographs obtained with their aid.

An analysis of the operation of Wilson magnetic chambers used for the study of heavy unstable particles was given by Blackett. We reproduce, from his Varennes lecture,⁴⁰ a table of the basic parameters of these installations. (See p. 385.) Diagrams of the arrangement of the chamber, magnet, absorbers, and controlling counters in several typical installations are given in Figs. 11–17.

1.4.2. Systems for selecting heavy unstable particles. The chamber control in almost all operating installations is effected by a system of counters, separated by lead absorbers, which selects penetrating showers of large energy, as a rule greater than 10 Bev. Thus, the existing installations record heavy unstable particles forming part of penetrating showers. In almost all installations, coincidences of pulses in G.–M. counters were used for shower registration. Thus, for example, to trigger the chamber in the installation of the Manchester group at Pic-du-Midi⁴¹ (Fig. 11), no less than a sixfold coincidence of discharges in three rows of counters \(A\), \(B\), and \(C\) was required: in row \(A\) no fewer than one counter had to operate, in row \(B\)—no fewer than three, and in row \(C\)—no fewer than two counters (coincidences \(A \geq 1\), \(B \geq 3\), \(C \geq 2\)). An estimate shows that, with such control, no less than 80% of the chamber triggers at Pic-du-Midi were caused by nuclear interactions in lead having an average energy of 20–40 Bev. The installation of the Pasadena group⁴²,⁴³ was controlled by coincidences (Fig. 12) \(A \geq n\), \(B \geq m\), where in different series of experiments the pairs of numbers \((n, m)\) took the values \((1, 3)\) or \((2, 3)\). The methods for selecting the controlling pulses in the remaining installations are indicated in the corresponding figures.

Fig. 11. Diagram of the installation of the Manchester group at Pic-du-Midi⁴¹.

Fig. 12. Diagram of the installation of the Pasadena group⁴².

HEAVY UNSTABLE PARTICLES

The use of Geiger–Müller counters for selecting penetrating showers has the disadvantage that the passage of several particles through one counter is indistinguishable from the passage of a single particle. Therefore some investigators introduced proportional counters into the system of controlling counters (the Manchester group at Jungfraujoch[^44], the Princeton group at Echo Lake[^45]—Figs. 13 and 14). In such systems, in order to produce the pulse controlling the expansion of the chamber, it is necessary that the pulse in the proportional

Fig. 13. Diagram of the apparatus of the Manchester group at Jungfraujoch. Slots in the magnet poles for illuminating the chamber are visible. Two proportional counters are connected in parallel[^44].

Visible labels in Fig. 13: PC.

Fig. 14. Diagram of the apparatus of the Princeton group[^45].

Visible labels in Fig. 14: Magnet; 10 cm Pb; 6.3 cm Cu; upper chamber cover; 15 cm; 38 cm Cu; 43 cm; B; C; D; 1.27 cm Pb; 6 proportional counters.

counter exceed, by a specified number of times, the pulse of minimum ionization from a relativistic particle. It is evident that a system with proportional counters makes it possible to exercise more flexible control of the chamber, since the number of particles in the registered shower can be increased or decreased by changing the magnitude of the minimum registered pulse from the proportional counters.

At present it is clear that the selection of penetrating showers of high energy is not the only possible, or fundamentally the best, method for searching for heavy unstable particles. Such showers are produced mainly by protons and neutrons, whose spectrum falls very rapidly with increasing energy. Thus, for example, at an altitude of 3–4 km the number of protons and neutrons with energy greater than 10 Bev is approximately 50 times smaller than the number of nucleons with energy from 1 to 10 Bev. If it is assumed that such nucleons are approximately 20 times less effective in producing heavy unstable

particles than first-group nucleons (such an assumption is consistent with experiments in the cosmotron), we nevertheless find that nucleons with an energy of \(1—10\) Bev produce \(2.5\) times more heavy unstable particles than do heavier nucleons. Therefore a selection system registering \(K\)-mesons and hyperons from low-energy interactions would increase the yield of these particles. Here, however, a difficulty arises connected with the fact that such a selection system, implemented by ordinary methods, would also select such frequent phenomena as \(\delta\)-particles, associated with fast \(\mu\)-mesons, soft showers, etc. This would overload the Wilson chamber and would reduce to nothing all the advantages of the increased yield of heavy unstable particles. Therefore the solution of this problem must consist in the development of fundamentally new methods for selecting heavy unstable particles not connected with the registration of correlated particles. The first attempt in this direction was made by Salvini \(^{46—48}\), who placed a large scintillating crystal in a Wilson chamber. By selecting scintillation pulses exceeding a threshold value, it was possible to make the Wilson chamber sensitive to nuclear interactions of moderate energy. This technique, however, was not used for the selection of \(V\)-decays. Barker, Sard, and Sowerby \(^{49}\) controlled a Wilson chamber by means of a system of neutron counters, hoping thereby to increase the efficiency of registering nuclear interactions of small energy. This method did not lead to an increase in the yield of \(V\)-particles. Further attempts to develop new selection methods were associated with the observation of \(K\)-particles stopped in plates and will be considered in Chapter VI.

1.4.3. Yield of \(V\)-particles. As is seen from Table I, the volumes of the Wilson chambers used for the study of \(V\)-particles lie within the range from \(3.5\) to \(130\) l. At first glance it may seem that an increase in the dimensions of Wilson chambers should be accompanied by a proportional increase in the number of registered heavy unstable particles. Examination of Table I shows, however, that there is no direct proportionality between the dimensions of the chambers and the counting rate of \(V\)-particles. Let us compare, for example, the two installations of the Manchester group, located on Pic du Midi (2867 m) and at Jungfraujoch (3460 m) (see Table I and Figs. 11 and 13). The Wilson chamber on Pic du Midi is among the smallest: its volume (3.5 l) is 13 times smaller than the volume of the installation located at Jungfraujoch. In spite of this, it registers only twice fewer particles than the second installation, which is situated 600 m higher. In exactly the same way, the chamber of the Polytechnic School with a volume of 130 l registers approximately the same number of \(V\)-decays as the chamber of the Manchester group located in the same laboratory on Pic du Midi. The reason for such a discrepancy between the dimensions of the chambers and the number of observed \(V\)-particles lies in the system

Table 1

Data on Wilson magnetic chambers controlled by penetrating showers

Group, altitude	Chamber dimensions (cm)	Area of horizontal section (cm²)	Solid angle (steradian)	Chamber volume (liters)	Field (gauss) and power	Approximate number of \(V\)-particles per week of measurements	Recovery time	Maximum measurable impulse (Bev/c)
Pic-du-Midi (2867 m)	25 (diameter) × 7 (depth)	200	0.50	3.5	7590 (12 kW)	10	2½	10 for 10-cm tracks
Jungfrau-Joch (3460 m)	50 × 50 × 18	900	0.36	45	6000 (30 kW)	20	4	4 for 25-cm tracks
Indiana (sea level)	55 × 27 × 12.5	340	0.11	18	7000 (40 kW)	2	4	50
Princeton (3260 m)	40 × 40 × 15	600	0.38	24	5400 (30 kW)	20	2½
Polytechnic School (2867 m)	68 × 64 × 30	2040	0.40	130	2600 (250 kW)	12	6	15 for tracks \(\sim 50\) cm
Pasadena (1600 m)	33 × 40 × 12 (2 chambers) 60 × 80 × 20 50 × 50 × 15 (1 chamber)	400 1200 750	0.25 0.20 0.30	15 96 37	5000 (13 kW) 7200 4000	10 10	2	2–5 for long tracks
Berkeley (sea level)	50 × 40 × 12	480	0.20	24	8000 (15 kW)

selection for penetrating showers. Indeed, the photographing frequency \(\frac{1}{N_P}\) is determined by the sum of the mean waiting time for a penetrating shower \(\frac{1}{N_C}\) and the chamber recovery time \(T_R=\frac{1}{N_R}\):

\[ \frac{1}{N_P}=\frac{1}{N_C}+\frac{1}{N_R}. \]

It follows from this that, for a sufficiently large number of operations of the control system \(N_C\), the photographing rate is determined by the chamber recovery time \(T\). Since \(N_C\)

Fig. 15. Layout of the installation of the Polytechnic School \(^{50,51}\).

increases very rapidly with altitude (the intensity of penetrating showers selected by the counter system increases with altitude exponentially, with absorption length \(z\sim120\ \text{g}/\text{cm}^2\)), this leads to the fact that, with existing selection systems and with ordinary recovery times \(T_R\sim2—6\) minutes, as the installation is raised to greater heights saturation in the photographing frequency \(N_P\) is quickly reached. Thus, for example, an elementary calculation given in the above-mentioned lecture by Blackett shows that if the number of \(V\)-particles registered by two Wilson chambers with identical \(T_R\), but with horizontal cross sections differing by a factor of 10 (200 and \(2000\ \text{cm}^2\)), differ at sea level by approximately a factor of 10, then the ratio of the number of \(V\)-particles registered

these two cameras, raised to a height of 3 km, will be only two. Thus, increasing the dimensions of cameras operating at high altitudes leads to a far from proportional increase in the rate of registration of \(V\)-particles. Increasing the dimensions of the cameras is important, however, in other respects, since it makes it possible to observe long tracks of \(V\)-particles and of the products of their decay, which is essential for the accurate measurement of particle momenta and of the angles between tracks, for measuring particle lifetimes from the distribution of decay points in the volume of the camera, and also for studying double decays, when one of the secondary particles also decays after traveling some distance in the camera. This explains the tendency toward increasing the dimensions of cameras, as well as the appearance of installations with doubled cameras, similar to the installations of the Pasadena group or of the group of the Polytechnic School \(^{50,51}\) (Figs. 12 and 15).

Typical cases of \(V^0\)- and \(V^\pm\)-decays in Wilson chambers are shown in Figs. 31, 33, 60, 61.

I.4.4. Methods of producing a magnetic field. The magnetic field in existing installations is produced in various ways. In some cases an “iron-free” method of producing the magnetic field is used, with the aid of two short solenoidal coils (Helmholtz coils), on whose axis, in the space between the coils, the Wilson chamber is placed. Such a method of obtaining the magnetic field was used, for example, in the installation of the Polytechnic School described below. The advantages of the two-solenoidal-coil method are the possibility of obtaining a strong uniform field, reducing to a minimum the amount of heavy material surrounding the chamber, and a considerable easing of the conditions for photographing. An unquestionable drawback is the large power dissipated in the solenoidal coils, which makes it difficult to stabilize the thermal regime of the chamber and makes operation more expensive. For example, the solenoidal coils of the Polytechnic School installation, producing a field of 2600 gauss, consume a power of 200 kW. The use of iron in such solenoidal coils makes it possible to reduce considerably the power consumed. In producing fields up to 6000 gauss by using iron poles and a relatively light iron yoke, one can achieve a tenfold reduction of the consumed power at approximately equal weights of iron and copper \(^{44}\). Thus, for example, the magnet of the Manchester group installation at Jungfraujoch consumes a power of 27 kW and produces a magnetic field of 5200 gauss for a chamber of dimensions \(55 \times 55 \times 16\ \mathrm{cm}^3\), with total weights of copper and iron of 6 and 8 t, respectively. Figure 16 shows a section of the electromagnet and the position of the chamber in the electromagnet of the Indian group \(^{52}\). Data on the parameters of this installation are given in Table I. A similar method of producing the magnetic field was also used in the installation of M. S. Kozodaev and A. P. Filippov \(^{53}\).

Another method of creating a magnetic field is the use of a permanent magnet, as was done in the cosmic-ray spectrometers of Alikhanian and co-workers\(^{54-56}\). With complete stability of the field in time and no heat release, a drawback of such magnets, once magnetized by a large current pulse, is the impossibility of changing the magnitude and sign of the field. This drawback is eliminated in the apparatus of Alikhanov and Eliseev\(^{57}\), where the permanent magnet, provided with magnetizing coils, also has a motor-generator for remagnetization. Of course, the drawback of such installations is the large volume of expensive magnetic alloy. Therefore, for example, in the last installation of Alikhanian and co-workers, where it was necessary to obtain a large field in a large volume and to have the possibility of changing its magnitude, an electromagnet was used.

Fig. 16. Cross section of the electromagnet and chamber in the installation of the Indian group\(^{52}\).

I.4.5. Accuracy of momentum measurement in Wilson chambers. It is of interest to estimate the accuracy of momentum measurement in existing installations\(^{40,58}\) and to compare it with the accuracy of measuring the quantity \(p\beta\) in a photoemulsion. Errors in momentum measurement in Wilson chambers are caused mainly by convection of the gas in the chamber. If this error can be minimized by stabilizing the thermal regime, then errors caused by diffusion of ions in the particle track and by scattering of the particle in the chamber gas begin to play a role. In addition, there is always a controllable systematic error caused by distortions introduced by the optical system. Errors caused by gas convection are of special importance for tracks of particles with large momentum (small sagitta), for which the errors due to scattering are small. To reduce errors from gas convection, in all the installations considered the chambers were carefully thermostated (to \(0.1^\circ\)—\(0.05^\circ\)); for this purpose they were surrounded by a jacket through which thermostated water was circulated. Gas diffusion in the track is the more important the shorter the track; for tracks longer than 10 cm in ordinary installations it has no substantial significance. The role of multiple scattering was considered in detail in work\(^{59}\).

The values of the maximum measurable momentum in existing installations are given in Table I. Comparison of these values with the maxi-

small measured quantity \(p\beta\) in emulsions shows that the accuracies attainable by the two methods are at present close to one another.

I.4.6. Multiplate Wilson chambers. Multiplate Wilson chambers for the study of cosmic radiation were already being used several years before the problem of heavy unstable particles arose. Thus, for example, Hazen\(^{60}\) in 1944 used a Wilson chamber with 9 lead plates to study the spectrum of electrons and photons at an altitude of 3 km from their cascade multiplication in lead. After him, Fretter\(^{61}\) in 1946 used a system of two chambers—a magnetic one and a multiplate one—to determine the masses of charged particles of cosmic radiation by measuring their momentum and range.

Although, because of the absence of a magnetic field in a multiplate chamber, it is impossible to determine the sign of the particles’ charge, it has a number of advantages in comparison with a Wilson chamber in a magnetic field. The presence of a large number of plates traversed by particles makes it possible, in addition to the ionization usually estimated in the chamber, also to measure the ranges of particles by the number of plates passed through and the multiple scattering of particles in the plates. A combination of any two of these measurements makes it possible to estimate the mass of a particle. In those cases where the mass of the particle is known, the presence of thin plates in the chamber makes it possible to establish very narrow limits for its range and, consequently, also for its energy. In addition, in such a chamber one can study nuclear interactions in the plates, distinguish penetrating particles from electrons and photons of high energy, and estimate the energies of the latter from the magnitude of the cascade showers caused by them. To this should be added that the construction of a multiplate chamber is considerably simpler than the construction of a magnetic chamber. Dividing the chamber into a large number of compartments bounded by the surfaces of the plates improves its thermal conductivity and prevents the occurrence of convection currents which, in magnetic chambers, occupy the whole volume. The problem of illumination and stereoscopic photography of a multiplate chamber is also considerably simpler than in the case of a magnetic chamber.

A detailed description of large multiplate Wilson chambers is given in the work of M. I. Daion and V. M. Fedorov and in the work of V. G. Kirillov-Ugryumov et al.\(^{62,63}\), who developed these chambers for the spectrometer of the Alagez laboratory.

In Fig. 17 are shown diagrams of typical installations with multiplate chambers. Fretter, May, and Nakada\(^{64}\) worked with a large chamber about 50 cm long at an altitude of 2700 m and at sea level (California). With the aid of this chamber the decay of neutral \(V^{0}\)-particles was investigated. The principal measurements were carried out with seven lead plates, each 1.25 cm thick, separated by a distance of 5 cm. Expansion of the chamber took place from the com-

of the occurrence of a pulse in one and only one of the counters of the upper row with pulses in both counters of the lower row. This arrangement is of interest because, during most of the experiments, there was only a thin roof above the chamber, and the production of neutral \(V^0\)-particles took place in the lead plates of the chamber, while the selection system did not require a large energy of the penetrating showers.

The rectangular multiplate chamber of the Massachusetts Institute of Technology group (Bridge, Peyrou, Rossi, Safford, and others)*) was installed at an altitude of \(3250\ \text{m}^{65,66}\). The area of the vertical cross section of the chamber was \(50 \times 50\ \text{cm}^2\), and the depth of the illuminated region was \(18\ \text{cm}\). In the principal measurements, either 11 lead plates \(7.1\ \text{g}/\text{cm}^2\) thick (\(0.64\ \text{cm}\)), covered on both sides with thin (\(0.8\ \text{cm}\)) glass mirrors to improve the illumination in the chamber, or brass plates \(1.25\ \text{cm}\) thick, were placed in the chamber. The chamber was controlled by a system situated above it consisting of counters enclosed in lead and sensitive to penetrating showers. For the chamber to be expanded, a fivefold coincidence of discharges was required, at least in one of the counters of the rows. Practically all such coincidences were caused by nuclear interactions occurring in the lead block. In approximately half of these cases the tracks of penetrating particles were visible in the chamber. The selection system operated on average 18 times per hour; the recovery time of the chamber was about 4 minutes, whence (see I.4.3) it follows that about 8 chamber expansions occurred per hour.

Fig. 17. Installations with a multiplate chamber. \(a\) — Freter and others; \(b\) — M.I.T. group\(^{64,65,66}\).

To illustrate the method of the multiplate chamber, let us consider several photographs obtained in such chambers. Fig. 18 shows the decay in flight of a \(V^0\)-particle produced in one of the plates of the chamber\(^{50}\). This particle apparently arose in a nuclear interact—

*) M.I.T. group.

...interactions in the fourth plate, caused by particles coming from above downward with relativistic ionization. From plate 4 emerge two strongly ionizing particles, stopping in the fifth plate, and a neutral \(V^0\)-particle, decaying in flight between plates 5 and 6 into two charged secondary particles (1) and (2).

Fig. 18. \(V_1\)-decay in a multilayer chamber of the M.T.I.

If, in the decay of the neutral \(V^0\)-particle, no other particles arise, then the flight trajectory of the \(V^0\)-particle must lie in the plane of the tracks 1, 2. Measurements made for this photograph show that the line of flight of the \(V^0\)-particle makes an angle with the plane of tracks 1 and 2 (the noncoplanarity angle \(\delta\)) of about \(1^\circ\), which is within the limits of measurement errors and confirms the assumption that the charged particles 1 and 2 were the only particles produced in the \(V^0\)-decay. The photograph under consideration also makes it possible to determine the nature of the secondary particles 1 and 2 from their range and ionization.

Another example of the decay of an unstable particle that stopped in one of the plates of the chamber (S-decay) is shown in Fig. 19. In the photograph one can also see the tracks of the decay products: a charged particle

Fig. 19. S-decay in the M.T.I. multiplate chamber. In addition to the secondary particle \((BC)\), in the decay of particle \(A\) there arises an electron cascade of three particles \((D)\). In this photograph the direction of motion of \((BD)\) is opposite to the direction of motion of the primary particle.

and an electron cascade produced by a \(\gamma\)-quantum emitted in the opposite direction \(^{67}\).

1.4.7. Magnetic spectrometer. Combination of a magnetic and a multiplate chamber in one installation. The magnetic spectrometer of Alikhanian, Alikhanov and co-workers \(^{54-56}\), described in detail in the authors’ papers and in Alikhanov’s review \(^{68}\), combines the possibilities of measuring the momentum and the residual range of charged particles. In one of such

HEAVY UNSTABLE PARTICLES

magnetic spectrometers^56a,b, installed in the laboratory on Mt. Alagez (3250 m), the magnetic field in a gap of \(100 \times 30 \times 12\) cm is produced by an electromagnet and can reach 19,000 gauss. To determine the momentum of a particle from its trajectory in the magnetic field, a telescope of 10 rows of small-diameter counters is used, placed in the magnetic field, as shown in Fig. 20. The range of the particle was determined from the triggering of “carpets” of counters located beneath the absorbers in the lower part of the spectrometer. To determine the ionizing ability of particles passing through the spectrometer, it was equipped with proportional counters^69.

A further modification of the spectrometer design, carried out in 1953^56b, consisted in connecting it with a large multi-plate Wilson chamber. In the instrument thus improved, the momentum of the particles was still determined by the hodoscopic system of counters located in

Labels in Fig. 20: Coordinate counters; Transverse counters; Proportional counters; Filters; Absorbing device; Side counters.

Fig. 20. Magnetic spectrometer for cosmic radiation of Alikhanian and collaborators^56.

magnetic field, whereas the analysis of the properties of the primary particle in the plate and of the properties of the secondary particles arising in its decay was carried out by means of a multiplate chamber, which replaced the complex system of absorbers and counters in the usual spectrometer design.

Fig. 21. Magnetic spectrometer connected with a multiplate chamber46.

The scheme of the apparatus modified in this way is shown in Fig. 21.

In 1954 one further improvement was made in the instrument: the block of substance above the spectrometer, in which the generation of heavy particles occurs, was replaced by a multiplate chamber62. In such an instrument one can observe the nuclear interaction in the plates of the upper chamber, the passage of the particle produced in this interaction through the magnetic field, and its stopping and decay in the plates of the lower chamber.

Another type of apparatus that makes possible magnetic and multiplate analysis is an apparatus consisting of a Wilson cloud chamber placed above a multiplate chamber. Such an instrument, which recorded particles stopping in the lower chamber, was used by M. S. Kozodaev and A. P. Filippov in measurements of the masses of \(S\)-particles, carried out by them at the Alagez laboratory in 1951–1953.^53 With a similar apparatus, controlled by penetrating showers, a group from the Polytechnic School*)^50,51 is working at the Pic du Midi (2850 m). The scheme of this apparatus is shown in Fig. 15; the parameters of its Wilson cloud chamber are given in Table I. The upper Wilson chamber serves to measure the momenta of \(V^{\pm}\)- and \(S\)-particles. In the lower chamber there are 15 plates (9 lead and 6 graphite). They are intended both for the analysis of secondary particles arising in \(S\)-decays and for the analysis of secondary particles arising from \(V\)-decays and penetrating into the lower chamber from the upper magnetic chamber. The apparatus is controlled by a telescope of Geiger–Müller counters, selecting penetrating showers. The “wings” \(A\), consisting of 14 Geiger–Müller counters connected in anticoincidence with the main telescope, protect the apparatus from triggering on broad showers.

II. METHODS OF ANALYSIS OF OBSERVATIONS

II.1. Analysis of the dynamical conditions of decay

In decays of \(V\)-particles observed in Wilson chambers, fast secondary particles most often arise, producing ionization close to minimum. The scheme of such decays cannot be established by direct measurement of the mass and energy of the secondary particles, since such measurements either cannot always be carried out, or they may be made with too large an error. Therefore, in studying \(V\)-decays, the analysis of the dynamical conditions of the decay, based on the application of the laws of conservation of momentum and energy, is of great importance. Such an analysis does not require knowledge of the particle masses. For it, measurements of the particle momenta and of the angles between the directions of the tracks are sufficient.

A characteristic and simplest example of such an analysis is the test of coplanarity, which was explained on p. 391 using the example of a photograph of the decay of a \(V_1^0\)-particle in a multiplate Wilson chamber (Fig. 18). Such an analysis makes it possible, even without resorting to momentum measurements, using only the measured angles between the tracks of the particles, to choose between decay schemes into two or a larger number of secondary particles.

Let us give other very simple examples of dynamical analysis.

*) P. Sh. group.

If a neutral \(V^0\)-particle decays into two particles, then the components of the momenta of both secondary particles perpendicular to the direction of flight of the primary particle must balance. On the other hand, if, in the decay of a particle of high energy, two particles of different masses arise, for example, a proton and a light meson, then the momentum carried away by the heavy particle must be greater than the momentum of the light particle. Thus, analysis of the momenta of the secondary particles makes it possible, without resorting to mass measurements, to choose between certain possible decay schemes.

Here we consider the most frequently used methods of dynamical analysis, following from the laws of conservation of energy and momentum for decay into two particles. This question was examined in detail by Podolansky and Armenteros \(^{70}\), who proposed several methods for analyzing experimental data. Such an analysis must not only establish whether decay into two or more particles occurs, but, in the case of decay into two particles, provide methods for obtaining certain decay parameters.

Let a particle with rest mass \(M\), charged or neutral, decay into two particles whose rest masses are \(m_1\) and \(m_2\):

\[ M \to m_1 + m_2 . \]

The momentum diagrams for such a decay in the center-of-mass system (C.M.) and in the laboratory system (L.S.) are shown in Fig. 22.

Fig. 22. Decay into two particles in the center-of-mass system and in the laboratory system.

The heavy line indicates the direction of motion of the primary particle with mass \(M\). In the C.M. system the momenta of both secondary particles are equal and antiparallel. We shall denote their magnitude \(^{*}\) by \(P^*\). The kinetic energy of the particles \(m_1\) and \(m_2\) in the C.M. system (this quantity will hereafter be called the decay energy) is equal to:

\[ Q = M - (m_1 + m_2), \]

\[ {}^{*}\ \text{Here and below Rossi’s system of units is used: velocity is measured in fractions of the speed of light, charge in electron charges, energy and momentum in eV and eV}/c \text{ respectively.} \]

and the quantity \(P^*\) can be found from the law of conservation of energy, which in relativistic form for the C.S. has the form

\[ M=(P^{*2}+m_1^2)^{1/2}+(P^{*2}+m_2^2)^{1/2}. \tag{1} \]

From (1) we obtain:

\[ P^*=\frac{1}{2M}\sqrt{[M^2-(m_1^2+m_2^2)]^2-(2m_1m_2)^2}. \]

In the L.S., where the momenta of the particles \(M\), \(m_1\), and \(m_2\) are equal to \(P\), \(P_1\), and \(P_2\), respectively, the laws of conservation of energy and momentum can be written in the form

\[ (P^2+M^2)^{1/2}=(P_1^2+m_1^2)^{1/2}+(P_2^2+m_2^2)^{1/2}, \]

\[ P^2=P_1^2+P_2^2+2P_1P_2\cos\varphi, \]

where \(\varphi=\varphi_1+\varphi_2\) (see Fig. 22) is the angle of divergence of the secondary particles. The transition from the C.S. to the L.S. is effected by a Lorentz transformation. This transformation does not change the component of momentum \(P_t\) perpendicular to the direction of the primary particle (transverse momentum). Therefore

\[ P_t=P^*\sin\vartheta^*=P_1\sin\varphi_1=P_2\sin\varphi_2. \tag{2} \]

a. Checking the isotropy of the decay and determining the quantity \(P^*\). The distribution of transverse momenta \(P_t\) in decay into two particles is easy to calculate if one assumes that the decay is isotropic, i.e., that all directions of emission of the secondary particles are equally probable. In this case the relative number of decays \(F(\vartheta^*)\,d\vartheta^*\), in which the secondary particles are emitted at an angle from \(\vartheta^*\) to \(\vartheta^*+d\vartheta^*\) with respect to the direction of motion of the primary particle, is proportional to the solid angle

\[ d\omega=2\pi\sin\vartheta^*\,d\vartheta^*, \]

i.e.

\[ F(\vartheta^*)\,d\vartheta^*=\sin\vartheta^*\,d\vartheta^*. \tag{3} \]

Since to each value of \(\vartheta^*\), according to (2), there corresponds its own value of \(P_t\), then, rewriting the distribution (3) in the variable \(P_t\), we obtain the distribution of transverse momenta

\[ W(P_t)\,dP_t=\frac{P_t}{P^*(P^{*2}-P_t^2)^{1/2}}\,dP_t. \tag{4} \]

It is evident that the least probable values are those of \(P_t\) close to zero (secondary particles with such \(P_t\) fly out in the direction of motion of the primary particle or in the opposite direction), and the most probable values are those of \(P_t\) close to \(P^*\) (particles with such values of \(P_t\) fly out perpendicular to the direction of motion of the primary particle, \(\vartheta^*\sim 90^\circ\)).

The obtained distribution of transverse momenta is shown in Fig. 23. By studying the distribution of transverse momenta for decays of a definite type, one can establish whether this distribution corresponds to decay into two particles and, in the case of agreement, determine the quantity \(P^*\), which is an important constant of the decay.

Fig. 23. Distribution of transverse momenta \(P_t\) in decay into two particles. The solid curve is equation (5); the dashed curve is the same, taking into account measurement errors.

The distribution measured in the experiment will, however, differ from distribution (4) because the quantity \(P_t\) is measured with a finite error equal to \(\Delta P\). Therefore the actual distribution has the form

\[ W(P_t)\,dP_T = dP_T \int_{0}^{P^*} \left\{ \frac{P_t}{P^*(P^{*2}-P_t^2)^{1/2}} \right\} \exp\left\{ -\frac{(P_t-P_T)^2}{2\Delta P^2} \right\} \,dP_t . \tag{5} \]

It is shown by the dashed line in Fig. 23 for the case \(\Delta P_t = 15\%\). Comparison of the two curves shows that the maximum of the measured distribution is shifted by an amount \(\sim \Delta P\) from the value \(P^*\) toward smaller momenta.

6. Dynamic analysis by means of the parameters \(\frac{1}{P}\), \(\alpha\), \(\varepsilon\)

For further analysis the parameters \(\frac{1}{P}\), \(\alpha\), and \(\varepsilon\) are introduced. The first of them is equal to the reciprocal value of the total momentum of the decaying particle; the second is the ratio of the difference of the longitudinal momenta to their sum,

\[ \alpha = \frac{P_{1l}-P_{2l}}{P_{1l}+P_{2l}} = \frac{P_{1l}-P_{2l}}{P}, \tag{6} \]

and the third is the ratio of the transverse momentum to one half of the total

of momentum \(\left(\varepsilon=2\dfrac{P_t}{P}\right)\). These parameters are considerably more convenient for analysis than the values of the angles and momenta themselves.

It is easy to prove the following relations:

\[ \alpha=\frac{m_1^2-m_2^2}{M^2}+2P^*\cos\vartheta^*\left(\frac{1}{M^2}+\frac{1}{P^2}\right)^{1/2}, \tag{7} \]

\[ \alpha=\frac{P_1^2-P_2^2}{P^2}, \tag{8} \]

\[ \alpha=-\sin(\varphi_1-\varphi_2)/\sin(\varphi_1+\varphi_2), \tag{9} \]

\[ \varepsilon=2P_t/P=2\sin\varphi_1\sin\varphi_2/\sin\varphi. \tag{10} \]

As is seen from these equalities, the parameters \(\alpha\) and \(\varepsilon\) can be determined, even without a magnetic field, from measurements of the angles between the tracks.

Let us denote the maximum value of \(\varepsilon\) by \(\varepsilon^*\):

\[ \varepsilon^*=\frac{2P^*}{P}. \]

Since in isotropic decay the mean value \(\cos\vartheta^*=0\), the mean value of \(\alpha\) is

\[ \overline{\alpha}=\frac{m_1^2-m_2^2}{M^2}. \]

These formulas explain the physical meaning of the parameters \(\overline{\alpha}\) and \(\varepsilon^*\). The parameter \(\overline{\alpha}\) characterizes the asymmetry of the decay. If the decay is symmetric, i.e., if \(m_1=m_2\), then \(\overline{\alpha}=0\). The parameter \(\varepsilon^*\) is a measure of the energy released in the decay. If \(\varepsilon^*=0\), both particles arise with zero velocities, and the decay energy \(Q=0\); while if \(\varepsilon^*=1\), then the entire rest mass of the primary particle is converted into the kinetic energy of motion of the particles (this occurs, for example, in the decay of the neutral \(\pi^0\)-meson: \(\pi^0\to\gamma+\gamma\)). From equation (7) it is easy to obtain:

\[ \frac{(\alpha-\overline{\alpha})^2}{(2P^*\cos\vartheta^*/M)^2} -\frac{\left(\dfrac{1}{P}\right)^2}{\left(\dfrac{1}{M}\right)^2} =1. \tag{11} \]

Taking into account that

\[ \left(\frac{1}{M^2}+\frac{1}{P^2}\right)^{1/2} =\frac{1}{M\beta}, \]

we obtain from (11):

\[ \frac{(\alpha-\overline{\alpha})^2}{(2P^*/M\beta)^2} +\frac{P_t^2}{P^{*2}}=1. \tag{12} \]

The obtained relations make it possible to establish whether the dynamic parameters \(\dfrac{1}{P}\), \(\alpha\), and \(\varepsilon\), measured experimentally, correspond to the proposed decay scheme. Thus, for example, if one uses (11)

and plot on the graph the dependence of \((\alpha-\bar\alpha)\) on \(\dfrac{1}{P}=\gamma M\beta\), then we obtain a hyperbola on which the points \((\alpha-\bar\alpha), \dfrac{1}{P}\) must lie for all decays with the given \(\gamma^*\).

If one represents graphically the dependence of \((\alpha-\bar\alpha)\) on \(P_t\), this will be an ellipse, whose equation is determined by (12). All points corresponding to the experimentally measured values of \((\alpha-\bar\alpha)\) and \(P_t\) for the given type of decays must lie on this ellipse (for \(\beta=\mathrm{const}\)).

Equation (12) may be written in the form

\[ \left(\frac{M\beta(\alpha-\bar\alpha)}{2}\right)^2+P_t^2=P^{*2}. \]

Therefore the dependence of \(\dfrac{1}{2}M\beta(\alpha-\alpha^*)\) on \(P_t\) is represented by a semicircle of radius \(P^*\). On this graph the angle formed by the radius \(P^*\) with the \(M\beta\) axis is equal to the angle \(\gamma^*\). Examples of dynamical analysis using some of the dependences obtained will be given below.

II.2. Determination of the mean lifetime from the time of flight

The mean lifetimes of various types of heavy unstable particles lie in the range \(\sim 10^{-10}\)—\(10^{-8}\) sec. Thus, for example, charged \(K\)-particles and \(\tau\)-mesons live relatively long: their mean lifetimes are of order \(10^{-9}\)—\(10^{-8}\) sec. Neutral \(K\)-mesons and hyperons have considerably shorter mean lifetimes, lying in the range \(\sim(1—5)\times10^{-10}\) sec, which cannot be measured by direct methods similar to those used for measuring the lifetimes of \(\mu\)- or \(\pi\)-mesons. In this case a suitable and accessible time scale is the time of flight of the unstable particle in the Wilson chamber before its decay.

Thus, for example, a particle moving with a speed equal to one half the speed of light travels \(10\) cm—the distance of the order of the size of the chamber—in a time of about \(6\times10^{-10}\) sec. Therefore, from the distribution of the points of decay of particles in the Wilson chamber (or photoemulsion chamber) one can obtain an idea of the mean lifetime. In Figs. 2, 18, 28, 31, 60, 61, etc., typical examples are shown of the formation and decay of a particle in the Wilson chamber and in the photoemulsion chamber. In the Wilson chamber the formation of the particle most often occurs in a block of material above the chamber, and only those portions of the tracks of the heavy particle and of the product of its decay which are located in the well-illuminated part of the chamber are accessible to observation. In the photoemulsion chamber, in contrast to the chamber

Vylsona, it is very often possible to observe both the point of origin and the point of decay of the particle. In both cases we shall denote by \(l\) the length of the observed part of the track traversed by the particle before decay. If \(M\) is the mass and \(P\) the momentum of the particle, then the flight time \(t\) (in the particle system) will be equal to:

\[ t=\frac{lM}{P}=\frac{l}{c\beta\gamma}, \qquad \text{where } \gamma=\frac{1}{\sqrt{1-\beta^2}} . \]

Thus, in order to determine the flight time before decay, it is necessary, in addition to \(l\), to measure the momentum and mass of the particle. After a certain number of decays of particles of the given type has been selected and the flight time before decay \(t_i\) has been determined for each particle, one can determine the mean lifetime of the particles under consideration \((\tau)\) from the observed values \(t_i\). To solve this problem it is necessary, in addition to the time \(t_i\), also to measure for each decay the so-called “potential” time, or the time “available for observing the decay” \((T_i)\). By this is meant the time required for the particle to traverse the entire path on which its decay could have been detected. If the potential time were considerably greater than the mean lifetime \((T_i=\infty,\ \text{or } T_i\gg\tau)\), then the quantity \(\tau\) would be determined simply as the arithmetic mean of the measured values \(t_i\):

\[ \tau=\frac{1}{N}\sum_{i=1}^{N} t_i . \]

The fact that the particle is accessible to observation for only a limited time \(T_i\) leads to a systematic selection of diminished values of \(t_i\), as a result of which the mean lifetime is not the arithmetic mean of the values \(t_i\).

Applying the method of the function of “maximum likelihood,” Bartlett \(^{71}\) obtained the following formula for calculating \(\tau\) from the measured pairs of values \(t_i\) and \(T_i\):

\[ \tau=\frac{1}{N}\sum_{i=1}^{N}\left(t_i+\frac{T_i}{\exp \frac{T_i}{\tau}-1}\right). \]

The second term in this expression gives the correction connected with the finiteness of the observation time for the decaying particle.

This same method, somewhat modified, can be used to determine the mean lifetime from observations of decays in a photographic-emulsion chamber \(^{72}\). The decays observed under these conditions can be divided into the following groups:

a) decay of a particle after stopping (\(T_i=\infty\), the decay time is greater than the slowing-down time \(t_i'\));

b) decay in flight, in which the decaying particle was at the end of its range and would have had to stop in the emulsion chamber (\(T_i=\infty\), the decay time is measurable and is equal to the flight time);

c) decay in flight; the continuation of the particle track emerges from the photographic-emulsion chamber (in this case \(t_l\) and \(T_l\) are known).

Application of the method of the “maximum-likelihood” function leads in this case\(^{72}\) to the following formula for determining \(\tau\):

\[ \tau=\frac{1}{n_b+n_c}\left(\sum_{i=1}^{n_a} t_i^0+\sum_{k=1}^{n_b} t_k+\sum_{l=1}^{n_c}\left(t_l+\frac{T_l}{\exp\{T_l/\tau\}-1}\right)\right), \]

where \(n_a\), \(n_b\), and \(n_c\) are the numbers of decays of types \(a\), \(b\), and \(c\).

The lower limit of mean lifetimes measurable by the time-of-flight method is determined by the fact that the track of the primary particle (or of its decay product) must be sufficiently long for the particle mass to be measured. Assuming that the velocity of the decaying particles is close to \(c\), and that the minimum track length necessary for “identifying” a particle is of the order of millimeters in a photographic emulsion and of the order of centimeters in a Wilson chamber, we obtain, for the lower limit of measurable time intervals, values of \(10^{-12}\) and \(10^{-10}\) sec, respectively. The upper limit of lifetimes measurable in a photographic emulsion chamber and in a Wilson chamber is of the order of \(10^9\) sec; for the photographic-emulsion chamber it is set by the time of ionization slowing-down of the particle in the emulsion material (times significantly greater than the slowing-down time are poorly measurable, since only a negligible fraction of particles will decay in flight), and for the Wilson chamber by the fact that, for \(\tau \gg 10^{-9}\) sec, the decay points will be distributed almost uniformly in the chamber, and observation of an extremely large number of decays will be required in order to establish a definite value of \(\tau\).

III. NEUTRAL PARTICLES

III.1. Introduction

Data on the nature of neutral unstable particles were obtained chiefly with the aid of Wilson chambers, in the study of characteristic \(V\)-shaped forks formed by the tracks of the two charged particles arising in the decay of a neutral particle. Already in the first stages of this study\(^{73–77}\) it became clear that, in addition to neutral particles decaying into a proton and a light meson (\(V_1^0\)-particles), there exist neutral particles whose decay gives rise to two light charged mesons (\(V_2^0\)-mesons).

At present the existence has been established of two types of neutral particles decaying according to the schemes:

\[ \Lambda^0 \to p+\pi^-+\sim 37\ \text{Mev}, \tag{1} \]

\[ \vartheta^0 \to \pi^+ + \pi^- + \sim 214\ \text{Mev}. \tag{2} \]

The first particle, heavier than the proton, was called the neutral hyperon (the \(\Lambda^0\)-particle). The second particle is called the \(\vartheta^0\)-meson. Thus, in the old notation the \(\Lambda^0\)- and \(\vartheta^0\)-particles are, respectively, \(V_1^0\)- and \(V_2^0\)-particles. The converse is not true, since \(V_1^0\)- and \(V_2^0\)-particles may exist whose decay schemes differ from (1) and (2). The final identification of the particles decaying according to schemes (1) and (2) required observation of a large number of \(V\)-decays in Wilson chambers: in all, more than 1000 \(V^0\)-decays were registered. This is explained by the difficulty of identifying semirelativistic protons and \(\pi\)-mesons in a Wilson chamber, and also by the fact that in a number of arrangements \(\vartheta^0\)-particles are recorded less often than \(\Lambda^0\)-particles; therefore, for a reliable separation of the two types of particles, observation of a considerable number of \(V\)-decays was required. Even after the presence of protons and \(\pi\)-mesons among the secondary particles had been reliably established, considerable effort was needed to prove that these particles are the only particles arising in \(\Lambda^0\)-decay.

Recently the decays of \(\Lambda^0\)- and \(\vartheta^0\)-particles have also been observed in photographic emulsions, and in much larger numbers in photographic-emulsion chambers. In contrast to the magnetic Wilson chamber, the ranges of the secondary particles—the proton and the \(\pi\)-meson arising in the decay of the \(\Lambda^0\)-particle—often lie wholly within the volume of the photographic-emulsion chamber. This made it possible, with a comparatively small number of observed decays, to confirm fully the results obtained earlier with Wilson chambers and to determine with greater accuracy the energy of the secondary particles and the mass of the primary particle.

III.2. \(V_1^0\)-particles; neutral hyperons \(\Lambda^0\)

III.2.1. Data of the Pasadena group.

We shall first consider the data on \(V^0\)-particles obtained with the aid of Wilson chambers. One of the most detailed investigations of the properties of \(V^0\)-particles was carried out by the Pasadena group\(^{77}\) at an altitude of 1750 m, using an arrangement of two magnetic Wilson chambers, the scheme of which is shown in Fig. 12. In 1953–1954 these investigations were continued at an altitude of 200 m with the aid of a similar arrangement of two magnetic Wilson chambers of considerably larger size\(^{78}\). The parameters of both arrangements are given in Table II.

At an altitude of 1750 m, among 23,000 photographs of penetrating showers, the authors observed 134 \(V^0\)-decays. For 87 \(V^0\)-decays it proved possible to measure the momentum of one or both secondary particles. From the momentum and the visually estimated ionization in the track, a rough estimate of the mass of the secondary particles was made: the particles were divided into two groups: “light” particles with mass less than \(700\,m_e\), and “heavy” ones with mass greater than \(700\,m_e\). The results of these

…estimates are given in Table II, from which it follows that in the overwhelming number of decays the secondary positive particles belong to the group of “heavy” particles, while the secondary negative particles belong to the group of “light” particles.

Table II

Classification of the masses of secondary particles for 87 \(V^0\)-decays

	1) \(m_- < 700\)	2) \(m_- > 700\)	3) \(m_-\) unclassified
a) \(m_+ < 700\,m_e\)	2	1	4
b) \(m_+ > 700\,m_e\)	42	0	3
c) \(m_+\) unclassified	29	0	6

Thus, for example, for 42 decays out of 45 in which it was possible to estimate the masses of both secondary particles (these data are enclosed by the dotted line in the table), the positively charged particle is “heavy” and the negatively charged particle is “light.” In addition to this conclusion, Table II implies the existence of a substantially smaller number of \(V^0\)-decays in which both secondary particles are “light”; this is the case for two of the indicated 45 decays. Thus, from these preliminary mass estimates it follows that the principal part of the \(V_1^0\)-particles decays into a heavy positive particle and a light meson (\(V_1^0\)-particles), and only a small part of the \(V^0\)-particles decays into two light mesons (\(V_2^0\)-mesons).

In the figure: “Positive particles (34 cases)”; “Negative particles (23 cases)”; \(\mu\), \(\pi\), \(p\); \(M, m_e\).

Fig. 24. Mass spectrum of secondary particles in \(V_1^0\)-decays\({}^{77}\). All measured mass values correspond to rectangles of equal area. Their width corresponds to the mass interval calculated from the central value of the measured momentum and from the extreme limits of the estimated ionization.

57 secondary particles with measured momenta possessed ionization more than twice the minimum ionization \((I > 2I_{\min})\), and for them more accurate mass measurements could be made, the results of which are given in Fig. 24. From the pre-

From the distributions presented it follows that the majority of the positive particles are protons, and the majority of the light ones are \(\pi\)-mesons. A remarkable feature of this plot is the sharp maximum for \(\pi\)-mesons, demonstrating the reliability of determining masses by the ionization–momentum method. In contrast to the \(\pi\)-mesons, the protons do not give such a sharp maximum, which is possibly explained by the fact that among the positive particles there is a small admixture of lighter particles. Let us also note that the masses of two negative particles lie in the interval \(500\text{–}1000\,m_e\).

The data considered indicate the existence of at least two types of \(V^0\)-particles. In the decay of particles of the first type a proton and a \(\pi^-\)-meson are formed. For such particles the following decay scheme was proposed:

\[ V_1^0 \to p + \pi^- + Q. \]

Checking the validity of this scheme can be carried out in several ways. First, knowing the masses and momenta of the secondary particles, one can calculate for each \(V_1^0\)-decay the value of the decay energy \(Q\). If these measurements were to give a single value of \(Q\), this would be the best confirmation that only two secondary particles are indeed produced in the decay. Since accurate measurements of \(Q\) require the observation of very rare cases of decay of slow particles, two more criteria for decay into two particles were also studied simultaneously, namely coplanarity and the distribution of the transverse components of the momentum. We shall consider mainly the evidence based on the measurement of \(Q\), since at present even it makes it possible to draw unambiguous conclusions. In the work of Leighton and collaborators\(^{77}\), values of \(Q\) were calculated for such decays when \(m_+ > 700\,m_e\) and \(m_- < 700\,m_e\) (group 1,b from Table II), and for less definite decays for which the measured quantity \(a > +0.5\) (group 1,c from Table II). The resulting distribution of \(Q\) values is shown in Fig. 25. The measured values of \(Q\) lie within the limits \(5\text{–}100\) MeV and have a sharply expressed maximum near \(Q \sim 40\) MeV, and a second, much less sharp maximum near \(Q \sim 80\) MeV. From this distribution the Pasadena group concluded that there exists

Fig. 25. Spectrum of \(Q\) values for \(V_1^0\)-decays\(^{77}\).

of two values of \(Q\): \(Q_1 = 35 \pm 3\) MeV and \(Q_2 = 75 \pm 5\) MeV for the decays \(V_1^0 \to p + \pi^- + Q\).

This conclusion was not, however, confirmed by other investigations, including subsequent measurements by this group,^78 which in 1954 reported 19 new measurements of \(Q\) for \(V_1^0\)-decays measured in an apparatus with two large Wilson chambers at an altitude of 200 m. For these 19 decays of slow \(V_1^0\)-particles, the probable error in measuring \(Q\) did not exceed 5 MeV.

Fig. 26. Spectrum of \(Q\) values for 19 \(V_1^0\)-decays according to the most precise measurements of the Pasadena group.^78 Each decay is represented by a rectangle with base 5 MeV and height inversely proportional to the square of the probable error.

The resulting distribution of \(Q\) (see Fig. 26) leaves no doubt that it is consistent with a single value of the decay energy, for which the weighted mean value obtained is

\[ Q = 34.7 \pm 1 \text{ MeV}. \]

Nevertheless, the authors themselves do not consider the question of a second value of \(Q\) to be settled, pointing out that their selection introduced a systematic shift of the selected cases toward small values of \(Q\).

III.2.2. Data of the Manchester group at Pic-du-Midi.

Detailed studies of the properties of \(V_1^0\)-particles were also carried out by the Manchester group^79,80 (Armenteros, Barker, Coates, Cseverbi). A diagram of the apparatus is given in Fig. 11. In work^80 they reported the results of an analysis of 22 \(V_1^0\)-decays observed from 1951 to 1953, in which all positively charged secondary particles were strongly ionizing \((I \geq 2I_{\min})\). In all cases in which momentum measurement was possible, the mass of these particles proved to be greater than \(100\,m_e\). Figure 27 shows a histogram of the values of \(Q\) for 22 \(V_1^0\)-decays: \(V_1^0 \to p + \pi^-\). The mean error in determining \(Q\) is close to 8 MeV. The resulting distribution of \(Q\) agrees well with the assumption of a single value of \(Q\), equal to \(42^{+3}_{-2}\) MeV, which is somewhat greater than the value \(Q = 34.7 \pm 1\) MeV obtained by the Pasadena group.

Fig. 27. Spectrum of \(Q\) values for \(V_1^0\)-decays of the Manchester group.^80

This histogram gives no indication of the presence of decays with a large value of \(Q\). Its asymmetric shape is explained by the fact that the errors in determining \(Q\) are proportional to the value of \(Q\). Thus, these data confirm that in the decay of a \(V^0_1\)-particle only two secondary particles are formed—a proton and a \(\pi\)-meson—and that this decay occurs with a single value of the decay energy \(Q\).

III.2.3. Data of the M.I.T. group. This group (Bridge, Peyrou, Rossi, Safford) during 1951–1953 obtained, by means of a multiplate Wilson chamber, data on the value of \(Q\) and on the coplanarity of \(V^0_1\)-decays \(^{81,82}\). A typical photograph of a \(V^0_1\)-decay in the M.I.T. multiplate chamber was shown in Fig. 18. The most important data on \(V^0_1\)-decay were obtained from 27 decays of \(V^0_1\)-particles that arose in nuclear disintegrations in the plates of the Wilson chamber. All the values of \(Q\) measured by this group for 22 decays, selected on the basis that one of the secondary particles is a light meson and the other particle has a considerably larger mass, with the exception of two cases (\(Q = 17\text{–}24\) and \(Q = 60\text{–}71\,M_{\mathrm{ev}}\)), overlap in the region \(35\text{–}40\,M_{\mathrm{ev}}\), and the authors consider that this distribution is consistent with a single value \(Q \sim 37\,M_{\mathrm{ev}}\), although they cannot completely exclude the supposition that a small fraction of the decays occurs with a large value of \(Q\). In 6 cases the heavy positive secondary particle came to rest in the plates. In doing so, no secondary particle emerging from the plate near the stopping point was found. This is one more confirmation that the heavy positive secondary particles are protons, and not heavy mesons. The nuclear interactions in which the \(V^0_1\)-particles under consideration arose occurred in the plates of the Wilson chamber. This made it possible, for all 22 decays, to measure the angle of non-coplanarity \(\delta\), which in 16 cases turned out to be \(\leqslant 2^\circ\), and in 6 cases \(\leqslant 5^\circ\). Such small angles of non-coplanarity exclude the supposition of the possibility of decay into three particles, for example, decays according to the schemes:

\[ V^0_1 \to p + \pi^- + \nu, \]

\[ V^0_1 \to p + \pi^- + \pi^0, \]

where the neutral secondary particles are a neutrino or a \(\pi^0\)-meson.

III.2.4. Neutral hyperons in photoemulsion. The experiments considered above show that the majority of \(V^0_1\)-decays observed in a Wilson chamber can be explained by the decay of a particle of one type, occurring according to the scheme \(V^0_1 \to p + \pi + \sim 37\,M_{\mathrm{ev}}\). This particle received the name of neutral hyperon (\(\Lambda^0\)).

In a magnetic Wilson chamber the decay of \(V\)-particles most often takes place in gas. In an emulsion chamber a \(V\)-decay takes place in

in the dense substance of the emulsion. (Fig. 28 gives an example of the decay of a neutral hyperon in an emulsion chamber, studied by Yasin\(^{95}\).) Unlike the Wilson chamber, their observation is made difficult by a background consisting of a large number of two-pronged stars produced by neutral particles in the dense substance of the emulsion. The most reliable method for identifying \(V^{0}\)-decays among such stars is apparently the following. If one constructs the distribution of the measured values \(Q\) for all \(V\)-shaped tracks formed by a proton—\(\pi\)-meson pair in the emulsion, then the values \(Q\) for two-pronged

Fig. 28. Decay of a neutral hyperon in an emulsion chamber.

stars will be distributed over a wide interval of values, whereas the presence of \(V_1^0\)-decays will show itself in the appearance of a sharp maximum near the value \(Q\) corresponding to the decay of the neutral hyperon \(\Lambda^{0}\). If there are several types of neutral \(V^{0}\)-particles decaying into a proton and a meson, but with other values of \(Q\), additional maxima will appear in this diagram.

A very careful determination of the value \(Q\) for \(\Lambda^{0}\)-decays observed in photoemulsion was carried out by Friedlander et al.\(^{83}\) of the Bristol group. They investigated 20 two-pronged stars produced by a neutral particle (stars of type \(2 + 0n\)) and formed by the tracks of a proton and a \(\pi\)-meson. The measured quantities are distributed in the interval of values from 0 to 90 \(Mэв\), but form a sharp maximum near 35–39 \(Mэв\). This last interval contains nine of the 11 decays in which both particles stopped in the emulsion. The weighted mean value of \(Q\) for these decays is

\[ Q = 36.92 \pm 0.22\ Mэв, \]

whence for the mass of the neutral hyperon one obtains the value

\[ M = 2181 \pm 1m_e, \]

if one takes \(M_p = 1836.13\) and \(M_\pi = 272.5\,m_e\).

It should be noted that the errors quoted here are greatly overestimated: they would be such if the range–energy relation, on the basis of which \(Q\) was calculated, were known exactly. Meanwhile, as is clear from Sections 1, 2, and 3, the range–energy relation itself is known with an accuracy of only a few percent.

Figure 29 presents the distribution of \(Q\) for all decays in emulsions and emulsion chambers, summarized at the Padua conference \(^{84}\). These values of \(Q\) were calculated under the assumption

Fig. 29. Spectrum of \(Q\) values for decays of neutral hyperons in emulsions and emulsion chambers \(^{84}\).

that the decay of \(V_1^0\)-particles proceeds according to the scheme \((p,\pi^-)\). The shaded and unshaded parts of the spectrum refer, respectively, to values of \(Q\) obtained in single plates and in photo-emulsion chambers. To each value of \(Q\) on the histogram there corresponds a rectangle of equal area; the base of this rectangle is proportional to the error in the determination of \(Q\) (the method of equal areas).

From the histogram it is clear that one can speak with complete certainty only of a single maximum, corresponding to the value \(Q = 37\) MeV. The remaining maxima are statistically unreliable and, at least at present, may be regarded as background connected in origin with two-prong stars produced by neutral particles, mainly neutrons.

Thus, from the data considered, obtained in the Wilson chamber and in photo-emulsions, it follows that if decays of \(V_1^0\)-particles with values of \(Q\) different from \(\sim 37\) MeV do exist, their number is very small in comparison with \(\Lambda^0\)-decays, for which \(Q \sim 37\) MeV. Reliable isolation of \(V_1^0\)-decays with \(Q > 37\) MeV by the Wilson-chamber method will therefore require the accumulation of an enormous number of \(V_1^0\)-decays. At the same time, the recently begun investigation of \(V_1^0\)-decays with the aid of photo-emulsion chambers will allow

in a shorter time, thanks to the considerably greater resolving power of this method, to determine whether the \(\Lambda^0\)-particle, decaying according to the scheme \(\Lambda^0 \to p + \pi^- + \sim 37\) MeV, is the only neutral hyperon.

In conclusion we give a table of the most accurate values of the decay energy \(Q\), obtained by various groups.

Table III

Author	Method	Number of decays	\(Q\) (MeV)	Particle mass
Leighton et al.\(^{78}\)	Magnetic chamber	19	\(34.7 \pm 1\)	—
Bridge et al.\(^{82}\)	Multiplate Wilson chamber	22	\(37\)	—
Armenteros et al.\(^{80}\)	Magnetic Wilson chamber	22	\(42^{+3}_{-2}\)	—
Friedlander et al.\(^{83}\)	Emulsion chamber	9	\(36.92 \pm 0.22\)	\(2181 \pm 1\,m_e\)

III.3. \(V_2^0\)-mesons; \(\vartheta^0\)-mesons

In the study of \(V^0\)-decays in a Wilson chamber, along with decays of neutral hyperons, a considerably smaller number of \(V^0\)-decays was found in which one of the secondary particles is a positive light meson. For a long time it was not possible to establish the scheme of such \(V\)-decays. At present it is clear that most of them represent the decay of a particle with a mass close to \(970\,m_e\) into two \(\pi\)-mesons:

\[ \vartheta^0 \to \pi^+ + \pi^- + \sim 214\ \text{MeV}. \]

This type of \(V_2^0\)-meson has received the name \(\vartheta^0\)-meson.

Here the most reliable evidence for the existence of such particles is considered.

Among the \(V^0\)-decays there was also observed a small number of decays which cannot be explained either as \(\Lambda^0\)- or as \(\vartheta^0\)-decays. Such “anomalous” \(V^0\)-decays are considered in Sec. III.3.6.

III.3.1. Data of the Manchester group at Pic-du-Midi

This group (Armenteros, Barker, Butler, Coates, Sowerby) analyzed 14 \(V^0\)-decays\(^{85}\), which are not \(V_1^0\)-decays, for which the error in measuring the momentum does not exceed 15–20%. Since all the secondary particles had ionization close to minimum, it was often impossible to distinguish protons from \(\pi\)-mesons.

was impossible. Therefore, in order that \(V_1^0\)-decays not be mixed in with the decays under study, it was required that the decay under study, considered as a \(V_1^0\)-decay, give a value of \(Q\) not less than \(100\) Mev. This excluded, with a large margin, decays of neutral hyperons:
\[ \Lambda^0 \to p+\pi^-+{\sim}37\ \text{Mev}. \]
Since a large part of the particles selected in this way were fast particles, the study of the data obtained was carried out by dynamical methods (check for coplanarity, \(P_t\)-distribution, graph \(P_t,\alpha\)), considered in Section I.5.1.

a) Check for coplanarity. Such a check requires establishing the point at which the \(V^0\)-particle was formed; it could be carried out only for 7 decays out of 14. Three \(V^0\)-particles permitting a check for coplanarity arose in the lead above the Wilson chamber, and four \(V^0\)-particles—in the lead plate located in the chamber. For all these decays the point at which the \(V^0\)-particle arose (to an accuracy of several degrees) does indeed lie in the plane of the tracks of both secondary particles. The deviations from coplanarity are very small and lie within the limits of the errors of angle measurements. The angles of noncoplanarity \(\delta\) are equal to \(3.5\pm3;\ 3\pm2;\ 6\pm3;\ 0\pm2;\ 4\pm2;\ 2\pm2;\ 2\pm2^\circ\); they are many times smaller than the angles between the direction of flight of the \(V^0\)-particle and the tracks of the secondary particles, whence it follows that the two charged particles produced in the decay are the only decay particles (if in these decays a third—neutral—particle is also emitted, then the momentum carried off by it must be no less than 2.5 times smaller than the momentum of the secondary charged particles). Thus, from the coplanarity check there follows the important conclusion about the existence of a \(V^0\)-particle, distinct from the neutral hyperon, which decays into two light mesons.

b) Distribution of transverse momenta. The distribution of transverse momenta for the 14 measured \(V_2^0\)-decays is shown in Fig. 30. The dashed curve gives the distribution \(P_t\) for decay into two particles at the value \(P^*=200\) Mev/c and with a mean error in the momentum measurement close to \(35\) Mev.

Fig. 30. Distribution of transverse momenta for \(V_2^0\)-decays\(^{85}\).

As is seen from the graph, there is excellent agreement between the histogram and the calculated curve. It follows from this that the greater part

\(V_2^0\)-decays actually occur into two charged particles, and that the magnitude of the momentum of the secondary particles in the center-of-mass system is close to \(P^* = 200\ \mathrm{MeV}/c\).

c) Graph \(p_t,\ A = -\dfrac{1}{2}M\beta(\alpha-\alpha^*)\). For further analysis,

Fig. 31. \(V^0\)-decay, interpreted according to the scheme \(V^0 \to \tau^- + \pi^+\). The positive secondary particle enters the lead plate placed between the chambers. The mass of the particle, estimated from ionization and momentum, is close to \(350\,m_e\). The mass of the negative secondary particle lies within \(450\text{—}1000\,m_e\), and it is very unlikely that it is a light meson. This decay is interpreted as a decay into a \(K\)-meson (for example, a \(\tau\)-meson) and a \(\pi^+\)-meson \(^{77}\).

two variants of decays were selected: decay into two \(\pi\)-mesons

\[ V_2^0 \to \pi^- + \pi^+ + Q_1 \tag{1} \]

and decay into \(\tau\)- and \(\pi\)-mesons

\[ V_3^0 \to \tau^- + \pi^+ + Q_2, \tag{2} \]

and an analysis was carried out of the values of \(p_t\) and \(A=-\dfrac{1}{2}M\beta(\alpha-\alpha^*)\), computed—

in the assumption of decay according to scheme (1) or (2). The latter decay scheme was proposed by Leighton et al.\(^{77}\), who found among the secondary particles in \(V^0\)-decays two negative particles with masses in the interval \(500\text{–}1000\,m_e\) (see Fig. 24). A photograph of one such decay is shown in Fig. 31.

The dependence of the transverse momentum \(p_t\) on the parameter \(A=-\dfrac{1}{2}M\beta(\alpha-\alpha^*)\) in the rectangular coordinate system \((p_t,A)\) is represented by a circle whose radius is equal to the momentum of the secondary particles in the center-of-mass system \(P^*\) (see I.5.1). In the graphs of Fig. 32 these circles are drawn for schemes (1) and (2); their radius is \(P^*=200\ \text{MeV}/c\), as follows from the analysis of the transverse momenta. This value of \(P^*\) corresponds to \(Q_1=208\) and \(Q_2=143\ \text{MeV}\). The points correspond to pairs of values \((p_t,A)\) for each decay. From the distribution of the points about the circles (the numbers near the points indicate the measured value of \(Q\) in MeV) it follows that the assumption of decay according to scheme (1) agrees considerably better with the experimental data than the assumption of decay according to scheme (2). Thus, of the 14 points corresponding to the 14 decays observed in the Manchester group’s work, ten points lie close to the circle and have values of \(Q\) close to \(210\ \text{MeV}\) \(\left(230^{+80}_{-50};\ 208^{+50}_{-40};\ 169^{+30}_{-20};\ 193^{+70}_{-20};\ 260^{+65}_{-45};\ 200^{+95}_{-55};\ 184^{+70}_{-40};\ 208^{+64}_{-40};\ 245^{+[[unclear: upper error]]}_{-70}\ \text{and}\ 180\right)\). The scatter of the remaining points may be caused by inaccuracies of measurement and, possibly, by the presence of a small number of particles whose decay scheme differs from

\[ V^0_2 \to \pi^-+\pi^+ + \sim 210\ \text{MeV}. \]

Fig. 32. Graph of \(p_t, A\) for \(V^0_2\)-decays\(^{85}\).

a) \(p_t,\ 100\ \text{MeV}/c;\quad A=2.46\beta\alpha,\ 100\ \text{MeV}/c^2\).

b) \(A=3.92\beta(\alpha+0.37),\ 100\ \text{MeV}/c^2\).

III.3.2. Data of the Indian group.

A considerable refinement of the information on \(V_2^0\)-decays was achieved in the work of the Indian group (Thompson et al.), carried out at sea level \(^{86-88}\) (the arrangement of the apparatus is shown in Fig. 16), which investigated 63 decays of very fast \(V^0\)-particles. Only two of the 126 observed secondary particles were strongly ionizing \((I > 2I_{\min})\). The momenta of the secondary particles were measured with an accuracy that was considerably superior to the accuracy of the measurements of the Manchester group.

Fig. 33. \(V_2^0\)-decay in a Wilson magnetic chamber \(^{87}\).

One such decay, recorded in a large magnetic chamber \(^{87}\), is shown in Fig. 33. The neutral particle that arose

in a penetrating shower, decays after traversing about \(1/8\) of the length of the illuminated part of the chamber. Track \(a\) (length \(43\ \text{cm}\)) of the V-shaped fork \((a,b)\) belongs to a positively charged particle with measured momentum \(0.67 \pm 0.02\ \text{Bev}/c\) and minimum ionization, which excludes a proton, which at the same momentum would ionize \(2.3\) times more strongly. The momentum of the negative particle \(b\) is \(0.094 \pm 0.008\ \text{Bev}/c\); its ionizing power exceeds the minimum by a factor of \(2\)—\(3\), whence it follows that this particle is a \(\pi\)- or \(\mu\)-meson. The value \(Q\), obtained for this case under the assumption of \((\pi,\pi)\)-decay, is \(215 \pm 7\ \text{Mev}\).

The results of the dynamical analysis of decays are given in Fig. 34. Instead of the parameters \((p_t,A)\), here the parameters \((p_t,\alpha)\) are used. The dependence of \(p_t\) on \(\alpha\) for \(\beta\) close to 1 (fast \(V^0\)-particles)

Fig. 34. Graph of \(p_t,\alpha\) for \(V_2^0\)-decays according to the data of the Indiana group \(^{88}\).

is represented by an ellipse. The large ellipse in Fig. 34 gives the dependence \(p_t(\alpha)\) for the symmetric decay of a particle with mass \(971\,m_e\) into two \(\pi\)-mesons:

\[ \vartheta^0 \to \pi^+ + \pi^- + \sim 214\ \text{Mev} \tag{1} \]

\[ (\alpha^* = 0). \]

The ellipse in the right-hand corner of the graph corresponds to the dependence \((p_t,\alpha)\) for the asymmetric decay of a neutral hyperon

\[ \Lambda^0 \to p + \pi^- + \sim 37\ \text{Mev} \tag{2} \]

\[ (\alpha^* = 0.67). \]

The decay shown in Fig. 33 corresponds to the case \(R\)-118 in Fig. 34.

The arrangement of the experimental points \((p_t,\alpha)\) for the most accurately measured decays relative to these two curves shows that almost all decays are indeed divided into two groups, corresponding to decays of \(\Lambda^0\)-particles and \(\vartheta^0\)-mesons.

Subsequently, Thompson and collaborators succeeded in increasing by somewhat more than a factor of two the number of carefully measured \(V_1^0\)- and \(V_2^0\)-decays\({}^{89}\).

Fig. 35. Graph of \(p_t,\alpha\) for \(V_2^0\)-decays according to the latest data of the Indiana group\({}^{89}\).

The resulting separation of \(\Lambda^0\)- and \(\vartheta^0\)-particles is shown in Fig. 35, which also includes the refined data of Fig. 34.

In work\({}^{86}\) the Indiana group gave the following values for the mass and decay energy of \(V_2^0\)-mesons decaying into two \(\pi\)-mesons (\(\vartheta^0\)-mesons):

\[ M_{\vartheta^0}=(971\pm 10)m_e, \]

\[ Q_{\vartheta^0}=(214\pm 5)\ \text{MeV}. \]

Thus, within the limits of the measurement errors, the mass of the \(\vartheta^0\)-meson coincides with the mass of the \(\tau\)-meson.

III.3.3. Slow \(V_2^0\)-mesons in a multiplate chamber. Nuclear interactions of secondary particles. \(V_2^0\)-particles were also observed in multiplate chambers. These observations make it possible to identify secondary particles by their nuclear interactions in plates and thereby to distinguish \(\mu\)-mesons from \(\pi\)-mesons. The M.T.I. group observed, among 27 \(V^0\)-decays of particles produced in the chamber plates, 4 \(V^0\)-decays distinct from \(V_1^0\)\({}^{82}\). Of greatest interest are the decays

\(V^0_2\)-particles of small energy. One such decay was observed by Dighton and Willard \(^{90}\). The \(V^0_2\)-meson arose in a nuclear interaction caused, apparently, by a \(\pi\)-meson, which in turn arose in a penetrating shower that produced an expansion of the chamber. The mass of one of the particles whose tracks form the \(V\)-shaped fork, estimated from ionization, scattering, and range in the plates, turns out to be less than \(900\,m_e\), which indicates a \(\pi\)- or \(\mu\)-meson. The other secondary particle undergoes a small nuclear interaction in the penultimate plate and a sudden change of ionization and, probably, is a \(\pi\)-meson. This decay reveals coplanarity, within the limits of the experimental errors, equal to \(\pm 10^\circ\). Assuming that in the present case the decay

\[ V^0_2 \to \pi + \pi + Q, \]

takes place, the authors obtain \(Q=(173 \div 198)\pm 11\) MeV, which is in agreement with the value of \(Q\) for \(\vartheta^0\)-decay.

Another very similar case, discovered later, was reported by Bridge at the Bangor conference \(^{91}\). For this case, assuming decay into two \(\pi\)-mesons, a lower limit for \(Q\) of \(155\) MeV was obtained, which agrees with the value of \(Q\) in \(\vartheta^0\)-decay.

The group of the Polytechnic School also reported the observation of several \(V^0_2\)-decays in the lower, multiplate chamber of their apparatus. In three cases they observed nuclear interaction of positive and negative secondary particles in the chamber plates. Reynolds reported two cases of nuclear interaction of secondary particles in \(V^0_2\)-decay \(^{92}\).

III.3.4. \(V^0_2\)-mesons in photographic emulsions. The number of \(V^0_2\)-particles registered in photographic emulsions is very small. Lal, Pal, and Peters \(^{93}\) observed in an emulsion chamber a two-pronged “fork” with a perfectly clean vertex, formed by two \(\pi\)-mesons. One of them stops in the emulsion and decays into a \(\mu\)-meson; the range of the other is \(1.2\) cm. From the measurement of scattering and grain density it follows that its mass is \(<450\,m_e\). Assuming that in the present case a decay according to the scheme

\[ V \to \pi + \pi + Q, \]

takes place, the authors obtain \(Q=132\pm 17\) MeV. This does not agree with the value of \(Q\) for \(\vartheta_0\)-decays, equal to \((214\pm 5)\) MeV. An analogous fork with a clean vertex was found in the emulsion chamber of Corato, Dilworth, and Scarsi \(^{94}\). One of the particles of the fork was identified as a \(\pi^{-}\)-meson by the \(\sigma\)-star at the end of its range, equal to \(1825\pm 70\) \((E=8.76\pm 0.20\) MeV). The second particle is traced in three emulsions over a path of \(16\) mm and emerges from the emulsion. Measurements of scattering

give for this particle \(p\beta = 960^{+180}_{-140}\) MeV. Assuming that the second particle is also a \(\pi\)-meson, i.e., decay according to the scheme \(\vartheta^0 \to \pi^+ + \pi^-\), the authors obtain the value \(Q = 220^{+35}_{-30}\), which is in agreement with the value of \(Q\) in \(\vartheta^0\)-decay.

The third example of \(\vartheta^0\)-decay was discovered by Yasin \(^{95}\) and is shown in Fig. 36. The vertex of the two-prong fork \(A\), with an opening angle of \(146^\circ\), is located at a distance of \(\sim 100\mu\) from the star \(C\), and the plane of the fork

Fig. 36. \(V^0_2\)-decay in an emulsion chamber. The negative meson produced in the decay (range \(3.1\) mm) comes to rest in the emulsion, forming at \(B\) a two-prong star. The calculated direction of flight of the \(\vartheta^0\)-meson, with an accuracy of an error of measurement \(\sim 2^\circ\), passes through \(C\)—the center of the disintegration in which the \(\vartheta^0\)-particle probably arose. If it is assumed that both secondary particles are \(\pi\)-mesons, then \(Q = 202 \pm 11\) MeV, and the mass of the \(\vartheta^0\)-meson is \(950m_e\) \(^{95}\).

is coplanar with the center of the star to within \(2^\circ\). One of the tracks of the fork belongs to a \(\pi^-\)-meson (for the continuation of its track see the right-hand part of Fig. 36), which forms at the end of its range (\(R = 3.1\) mm), at point \(B\), a one-prong \(\sigma\)-star. The second track belongs to a light-

to a \((\mu\)- or \(\pi)\)-meson, identified from the measured scattering and grain density, which leaves the emulsion after traversing \(54\) mm in it. Under the assumption of decay according to the scheme \(\vartheta^{0}\to \pi^{+}+\pi^{-}\),

\[ Q=202\pm 11\ \text{MeV}. \]

III.3.5. Mean lifetime of neutral particles. The mean lifetime of neutral hyperons has been determined by many authors who measured the flight times of neutral particles from the point of production to the point of decay. This, at present the only possible, method is described in I.5.2. It requires the analysis of a very large number of \(\Lambda^{0}\)-decays, from which it is necessary to select the decays of slow \(\Lambda^{0}\)-particles most valuable for determining the mean lifetime, since they permit determination of the flight time. Thus, for example, Page and Nutt\(^{96}\) found 26 suitable \(\Lambda^{0}\)-decays among 200 \(V\)-decays. Page\(^{97}\) additionally found 23 suitable \(\Lambda^{0}\)-decays among 357 \(V\)-decays. Table IV gives the measured values of the mean lifetimes

Table IV

Mean lifetime of neutral hyperons

Authors	Number of \(\Lambda^{0}\)-decays	Mean lifetime (in \(10^{-10}\) sec)
Alford and Leighton (1953)\(^{98}\)	74	\(2.5\pm0.7\)
Bridge et al. (1953)\(^{98}\)	21	\(3.5\pm1.2\)
Deichmann et al. (1953)\(^{100,101}\)	22	\(4.8^{+2.6}_{-1.3}\)
Geiter (1954)\(^{103}\)	21	\(4.0^{+3.1}_{-1.2}\)
Page and Prowse (1954)\(^{96}\)	26	\(3.7^{+3.9}_{-1.3}\)
Page (1954)\(^{97}\)	23	\(3.6^{+1.1}_{-0.7}\)

\[ T_{\Lambda^{0}}=\left(3.7^{+0.6}_{-0.5}\right)\times 10^{-10}\ \text{sec} \]

of neutral hyperons. As can be seen from this table, the values of the mean lifetimes obtained in different experiments, in which neutral hyperons of different energies were selected, are in good agreement. The weighted mean value \(T_{\Lambda^{0}}\), obtained by Page\(^{97}\)

according to the data of this table, is equal to:

\[ T_{\Lambda^0}=\left(3.7^{+0.6}_{-0.5}\right)\times 10^{-10}\ \text{sec}. \]

The errors indicated here are statistical in character. The systematic errors in the measurements of Page and Nuttall are estimated by the authors, who consider them to be 2–3 times smaller than the statistical errors. Among the 23 \(\Lambda^0\)-decays used by Page, \(^{97}\)

Fig. 37. Rare case of the decay of a neutral hyperon in the Wilson magnetic chamber: the proton stopped in the gas of the chamber. \(^{97}\)

there is one apparently unique case in which the slow proton emitted in the \(\Lambda^0\)-decay stopped in the gas of the Wilson chamber (after traversing a path of \(9.1\ \text{cm}\)). This photograph is reproduced in Fig. 37. The decay energy for this case is equal to \(34.5^{+6.5}_{-4.5}\ \text{MeV}\). The flight time of the \(\Lambda^0\)-particle in the chamber before decay (in the particle’s system) is close to \(1\times 10^{-9}\ \text{sec}\).

One of the first estimates of the mean lifetime of \(\vartheta^0\)-particles was made by Deichmann \(^{100,101}\), who selected, among 46 \(V^0\)-decays in a large multiplate Wilson chamber, 9 \(V_2^0\)-decays for which \(Q > 150\) MeV. Astbury reported at the conference in Bagnères-de-Bigorre \(^{104}\) on measurements, made by the Manchester group at Jungfraujoch, of the mean lifetime from 11 decays of slow \(V^0\)-particles. Geiter \(^{102}\) selected among 50 decays 8 decays of slow \(\vartheta^0\)-particles and measured their mean lifetime. The last measurement published in the literature was made by Page \(^{103}\), who selected 14 \(\vartheta^0\)-decays among 327 \(V^0\)-decays. The admixture of decays of other neutral particles among all these decays, from which the mean lifetime of the \(\vartheta^0\)-particles was determined, does not exceed 10%. The majority of the extraneous \(V^0\)-particles in this admixture are \(\Lambda^0\)-particles, for which it is known that their mean lifetime is of the same order as the mean lifetime of the \(\vartheta^0\)-particles. Therefore one may assume that the error in determining the mean lifetime of the \(\vartheta^0\)-particles caused by imperfections in their selection is insignificant. The data obtained by the authors listed are given in Table V.

Table V

Mean lifetime of \(\vartheta^0\)-mesons

Authors	Number of \(\vartheta^0\)-decays	Mean lifetime (in \(10^{-10}\) sec)
Deichmann (1953) \(^{100,101}\)	9	\(2.5 \pm 1.5\)
Astbury (1953) \(^{104}\)	11	\(1.7^{+2}_{-0.6}\)
Bridge (1953) \(^{99}\)	6	\(0.9^{+1.6}_{-0.7}\)
Geiter (1954) \(^{102}\)	8	\(1.2^{+0.8}_{-0.3}\)
Page (1955) \(^{103}\)	14	\(0.7^{+0.3}_{-0.2}\)

\[ T_{\vartheta^0}=\left(1.5^{+0.4}_{-0.3}\right)\times 10^{-10}\ \text{sec} \]

The weighted mean of the values presented is equal to:

\[ T_{\vartheta^0}=1.5^{+0.4}_{-0.3}, \]

which is approximately 2.5 times less than the mean lifetime of neutral hyperons.

III.3.6. Anomalous \(V_2^0\)-decays. The majority of the observed \(V^0\)-decays can be understood as the decay of a neutral hyperon (\(\Lambda^0 \to p + \pi^- + \sim 37\ \text{MeV}\)) and of a \(\vartheta^0\)-meson (\(\vartheta^0 \to \pi^+ + \pi^- + \sim 214\ \text{MeV}\)). We have already encountered, however, \(V^0\)-decays which can be neither \(\Lambda^0\)- nor \(\vartheta^0\)-decays. Thus, for example, the Pasadena group \(^{42}\) attempted to interpret a portion of the decays different from \(\Lambda^0\)- and \(\vartheta^0\)-decays according to the scheme

\[ V_3^0 \to \tau^\pm + \pi^\mp . \]

Thompson et al. reported two \(V_2^0\)-decays with anomalously low values \(Q = 86 \pm 6\) and \(50\ \text{MeV}\).

Precisely measured \(V_1^0\)-decays are also known with values of \(Q\) considerably greater and considerably less than \(37\ \text{MeV}\). Such \(V_1^0\)-decays were reported by the Pasadena group, which measured \(Q = 10 \pm 3\), \(72 \pm 10\), and \(79 \pm 15\ \text{MeV}^{42}\), by the M.T.I. group (see II.2.3), and by other investigators. The data known by the time of the Padua conference on 17 anomalous \(V^0\)-decays were considered by Astbury \(^{105}\). Recently Van Lint, Anderson, Cowan, Leighton, and York reported six new \(V_2^0\)-decays for which the energy \(Q\) is considerably less than \(214\ \text{MeV}^{106}\).

These 23 anomalous \(V^0\)-decays were recorded from observations in Wilson cloud chambers. Above we have seen what efforts were required for the reliable identification of \(\Lambda^0\)- and \(\vartheta^0\)-decays: more than a thousand \(V^0\)-decays were observed and several hundred tracks of secondary particles were measured. The large number of observed decays made it possible to apply the methods of dynamical analysis. It is therefore clear that the 23 more or less accurately measured anomalous cases of \(V^0\)-decays currently available are wholly insufficient for the identification of extremely rare \(V^0\)-particles different from \(\Lambda^0\)- and \(\vartheta^0\)-particles. The situation is complicated by the fact that, with a large number of measured tracks of secondary particles, one may expect, even on the assumption of a Gaussian distribution of errors, that several values of measured momenta will lie outside the limits of 2–4 standard deviations. With the existing accuracy of momentum measurements this leads to the result that a significant fraction of the decays that appear anomalous are ordinary \(\Lambda^0\)- and \(\vartheta^0\)-decays. Nevertheless, it is worthwhile to consider such decays in order to clarify what new hypothetical decay schemes of \(V^0\)-particles can be put forward to explain the data obtained.

The 23 anomalous decays mentioned were interpreted in those cases where the data on the masses of the secondary particles permitted...

HEAVY UNSTABLE PARTICLES

this either as \(V_1^0\)-, or as \(V_2^0\)-, or as \(V_3^0\)-decays. In accordance with this interpretation, the values \(Q_{V_1^0}\), \(Q_{V_2^0}\), and \(Q_{V_3^0}^{10b}\) were calculated. The calculated values of \(Q_{V_2^0}\) lie in the range \(27\text{–}148\) MeV, i.e. below the decay energy of the \(\vartheta\)-meson, equal to \(Q = 214\) MeV, and do not agree with the assumption of a single value of \(Q\) different from \(214\) MeV. They could be explained by the presence of two new types of \(V_2^0\)-particles, decaying according to the schemes

\[ V_2^0 \to \pi + \pi + \sim 50\ \text{MeV}, \]

\[ V_2^0 \to \pi + \pi + \sim 110\ \text{MeV}. \]

The values of \(Q_{V_3^0}\) also lie in a broad energy interval, and a large part of these decay energies is contained in the interval \(30\text{–}90\) MeV. Thus, these calculations do not agree with the assumption of a single value of \(Q\) for \(V_3^0\)-decay, although some anomalous decays can be explained in this way. One may try to explain some of the cited cases by decay into three particles. In considering the decay schemes of \(\tau\)-mesons, evidence will be given for an anomalous decay of a \(\tau\)-meson (see II.1.3), in which, along with three charged \(\pi\)-mesons, there arises a fourth, neutral particle, apparently a \(\gamma\)-quantum\(^{10}\), carrying away a considerable part of the decay energy. One may suppose that the decay of the \(\vartheta^0\)-particle also proceeds in some cases according to the scheme

\[ \vartheta^0 \to \pi^+ + \pi^- + \gamma + Q. \tag{1} \]

Such decays must give an apparent value of \(Q\) less than \(214\) MeV. In 40 \(\tau\)-decays in emulsion, one \(\tau\)-decay of the type \(\tau \to 3\pi + \gamma\) was observed, and since up to now on the order of a hundred \(\vartheta^0\)-decays have been observed, it may be expected that a certain number of anomalous \(V_2^0\)-decays can be explained in this way. Of course, decay into three particles violates coplanarity, but for the majority of anomalous \(V_2^0\)-decays coplanarity has not been established, or has been established with great inaccuracy; in the remaining few cases a sharp non-coplanarity is observed.

In addition to hypothesis (1), a hypothesis analogous to it may be proposed concerning another alternative decay of the \(\vartheta^0\)-meson into \(\pi\)- and \(\mu\)-mesons and a neutrino

\[ \vartheta^0 \to \pi + \mu + \nu. \tag{2} \]

Both of these hypotheses are sufficiently broad to explain a considerable number of the anomalous \(V_2^0\)-decays. As a hypothesis concerning decay into 3 particles, one may also admit the existence of the \(\tau^0\)-particle—a neutral \(\tau\)-meson decaying according to the scheme

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

This scheme could explain those \(V_2^0\)-decays for which \(Q<80\) MeV. We have presented the simplest of the currently possible explanations of anomalous \(V_2^0\)-decays. The statistical reliability of the available data is far from sufficient for testing the hypotheses presented. They can be confirmed or refuted only after the number of such decays increases by at least an order of magnitude, which will make it possible to study such decays by means of the usual dynamical methods that have played such an important role in the identification of \(\Lambda^0\)- and \(\vartheta^0\)-particles. Apparently, the solution of these questions, even with the use of accelerator experiments, will require prolonged observations. One may hope that individual observations in large emulsion chambers, in which it will be possible to observe the stopping of secondary particles arising in anomalous \(V^0\)-decays, will play a significant role in solving this problem.

IV. CHARGED HYPERONS

IV.1. Introduction

During 1953–1955 there was a gradual accumulation of data obtained in cosmic radiation and at the cosmotron, indicating the existence not only of neutral particles but also of charged particles heavier than protons. These particles were given the name charged hyperons. In 1953–1954 Alikhanian and collaborators reported the observation of several positively charged unstable particles heavier than the proton \(^{107,108}\). The particles passed through the magnetic field of a mass spectrometer and decayed in the copper plates of a Wilson chamber located beneath the spectrometer. The mass of two such particles, measured from the momentum and range in the plates of the chamber, proved to be \(2230 \pm 150\,m_e\) in one case and within the limits \(1460—3200\,m_e\) in the second \(^{107}\). In 1953 York, Leighton, and Bjorknerud, in their apparatus, the arrangement of which is shown in Fig. 12, found that two fast charged particles produced in a lead plate between the chambers and decaying in flight in the gas of the lower chamber form, upon decay, charged secondary particles whose mass is close to the proton mass (see the mass spectrum in Fig. 62). They suggested, by analogy with the decay of the neutral hyperon, that both these decays represent the decay of a heavy particle into a proton and a \(\pi\)-meson:

\(Y^+ \to p+\pi^0\),

and put forward the hypothesis of the existence of an alternative decay scheme for these particles:

\(Y^\pm \to n+\pi^\pm\).

Bonetti et al. \(^{109}\) in 1953 discovered the decay of a particle stopped in emulsion, for which the measurement of the mass by scattering and range, carried out by the constant-sagitta method, gave the value \(2210 \pm 250\,m_e\). Detailed measurements of the track of the secondary particle

could not be carried out (the track length is only 120 μ, the particle leaves the emulsion), and one could only assert that the secondary particle is heavier than the electron.

Following these first works, there soon appeared a considerable number of papers reporting the observation of charged hyperons, whose decay produces either a proton or a light meson.

IV.2. Mass measurements

Table VI summarizes the data on all decays of charged hyperons known from the literature by the beginning of 19551. In column 7 of this table the mass values are given and the method of measurement is indicated. The tracks of most hyperons have small lengths (less than 1 cm), and therefore the error of individual mass determinations is in most cases large. At the same time, the diversity of the measurement methods and the large scatter of the data make it pointless to obtain weighted mean values. All measured mass values, as is seen from the table, lie within the range \(\sim 1800 — 2800 m_e\). The significantly more accurate mass values obtained on the basis of the decay scheme and the energy of the particles arising in the decay agree, as will be shown below, with these mass estimates.

IV.3. Charged hyperons producing a proton upon decay

In their second paper Bonetti et al.2 reported two new decays of charged hyperons, one of which is analogous to that described above.

In the other decay the secondary particle is a proton stopping in the emulsion. After this, it was possible to observe no fewer than five analogous decays. One of them was observed when a stack of photographic emulsions was irradiated with protons of energy \(\sim 3Bэв\) at the cosmotron3.

This decay is shown in Fig. 38. A charged hyperon (track \(Y+\)) arose in a star produced by a proton (track \(P\)), consisting of three “black” and three “thin” tracks. At point \(A\) the hyperon \(Y+\) decays, and the proton produced in its decay stops in the adjacent emulsion, having traversed a path of 1.78 mm. Data on five decays of a stopped charged hyperon into a proton are given in Table VI (decays Y-GeM\(_3\), Y-Pd\(_2\), Y-Br\(_7\), Y-Br\(_{11}\), Y-R\(_6\); the cosmotron hyperon is not included in the table). It is seen from the table that the secondary protons in all five decays have extremely close ranges (1.67, 1.67, 1.67, 1.68, and 1.60 mm of emulsion). This shows that the charged hyperons decayed after complete slowing down and that only two secondary particles were produced in the decay.

By analogy with the decay of the neutral hyperon: \(\Lambda_0 \to p + \pi^-\), the following decay scheme of the charged hyperon was proposed:

\[ Y^+ \to p + \pi^0 + Q. \]

The values of \(Q\), calculated under the assumption of decay according to this scheme, are given in Table VI. The mean weighted value of \(Q\) for the six decays considered is \(116 \pm 0.7\) MeV; such a value of \(Q\) corresponds to a mass of the \(Y^+\)-particle equal to \(2333 \pm 1.5\,m_e\).

The six decays considered give no positive indications as to the nature of the neutral secondary particles.

Friedlander et al.^113 searched for an electron pair that could have arisen from conversion of the \(\gamma\)-quantum formed in the decay of the \(\pi^0\)-meson. Such a pair was not found for either of the two decays observed by them (\(Y\)-Br\(_7\), \(Y\)-Br\(_{11}\), Table VI), although the probability of its detection in the case of \(Y\)-Br\(_7\) is \(\sim 12\%\). Finding such pairs could resolve the question of the nature of the neutral particle arising in the decay of the charged hyperon: if this particle is a \(\gamma\)-quantum, then the direction of the pair is opposite to the direction of the proton; if, however, the neutral particle is a \(\pi^0\)-meson, then the direction of the pair makes an angle with the direction of the proton which, in most cases, is close to \(162^\circ\).

Fig. 38. Decay of a charged hyperon into a proton stopping in emulsion.^112

In addition to the six decays of stopped hyperons, four decays in flight were also observed, in which protons arise

Table VI

Particle	Reference	Primary particle: \(L\) (mm)	\(n\)	\(\beta_e\)	\(\beta_d\)	\(M\) (\(m_e\))	\(t_r\) (s)	\(T_r\)	Star	Secondary particle: \(L\) (mm)	\(n\)	\(\vartheta\)	\(P^\beta\) (MeV/c)	\(E\) (MeV)	\(\beta_e\)	\(\beta_e^*\)	\(P^t\) (MeV/c)	\(P^*\) (MeV/c)	\(J/J_0\)	\(M\) (\(m_e\))	\(Q\) (MeV)	Note
Y-Bo\(_1\)	Conference in Bagnères-de-Bigorre; Phys. Rev. 92, 438 (1953)	19	Ph.E.		decay \(118 \pm 5\) MeV/c	\(2200^{+600}_{-400}\) \((d,R)\); \(2500 \pm 380\) \((g,R)\)	\(2.08\cdot10^{-10}\)	\(\infty\)	\(13+10\alpha\) (\(\tau\))	14			\(160 \pm 13\)	\(103 \pm 9\)					1.26	\(330 \pm 60\)	\(135 \pm 35\)
Y-Bo\(_2\)	Same	8			in flight	\(2460 \pm 500\) \((a,g)\)		\(\infty\)	\(17+6p\)	0.572									\(1.25 \pm 0.1\)		\(110 \pm 25\)
Y-Bo\(_3\)	” ”	5.4			” ”	\(2610^{+300}_{-250}\) \((a,g)\)			\(24+6p\)	12.450										1950 p	\(129 \pm 11\)
Y-Bo\(_4\)	” ”	24			” ”	\(2775 \pm 185\) \((a,g)\)			\(17+12p\)	0.824										p	\(225 \pm 25\)
Y-Bo\(_5\)	” ”	4.22			” ”	\(2470 \pm 300\) \((a,g)\)			\(1+2\)	116											\(212 \pm 22\)
Y-Br\(_1\)	Padua Conference (1954)	4.72	1 Ph.E.		\(0.26 \pm 0.01\)	\(2750 \pm 500\)	\(5.8\cdot10^{-11}\)		\(26+14p\)	\(\sim13\)	11 Ph.E.	\(145^\circ5\)	\(85 \pm 5\) 1/10		\(0.68 \pm 0.01\)	\(0.78 \pm 0.01\)	\(72 \pm 2\)	\(176 \pm 6\)	\(1.34 \pm 0.02\)		\(100 \pm 6\)
Y-Br\(_4\)	Same	4.4	Ph.E.		\(0.6 \pm 0.2\)	\(2500 \pm 500\)	\(\sim1\cdot10^{-11}\)		\(9+8p\)	3/em. layer, 2.5 cm	8 Ph.E.	\(24^\circ4\)	\(160 \pm 20\)						\(0.98 \pm 0.5\)		\(36 \pm 10\)
Y-Br\(_3\)	” ”	15	1		\((J/J_0=1.9)\)	\(2200 \pm 300\)			\(15+16\)	1/em. layer	16								\(1.15 \pm 0.05\)		\(65 \pm 20\)
Y-Br\(_5\)	” ”	9			\(0.54 \pm 0.02\)	\(2350 \pm 350\)	\(4\cdot10^{-11}\)		\(19+3n\) (K)	0.7/em. layer		\(46^\circ\)	180						\(\sim1\)		\(>85\)
Y-GeMi\(_1\)	Nuovo Cimento, 10, 345 (1953)	15.76	2		at rest	\(2210 \pm 250\) \((a,R)\)	\(2.14\cdot10^{-10}\)	\(\infty\)		0.12	1								\(\sim1\)			heavy electrons
Y-GeMi\(_2\)	Conference in Bagnères-de-Bigorre; Nuovo Cimento, 10, 1736 (1953)	1.25	1		at rest	\(2340 \pm 700\)	\(3.45\cdot10^{-11}\)	\(\sim\)		0.25									\(\sim1\)
Y-GeMi\(_3\)	Same	0.9	1		” ”	\(2300 \pm 800\)	\(2.72\cdot10^{-11}\)	\(\sim\)		1.670				\(18.7 \pm 2\)						\(2030^{+530}_{-480}\) \((a,R)\); \(1840 \pm 670\) \((g,R)\) p	\(115 \pm 3\)
Y-GeMi\(_4\)	Padua Conference (1954)	0.6	1		in flight				\(3+1n\)	0.1	1								\(\sim1\)
Y-GeMi\(_5\)	Same	5.82	6 Ph.E.		at rest	\(2300 \pm 600\)	\(1\cdot10^{-11}\)	\(\sim\)	\(27+5n\)	0.7 em. layer									\(\sim1\)
Y-GeMi\(_6\)	” ”	0.6	1 Ph.E.	\(0.31 \pm 0.02\)	\(0.31 \pm 0.02\)	\(2700 \pm 1350\) \((a,g)\)	\(7\cdot10\)	\(\sim\)	\(K-\)	4 em. layers	7	\(32^\circ\)	\(204 \pm 21\) \((\alpha)\)	133	0.86	0.77	126	\(167 \pm 20\)	\(1.07 \pm 0.02\)		\(95 \pm 21\)
Y-GeMi\(_7\)	” ”	4.14	2 Ph.E.	\(0.23 \pm 0.02\)	\(0.19 \pm 0.02\)	\(2700 \pm 600\) \((a,g)\)	\(5.6\cdot10\)	\(\sim\)	\(7+1n\)	2.2 em. layers	5	\(23^\circ\)	\(166 \pm 17\) \((\alpha)\)	104	0.82	0.75	79	\(160 \pm 20\)	\(1.1 \pm 0.02\)		\(90 \pm 20\)
Y-Jt\(_1\)	” ”	0.8		0.20	0.20	\(2500 \pm 900\)	\(1.4\cdot10\)			0.9		\(90^\circ+1\)		\(53 \pm 20\)					\(1.6 \pm 0.1\)	\(300 \pm 75\)	\(72 \pm 20\)
Y-Pd\(_1\)	Conference in Bagnères-de-Bigorre; Nuovo Cimento, 10, 1207 (1953)	3.25	1		0.23	\(2100 \pm 400\)	\(4.6\cdot10\)		\(11+1n\)	4.3	1	\(14^\circ\)		70						\(286 \pm 30\)	\(131 \pm 24\)
Y-Pd\(_2\)	Padua Conference (1954)	0.95	1 Ph.E.		at rest	1840	\(2.9\cdot10\)	\(\sim\)	\(5+1n\)	1.68				\(18.5 \pm 0.03\)						\(2200^{+600}_{-406}\) p	\(116 \pm 2\)
Y-Pd\(_3\)	Same	15	8 Ph.E.		\(0.371 \pm 0.007\)	\(1900 \pm 250\)	\(1.4\cdot10\)		\(11+3n\)	28.7	10	\(26^\circ\)		\(97.7 \pm 1.2\)						p	\(125 \pm 30\)
Y-Rc\(_1\)	” ”	1.8	1 Ph.E.	0.29	0.29	\(2390 \pm 500\) \((a,g)\)	\(2.1\cdot10\)		\(25+5n\)	0.7 em. layer		\(43^\circ13\)	\(195 \pm 30\) \((J/J_0)\)	\(132 \pm 30\)	\(0.855 \pm 0.13\)	\(0.806 \pm 0.13\)	\(155 \pm 3\)	\(191 \pm 35\)	\(1.015 \pm 0.05\)		\(116 \pm 50\)
Y-Ro\(_1\)	” ”	4.29	0 Ph.E.	0.219	at rest	\(1480 \pm 500\) \((a,R)\); \(3000 \pm 500\) \((g,R)\)	\(0.79\cdot10\)	\(\sim\)	\(1+0n\)	12	1 Ph.E.		50						1
Y-Ro\(_2\)	” ”	31.97	22 Ph.E.	0.4	0.17	3400; \(2100 \pm 150\) \((g,R)\)	\(3\cdot10\)		\(>8\)	7.2	7	\(55^\circ\)	\(170 \pm 30\)		\(0.821 \pm 0.04\)				\(1.25 \pm 0.08\)
Y-Ws\(_1\)	Phys. Rev. 92, 838 (1953)	3.7			at rest	\(2860 \pm 860\)	\(0.74\cdot10^{-10}\)	\(\sim\)		2.2			\(150 \pm 35\)							\(330 \pm 90\)	\(114 \pm 32\)
Y-Ww\(_1\)	Padua Conference (1954)	2.9			0.33	\(1900^{+450}_{-300}\)	\(2.9\cdot10^{-11}\)		\(17+10p\)	3		\(22^\circ\)	\(186 \pm 30\)	122						\(2000^{+450}_{-300}\) p	\(146 \pm 40\)
Data published after the Padua Conference
Y-Gi\(_1\)	Nuovo Cimento, 1955, 2, 284	1.6	3 e.k.		in flight				\(28+29p\) (\(\tau\)-meson)	23.1	34									\(271^{+195}_{-106}\)	\(135^{+15}_{-19}\); \(97^{+12}_{-15}\)	if \(\pi^\pm+n\); if \(\mu^\pm+n\)
Y-Br\(_3\)	Nuovo Cimento, 1955, 3, 482	14.6	1 e.k.		\(0.61 \pm 0.02\)	\(2500 \pm 250\) \((a,g)\)	\(0.54\cdot10^{-10}\)	\(1.84\cdot10^{-10}\)	\(12+7p\)	8.3	10	42.4		\(99 \pm 14\) by ionization							\(60 \pm 11\); \(59 \pm 11\)	if \(Y\to n+\pi\); if \(Y\to \Lambda^0+\pi\)
Y-Br\(_7\)	Same	3.6	4 e.k.		after stop.	\(2100 \pm 300\)	\(7.2\cdot10^{-11}\)		\(1+0n\)	1.67	3			\(18.77 \pm 0.19\)							\(115.8 \pm 1.0\)
Y-Br\(_8\)	” ”	13.86	1 e.k.		\(0.11 \pm 0.05\)	\(2500^{+440}_{-320}\), change in ionization	\(1.8\cdot10^{-10}\)	\(1.90\cdot10\)	\(25+2p\)	62.9	70	\(112 \pm 1\)		\(87.4 \pm 3.5\) by ionization							\(115 \pm 7\)
Y-Br\(_9\)	” ”	8.79	9 e.k.		\(0.245 \pm 0.005\)	\(>1840\), change in ionization	\(0.02\cdot10^{-10}\)	\(0.86\cdot10\)	\(13+0p\)	22.9	9	\(54.7 \pm 2\)		\(107.9 \pm 10\) by ionization							\(103 \pm 10.5\)
Y-Br\(_{11}\)	” ”	2.01	2 e.k.		after stop.	\(\sim2000\)	\(4.8\cdot10^{-11}\)	\(\sim\)	\(15+3n\)	1.602	2			\(18.32 \pm 0.32\)							\(113.5 \pm 1.7\)
Y-Br\(_6\)	Phil. Mag., 1954, No. 3, 855	17.5	e.k.		in flight	\(1850 \pm 250\) \((a,g)\)			\(19+3p\) (\(K\)-meson)	5.0 em. layer			\(190 \pm 10\)						\(1.02 \pm 0.02\)		\(116 \pm 5\)
Y-T\(_0\)	Nuovo Cim., 1955, No. 6					\(2300^{+270}_{-640}\) \((a,g)\)			\(11+14\alpha\)	16.59		\(147^\circ16' \pm 15'\)		\(30.54 \pm 0.86\)							\(97 \pm 15\); \(107 \pm 15\)	if \(Y^-\to\Lambda^0+\pi^-\); if \(Y^-\to n+\pi^-\)
Y-R\(_0\)	Nuovo Cim., 1954, No. 3, 464	1.25				\(2800^{+1500}_{-900}\) \((a,R)\); \(2670 \pm 500\) \((g,R)\)			\(p\,(17.3)\); 10; \(K\)-meson	\(1.675 \pm 0.37\)										\(>\) mass of \(\pi\)-meson	\(117 \pm 13\)

(table VI). The spectrum of values of \(Q\), calculated for all decays into a proton, according to the data of the Padua conference, is shown in the histogram of Fig. 39.

Fig. 39. Spectrum of \(Q\) values in the decay of charged hyperons \(^{111}\).

IV.4. Charged hyperons which, on decay, give a light meson

In addition to decay into a proton, decays of charged hyperons were observed both after coming to rest and in flight, in which light mesons arise. The identification of these light mesons, which have considerable energy, is associated with difficulties completely analogous to those in identifying light mesons from \(K\)-decay. In some cases the mass of the light meson could be measured. The mass values obtained in these cases are (see Table VI) \(330 \pm 60\); \(271^{+195}_{-106}\); \(300 \pm 75\); \(286 \pm 30\); \(330 \pm 90\,m_e\), and they indicate the production of \(\pi\)-mesons in such decays.

Debenедetti et al. (1955) \(^{114}\) reported the decay of a negatively charged hyperon in which a negative \(\pi\)-meson is produced. This photograph, which is the only well-defined case of the decay of a negative hyperon in emulsion, is reproduced in Fig. 40. The mass of the charged hyperon, produced in star \(11+14\alpha\), is \(2300^{+270}_{-640}\,m_e\); \((g,\alpha)\). It decays in flight at point \(A\), emitting a light meson which comes to rest in the emulsion, forming a \(\sigma\)-star characteristic of the capture of a \(\pi^-\)-meson. Details of this decay are given in Table VI. Together with the decay of a negative hyperon observed in a cosmic-ray Wilson chamber

group 173, this decay indicates that, alongside the decay \(Y^{+}\to n+\pi^{+}+Q\), there also exists the decay \(Y^{-}\to n+\pi^{-}+Q\).

Fig. 40. Decay in flight of a negative hyperon. The secondary particle is a \(\pi^{-}\)-meson and forms a characteristic \(\sigma\)-star \({}^{114}\).

The data presented on hyperon decay can thus be described by the following schemes:

\[ Y_p^{+}\to p+\pi^{0}+Q_1, \tag{1} \]

\[ Y_L^{\pm}\to n+\pi^{\pm}+Q_2. \tag{2} \]

If the particles \(Y_p\) and \(Y_L\), decaying according to schemes (1) and (2), have one and the same mass, then

\[ Q_1-Q_2=n-p+(\pi-\pi^{0}), \]

from which it follows that \(Q_1 = Q_2 + \sim 6\) Mev. Therefore an exact determination of the quantities \(Q_1\) and \(Q_2\) should help in deciding the question of the identity of the charged hyperons which, in the decay, form a proton and a charged \(\pi\)-meson.

In Fig. 39 are shown histograms of the values of \(Q\), constructed from the data of the Padua conference for decays which could be assigned either to scheme (1) or to scheme (2). The maxima of the distributions \(Q_1\) and \(Q_2\) are indeed shifted by an amount smaller than 10 Mev, which is an argument in favor of the hypothesis of two competing decays of a \(Y\)-particle with a mass close to \(2300m_e\).

Not all decays found in emulsion can be explained by schemes (1) and (2) with values \(Q_1 \simeq 116\) and \(Q_2 \simeq 110\) Mev. Thus, for example, for two decays into a proton the values \(Q = 212 \pm 22\) and \(225 \pm 25\) Mev were obtained (see Table VI, decays Bo\(_5\) and Bo\(_4\), and Fig. 39). In decays into a light meson the values \(Q = 36 \pm 10,\ 72 \pm 20,\ 65 \pm 20\), and \(60 \pm 11\) Mev were obtained (see Table VI, decays Br\(_4\), Jt\(_1\), Br\(_3\)), and the histogram of the values of \(Q\) for \(Y_\pi\)-decay shows a scatter considerably exceeding the scatter in the case of \(Y_p\)-decays. It could be explained by the hypothesis of decay into three particles. Low values \(Q \sim 60\text{--}70\) Mev can be understood if one assumes that there exists still another type of charged hyperon, decaying into a neutral hyperon \(\Lambda^0\) and a \(\pi\)-meson:

\[ Y \to \Lambda^0 + \pi + \sim (60\text{--}70)\ \text{Mev}. \tag{3} \]

IV.5. Cascade decays in the Wilson chamber

In the Wilson chamber 5 decays have been found which can be interpreted according to scheme (3)\(^{115-118}\). They are detected by the characteristic double decays of a charged (\(Y\)) and a neutral (\(\Lambda^0\)) hyperon (cascade decay). The first case of a cascade decay was found by the Manchester group at Pic-du-Midi in 1951\(^{115}\). One of the three cascade decays found by the Pasadena group\(^{117}\) is shown in Fig. 41. A negatively charged \(Y^-\)-particle decays in the upper left corner of the chamber, forming a meson which goes upward to the right, and a neutral \(V^0\)-particle which decays after traveling 1.6 cm from the point of decay of the \(Y^-\). The difficulty of interpreting decays of this type as cascade decays lies in the fact that the inaccuracies in measuring the angles between tracks do not make it possible to exclude the possibility that these decays may have been produced by two particles, \(Y^-\) and \(\Lambda^0\), born in a common nuclear interaction and emitted in nearby directions. The decay shown in Fig. 41 excludes such a possibility, since the angles are measured accurately enough to assert that the tracks of the \(Y^-\) and \(\Lambda^0\) particles do not issue from a common point.

The momentum arising in the \(\Lambda^0\)-decay of the positive particle is equal to \(730 \pm 100\ \mathrm{MeV}/c\), the ionization is \((2.35 \pm 0.26)\, I_{\min}\), whence for the mass there follows the value \(2050 \pm 350\, m_e\), close to the proton mass. From the measured momentum of the negative particle \((295 \pm 40\ \mathrm{MeV}/c)\), its ionization \((1.25 \pm 0.14)\), and the angle between the prongs of the fork \((6.5^\circ \pm 1)\), the value \(Q = 40 \pm 13\ \mathrm{MeV}\) was obtained. These

Fig. 41. Cascade decay of a negatively charged hyperon in a Wilson magnetic chamber \({}^{117}\).

data make it possible with confidence to identify the observed \(V^0\)-shaped track with the decay of a neutral hyperon

\[ \Lambda^0 \to p + \pi^- + \sim 37\ \mathrm{MeV}. \]

The light meson arising in the decay of the \(Y^-\)-particle has a momentum of \(69 \pm 10\ \mathrm{MeV}/c\) and an ionization of \(3.4\, I_{\min}\), which makes it possible to identify it with a \(\pi\)-meson, which at the same momentum would have had an ionization of \(3.7\, I_{\min}\). Thus, the cascade decay under consideration can be described by the following scheme:

\[ Y^- \to \Lambda^0 + \pi^- \]

\[ \downarrow p + \pi^- + 37\ \mathrm{MeV}. \]

The value \(Q\) for the decay \(Y^- \to \Lambda^0 + \pi^- + Q\) is equal to \(67 \pm 12\ \mathrm{MeV}\), whence for the mass of the cascade-decaying hyperon we obtain

\[ M \simeq 2600 \pm 34\, m_e . \]

IV.6. Mean Lifetime of Charged Hyperons

The mean lifetime of charged hyperons was estimated from their flight time in a photographic emulsion. Of the 30 hyperons that decayed in the emulsion (see Table VI), 23 decayed in flight and only 7 after stopping. It follows from this that their mean lifetime is comparable with the mean flight time in an emulsion chamber, which is of the order of \(10^{-11}\)—\(10^{-10}\) sec. Amaldi, Castagnoli, and others\(^{119,120}\) estimated the mean lifetime by extending the flight-time method, developed for the Wilson chamber, to measurements in an emulsion chamber (see I.5.2.). The value of the mean lifetime obtained by them from an analysis of ten decays is

\[ \left(2.9^{+4.8}_{-1.1}\right)\cdot 10^{-10}\ \text{sec}. \]

This value was calculated under the assumption that all types of hyperons have the same lifetime.

(To be concluded in the next issue)

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