From Current Literature

DIRECT METHODS FOR MEASURING LIFETIMES AND A NEW METHOD FOR SELECTING HEAVY UNSTABLE PARTICLES IN COSMIC RADIATION

The mean lifetime of an unstable particle, along with its charge, mass, spin, and decay scheme, is its most important characteristic. On the nuclear scale of time, the mean lifetimes of the heavy unstable particles known at present are extraordinarily long. However, from the point of view of the capabilities of experimental technique, these times are very small, and until recently almost the only method for determining them was the measurement of the flight time of heavy unstable particles before decay in a Wilson chamber[^1] or in photographic emulsions[^2]. Averaging the most reliable values of the mean lifetimes of hyperons (particles with masses greater than the neutron mass) and \(K\)-mesons (particles with masses between the mass of the \(\pi\)-meson and the neutron mass), obtained by this method by various investigators, led to the following results[^1,^2]. The particle most frequently registered—the neutral hyperon (\(\Lambda^0\)-particle in the new notation and \(V_1^0\)-particle in the old notation), with mass \(2181 \pm 1\,m_e\), decaying into a proton and a \(\pi\)-meson, has a mean lifetime equal to

\[ T_{\Lambda^0} = (3.7^{+0.8}_{-0.6}) \times 10^{-10}\ \text{sec}. \]

The neutral \(K^0\)-meson (\(\vartheta^0\)-particle in the new notation, \(V_2^0\) in the old notation) has a mass close to \(970\,m_e\), decays into two charged \(\pi\)-mesons, is encountered 4–5 times less often than the \(\Lambda^0\)-particle, and its mean lifetime is

\[ T_{\vartheta^0} = (1.7^{+1.6}_{-0.7}) \times 10^{-10}\ \text{sec}. \]

The mean lifetimes of charged hyperons are also of the order of \(10^{-10}\) sec. They were estimated from the flight time of these particles before decay in photographic-emulsion chambers. Thus, for example, from an analysis of ten decays[^2] the following value was obtained for the lifetime of charged hyperons:

\[ T_Y = (2.9^{+4.8}_{-1.1}) \times 10^{-10}\ \text{sec}. \]

The quoted values of the mean lifetimes cannot be measured by direct radio-technical methods similar to those which in their time were used to measure the lifetimes of \(\mu\)-mesons and, later, with the appearance of scintillation counters, of \(\pi\)-mesons. Indeed,

even when the fastest electronic circuits are used; the resolving time of fast scintillation and Cherenkov counters used in combination with ordinary photomultipliers is of the order of \(10^{-9}\) sec., which is the lower limit of the lifetimes measurable by means of these counters.

Among the heavy unstable particles, however, there is a large group of particles whose mean lifetime is approximately two orders of magnitude greater than the mean lifetime of hyperons and \(\vartheta\)-particles, and therefore can be measured by direct methods. These particles apparently include all or almost all varieties of charged \(K\)-mesons, to which we shall now turn.

The best-studied particle of this group is the \(\tau\)-meson. Its mass is \(966 \pm 1\,m_e\); it decays into three \(\pi\)-mesons according to the scheme

\[ \tau^\pm \to \pi^\pm + \pi^+ + \pi^- . \tag{1} \]

In all, in emulsions and emulsion chambers, about 50 \(\tau\)-decays have so far been observed. In all these cases the decays occurred after the particles had come to rest, whence it follows that the mean lifetime of \(\tau\)-mesons cannot be less than their total slowing-down time, close to \(10^{-8}\) sec.\(^3\). It is also known\(^3\) that there exists a competing branch of \(\tau\)-decay: the \(\tau\)-meson can decay into a charged and two neutral \(\pi\)-mesons,

\[ \tau^\pm \to \pi^\pm + \pi^0 + \pi^0 \tag{2} \]

and theory predicts\(^4\) that such decays should constitute an appreciable fraction \(\left(\dfrac{1}{4} \div \dfrac{1}{2}\right)\) of the decays along the principal branch (1).

In the works of A. I. Alikhanian and collaborators it was shown that there exist positively and negatively charged particles with a mass of about \(950\,m_e\). These particles were observed in an extended apparatus in which the length of the trajectories was close to 1.5 meters, whence it follows that the mean lifetime of these particles is not less than \(5 \cdot 10^{-9}\) sec.\(^5\).

Data obtained with emulsions and emulsion chambers\(^6\) also indicate that, besides \(\tau\)-mesons, there exist \(K\)-mesons with a mass close to \(970\,m_e\), decaying according to the schemes:

\[ \chi^\pm \to \mu^\pm + ? + ? \tag{3} \]

\[ \chi^\pm \to \pi^\pm + ? \tag{4} \]

The energy of the \(\mu\)-mesons arising in the decay of \(\chi\)-mesons into three particles is distributed over a wide range of values, whereas the decay of stopped \(\chi\)-mesons gives rise to monochromatic \(\pi\)-mesons. Experiments with magnetic and multi-plate Wilson chambers\(^7\) confirmed the presence of mesons with a mass of about \(1000\,m_e\), decaying into \(\mu\)- and \(\pi\)-mesons, and supplemented our information about such decays by showing that among the neutral particles formed in decays (3) and (4) there are \(\gamma\)-quanta, arising either directly or in the decay of a \(\pi^0\)-meson:

\[ \chi^\pm \to \mu^\pm + \gamma + ? \tag{3'} \]

\[ \chi^\pm \to \pi^\pm + \pi^0 \quad \text{(energy of the \(\pi^\pm\)-mesons \(\sim 108\) MeV, range \(\sim 60\ \mathrm{g/cm^2}\)).} \tag{4'} \]

Estimates of the lifetime of charged \(K\)-mesons, made by measuring

their flight times in Wilson chambers, confirmed that the mean lifetimes of these particles are large, namely, lie within the range \(4\cdot 10^{-9}—10^{-8}\) sec.\(^{1}\)

It should be noted that recently data have been obtained indicating that electrons sometimes arise in the decay of charged \(K\)-mesons.\(^{8}\) In such decays, apparently, two more neutral particles also arise:

\[ K \to e + ? + ? \tag{5} \]

In addition, French physicists,\(^{9}\) who studied the stopping of heavy mesons in a multiplate Wilson chamber, above which was placed a magnetic Wilson chamber used to measure the momentum of the decaying particles, came to the conclusion that the decays they observed were caused by particles with a mass of about \(920\,m_e\), decaying into a \(\mu\)-meson and a neutrino:

\[ K \to \mu + \nu, \tag{6} \]

and having mean lifetimes close to \(10^{-8}\) sec.\(^{9}\) From this list of possible decay schemes for \(K\)-particles it follows that the whole problem of the decay of \(K\)-particles is at present far from clear. Nevertheless, all estimates of the mean lifetimes of \(K\)-particles show that these times are large enough that one may try to measure them by a direct method. The main difficulty arising in such measurements is that the fluxes of these particles in cosmic radiation are extremely small, while the background caused by various phenomena that imitate decay (for example, fluctuations of the onset of a pulse in a counter, or air-shower particles shifted in time), is extraordinarily large in comparison with the effect being studied. In addition, it must be borne in mind that, since the decay schemes of \(K\)-mesons have not been definitively established and it is not even clear whether the schemes given above belong to different particles or are competing decay schemes of one and the same particle with a mass of about \(970\,m_e\), in planning and interpreting such experiments there is a difficulty connected with assigning the measured lifetime to definite particles.

The first direct measurement of the lifetime of \(K\)-mesons was carried out in work \(^{10}\). The arrangement of the apparatus is shown in Fig. 1. It consists of a liquid scintillation counter \(S\), two Cherenkov counters \(C\), three rows of Geiger counters \(g_1, g_2, g_3\), connected in coincidence, and lead and aluminum absorbers. In the work, directional Cherenkov counters are used, consisting of a Lucite vessel filled with distilled water, blackened below and viewed from above by the photomultiplier \(У\). The counter efficiency is 90% for fast \(\mu\)-mesons moving from below upward, i.e. toward the photomultiplier, and 0.4% for particles moving from above downward.

Fig. 1.

This apparatus and the associated radio-engineering circuit select events of the following type. A charged unstable particle, born in a high-energy nuclear interaction in the upper “generating” layer of lead, crosses the scintillation counter \(S\) and is stopped in one of the Cherenkov counters \(C\) or near it. Then it decays, and if the secondary particle is emitted upward and has a velocity exceeding the threshold velocity of the Cherenkov counter, it is registered by it.

In this case the counter remains insensitive to shower particles passing through it in the opposite direction, from top to bottom. The time interval between the triggering of counters \(S\) and \(C\) was measured by means of a 17-channel time-measuring circuit of the “chronotron” type\(^{11}\). The hodoscopic system of counters \(g_1, g_2, g_3\) made it possible to exclude from consideration delays connected with the passage of shower particles through the setup.

The threshold value of the particle velocity causing the Cherenkov counter to operate was checked experimentally: the counter registers particles with velocity \(v_c \ge 0.76c\), which corresponds to electrons, \(\mu\)-mesons, and \(\pi\)-mesons with energies greater than 250 kev, 50 Mev, and 70 Mev, respectively.

With such a threshold, the system will obviously not register charged \(\pi\)-mesons arising in the decay of \(\tau\)-mesons (1) or (2), since the maximum energy of these mesons is close to 50 Mev, i.e. less than the threshold energy. However, the \(\pi^0\)-mesons arising in the second branch of \(\tau\)-decay, because of their short lifetime (\(10^{-15}\) sec), will not have time to move far from the stopping point of the \(\tau\)-meson and will give \(\gamma\)-quanta, which will be registered by the Cherenkov counter through secondary electrons. Therefore the system considered is undoubtedly sensitive to the second type of \(\tau\)-decay, which, according to recent data\(^{3}\), constitutes a considerable part of the main branch. As for decays of \(K\)-particles into \(\mu\)- and \(\pi\)-mesons or into electrons, decays of the type (4), (5), and (6) will certainly be registered by the system, while decays (3) will be registered in those cases in which the \(\mu\)-meson acquires sufficiently large energy in the decay.

Fig. 2.

The results of the measurements are presented in Fig. 2, where the decay curve obtained is shown. Along the abscissa is plotted the time in \(10^{-9}\) sec, and along the ordinate the number of decay events falling within a time interval of \(3.1 \cdot 10^{-9}\) sec. The “bell-shaped” part of the curve, with tails extending into the region of positive and negative shifts, corresponds to random shifts caused by fluctuations in the time of appearance of pulses in counters \(S\) and \(C\) and by shifts due to shower particles. These shifts, ...

...constituting the background of the measurements, were measured separately, and the corresponding data are shown in Fig. 2 by the dotted line. The straight portion in Fig. 2 corresponds to the exponential decay law. Analyzing this portion of the decay curve under the assumption of a single decay time, the authors obtained for the mean lifetime of the \(K\)-particles the value:

\[ T_K = (8.7 \pm 1.0)10^{-9}\ \text{sec}. \]

In the second group of papers under consideration \(^{12,13}\), simultaneously with the measurement of the lifetime of charged \(K\)-particles by a method close to that examined \(^{13}\), the tracks of these particles were photographed in Wilson chambers \(^{12}\) (altitude 2850 m, Pic du Midi). The experimental setup included (Fig. 3; the timing scheme is not shown in the figure)

Fig. 3.

a multi-plate Wilson chamber (six lead plates 1 cm thick), in which there was also a Cherenkov counter \(C_2\) with a photomultiplier. The system of controlling counters, located above the chamber, consisted of a Cherenkov counter \(C_1\), two scintillation counters (\(S_1\)—a solution of terphenyl in xylene, \(S_2\)—a solution of terphenyl in phenylcyclohexane), and two rows of Geiger counters \(g\). The Cherenkov counters were triggered only by a particle passing through at high velocity. The system of counters above the chamber selected coincidences of pulses from the counters \(S_1, S_2, g\), not accompanied by a pulse from the Cherenkov counter \(C_1\) (coincidences \(H = S_1 + S_2 + g - C_1\)). These coincidences \(H\), evidently, were caused by a heavy particle that had passed through the entire system and, because of its low velocity, had not produced a signal in the Cherenkov counter \(C_1\). The Cherenkov counter \(C_1\) was filled with distilled water. In work \(^{14}\) it was shown that the critical velocity for such a counter is determined by the relation \(M_0 c^2 \geq 6.8 R_0\,M\text{eV}\), where \(R_0\) is the thickness of the layer of material between \(C_1\) and \(g_1\), expressed in g/cm\(^2\). Particles whose mass is less than \(M_0\), passing through the absorber \(R_0\), will have a velocity greater than the critical one and will cause the counter \(C_1\) to operate. \(R_0\) was chosen so that \(M_0 \geq 300 m_e\). Thus, \(\mu\)- and \(\pi\)-mesons passing through the system caused the counter \(C_1\) to operate and were not registered by the system, whereas heavier particles, if their velocity was less than the critical one, were not recorded by counter \(C_1\) and gave coincidences \(H\).

The expansion of the chamber was controlled by coincidences \(H + C_2\), occurring within the resolving time \(5 \cdot 10^{-6}\) sec. The critical speed for the counter \(C_2\), filled with a mixture of equal volumes of glycerin and water, was \(0.71c\), and it was triggered by electrons and \(\mu\)-mesons with energies close to the triggering energy of the counter in work \({}^{11}\). Thus, the system considered was specially adjusted to select single slow heavy particles with mass greater than \(300\,m_e\), traveling without accompaniment by other particles, which after stopping in the multiplate Wilson chamber emit fast charged particles or annihilation products. Such a method of selecting heavy particles when working with a Wilson chamber is of great interest, since the installations that have existed up to now selected penetrating showers in which heavy unstable particles were found. The only exception in this respect is the mass spectrometer of Alikhanian and his co-workers, which also recorded single particles.

The amplitude of the signal from counter \(C_2\) in coincidences \(H + C_2\) was recorded by means of a cathode oscillograph, and, for a known path length of the charged particle in \(C_2\), could serve as a measure of its speed. Above the whole installation there was a layer of lead (14.5 cm) or paraffin (80 cm), not shown in Fig. 3, which served as a “generator” of heavy mesons. The base of the “generating” layer was 80 cm away from the counter \(C_1\), so that shower particles had time to diverge. This increased the probability that a single heavy particle traveling without accompaniment would enter the system.

The selection system recorded 67 \((H + C)\) coincidences per day. Since the chamber recovery time is 5 minutes, the number of photographs taken is somewhat smaller, namely 56 per day. In this case, only 0.1 photograph per day corresponds to the sought effect: the stopping of a heavy particle in one of the plates of the chamber and the emergence from this plate of a fast secondary particle passing through the counter \(C_2\). A sketch of one such case, representing typical \(S\)-decays \({}^{7*}\), is given in Fig. 4. Thus

Fig. 4.

in this way, 99.8% of all photographs constitute a background of measurements, consisting of electron showers that did not strike the counter \(C\) (19 photographs per day), slow protons entering directly onto the photocathode or the first dynode of the multiplier of counter \(C_2\) and thereby producing an impulse at its output (3 per day), single particles passing through the system and not causing the counter \(C_1\) to be triggered because of fluctuations in—

* Heavy unstable particles stopping in the plates of the Wilson chamber and emitting a secondary charged particle are called \(S\)-particles (from the word stopped); decays of this type are \(S\)-decays.

of Čerenkov radiation (10 photographs); in addition, 21 photographs per day are not associated with the passage of a charged particle through \(C_2\), but are explained by the presence of \(\gamma\)-rays accompanying showers and producing secondary electrons in \(C_2\), and 3 photographs per day are caused by slow protons stopping in the plates of the chamber and causing the appearance of \(\gamma\)-quanta from excited nuclei.

The results of this experiment are as follows. In all, during 2000 hours of operation, 8 particles were observed which stopped in the lead plates in the well-illuminated part of the Wilson chamber and emitted secondary charged particles that entered counter \(C_2\). The secondary particles do not multiply and are not scattered appreciably in the lead plates, whence it follows that they are not electrons. Nor were any soft electronic cascades from \(\gamma\)-rays connected with the decay detected; but the small number of observed decays does not, of course, allow one on this basis to reject possible decay schemes (3) or (4). In three cases the range of the secondary particles proved to be greater than \(60\ \mathrm{g}/\mathrm{cm}^2\), i.e. greater than the range of the \(\pi\)-mesons arising in decay according to scheme (4′).

In principle, as already indicated, the velocity of the particle in \(C_2\) can be determined from the magnitude of the signal and from the length of its path. In reality, such measurements with statistically insufficient material have little value because of fluctuations in the magnitude of the signal in \(C_2\). However, the authors consider it possible, on the basis of their measurements, to estimate the mean momentum of the secondary particles, assuming preliminarily that all of them are monochromatic \(\mu\)-mesons, i.e. that the decay proceeded according to scheme (6). The value they obtained,
\(P_{\mu}=275^{+160}_{-60}\ \mathrm{MeV}/c\), is in agreement with the assumption made, since the momentum of \(\mu\)-mesons arising in the decay of particles of mass about \(970\,m_e\) according to scheme (6) should be about \(\sim 240\ \mathrm{MeV}/c\).

It is of interest to compare the flux of \(K\)-particles with the flux of protons. The authors indicate that for each \(K\)-particle, 1750 slow protons pass through their apparatus and stop in the plates of the chamber. If corrections are introduced that take into account the small geometrical efficiency of the system for detecting secondary charged particles by means of counter \(C_2\), then one \(K\)-particle corresponds to 300 protons.

The installation described is sensitive to antiprotons annihilating in the lead plates and producing relativistic annihilation products that pass through \(C_2\). Despite the fact that during 2000 hours of operation of the installation \(5\cdot 10^4\) protons passed through the system, not a single event resembling antiproton annihilation was recorded.

As indicated above, in this experiment a measurement was also made of the time between the firing of counters \(S_1\) and \(C_2\) for the observed decays \(^{13}\). After introducing the appropriate corrections for the flight time of the primary and secondary particles, from the 8 measured lifetimes one can statistically obtain the “most probable” mean lifetime of the \(K\)-particles, of course on the assumption that this is a homogeneous group of particles decaying according to a single exponential. The value obtained in this way is:

\[ T_K=\left(15.8^{+8.7}_{-4.0}\right)\times 10^{-9}\ \text{sec}. \]

If the five additional decays detected in the poorly illuminated parts of the chamber are included in the consideration, we obtain:

\[ T_K=\left(11.0^{+4.0}_{-2.4}\right)\times 10^{-9}\ \text{sec}. \]

Both these values, within the limits of the measurement error, agree with the result of the preceding work \(^{10}\) and with all the estimates of the mean lifetime of \(K\)-particles given above.

In conclusion, let us compare the yield of \(K\)-mesons with the particle-selection method used by the authors with the yield of heavy mesons in other methods. According to Fowler’s data, \(3 \cdot 10^{-3}\) heavy mesons per day per gram of absorber are found in a stack of nuclear emulsions placed under 30 cm of lead at an altitude of 3300 m. In the Alps, Briddige, in his multiplate chamber, triggered by penetrating showers, recorded \(0.6 \cdot 10^{-6}\) \(S\)-particles per day per gram of absorber (altitude 3000 m). In the present work about \(1.4 \cdot 10^{-6}\) \(S\)-particles per gram of absorber per day were recorded; that is, despite the fact that these estimates are very approximate, it is clear that the new selection system proved to be considerably more effective than selection by penetrating showers. At the same time, comparison of these figures with the yield of unstable particles in the emulsion method indicates the possibility of further increasing the yield of heavy unstable particles in observations with chambers.

A. V.

References Cited

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