Full Text
HEAVY UNSTABLE PARTICLES*)
(Hyperons and \(K\)-Mesons)
A. O. Weisenberg
CONTENTS
V. Charged \(K\)-mesons . . . . . . . . . . . . . . . . . . . . . 631
VI. Charged \(V^{\pm}\)-particles . . . . . . . . . . . . . . . . . 667
VII. Generation of hyperons and \(K\)-mesons and their interaction with nuclei . . 673
V. CHARGED \(K\)-MESONS
V.1. \(\tau\)-mesons
V.1.1. Decay scheme. Charged particles that decay into three \(\pi\)-mesons are called \(\tau\)-mesons:
\[ \tau^{\pm} \to \pi^{+}+\pi^{-}+\pi^{\pm}. \]
Two examples of \(\tau\)-decays were given in Figs. 1 and 2. Of all types of charged \(K\)-particles, the \(\tau\)-mesons have been studied in the greatest detail. This is explained by the fact that they live relatively long (\(\sim 10^{-8}\) sec), and therefore decay after coming to rest in the emulsion, while the secondary \(\pi\)-mesons carry away a relatively small energy, close to \(\sim 75\) MeV, so that the mean range of the secondary \(\pi\)-mesons in the emulsion is small. Therefore, even in single emulsions it was quite often possible to observe the stopping of the secondary particles, which greatly facilitated the establishment of the \(\tau\)-meson decay scheme from the very first observations of this particle. By the present time, more than 40 decays of \(\tau\)-mesons stopped in emulsion have been examined\(^{121}\); their principal decay scheme has been established with complete reliability, and the value of \(Q\), and consequently also the mass of the \(\tau\)-meson, have been measured with great accuracy. However, if one disregards the accuracy of the measurements, it should be noted that, in essence, everything that we now know about the principal decay scheme of the \(\tau\)-meson was stated by Brown, Camerini, and others\(^{1}\) as the most probable variant of the decay scheme, on the basis of an analysis of the first \(\tau\)-decay (Fig. 1), recorded by Young and Yox in the first experiments with emulsions sensitive to electrons.
*) For the beginning of the article see UFN, Vol. LVII, issue 3, p. 362.
A detailed analysis of the data on \(\tau\)-mesons published up to the middle of 1954 is given in the report of the Committee on \(\tau\)-mesons at the Padua Conference\(^{121}\). In this section we consider the conclusions of that report, supplemented by the most important papers published later.
From the totality of the available data it follows that the three charged \(\pi\)-mesons arising in the decay of \(\tau\)-mesons are the only secondary particles. This follows from the coplanarity of the momenta of the three \(\pi\)-mesons formed in the decay of a \(\tau\)-meson stopped in an emulsion, and from the uniqueness of the values of \(Q\) for the observed \(\tau\)-decays. Thus, the basic decay scheme of the \(\tau\)-meson has the form
\[ \tau^{\pm} \to \pi^{\pm} + \pi^{+} + \pi^{-} + Q. \]
V.1.2. The value of \(Q\) and the mass of the \(\tau\)-meson. The mean weighted value of the kinetic energy \(Q\) of the three \(\pi\)-mesons arising in \(\tau\)-decay, measured for decays in emulsion chambers, is
\[ Q = 74.7 \pm 0.3\ \text{MeV}. \]
The mass of the \(\tau\)-meson obtained from this value of \(Q\) is
\[ M_{\tau} = 2m_{\pi^{+}} + m_{\pi^{-}} + Q = (819.3 \pm 0.4) + Q = (965.5 \pm 0.7)m_e. \]
The results of a direct measurement of the masses of \(\tau\)-mesons in an emulsion chamber are presented in Fig. 42, where the mass values were plotted
Fig. 42. Results of direct measurement of masses for \(\tau\)-mesons\(^{124}\).
by the method of equal areas. The mean weighted value of these determinations of the masses, \(M_{\tau} = (960 \pm 40)m_e\), is in agreement with the value \(M_{\tau}\) determined from the decay scheme.
V.1.3. Competing decay schemes of the τ-meson. τ′-meson.
Recently, besides decay into three π-mesons, other types of decay of particles with a mass close to the mass of the τ-meson, stopping in photographic emulsion, have been discovered; these may be competing decay schemes of the τ-meson.
By the time of the Padua conference, seven cases had been observed of the decay of particles with a mass close to that of the τ-meson into a charged π-meson, which are interpreted as an alternative decay of the τ-meson into a charged π-meson and two neutral π⁰-mesons:
\[ \tau^{\pm}\to\pi^{\pm}+\pi^{0}+\pi^{0}. \]
The τ-meson decaying according to this scheme was given the designation \((\tau)_{K\pi}\), or τ′-meson.
One example of the proposed decay of the τ′-meson is shown in Fig. 43[^122]. A particle with a mass close to that of the τ-meson emerged
Fig. 43. Decay of a τ′-meson
\[
\tau' \to \pi^{+}+\pi^{0}+\pi^{0}.
\]
The sign of the charge of the π-meson is determined by the decay
\[
\pi \to \mu \to e
\]
[^122].
from a star and stopped in the emulsion. In its decay a π-meson arose, identified by the \(\pi\to\mu\to e\) decay. The maximum energy that the π-meson can receive in the decay of the τ′-meson is 57 MeV. It receives such an energy if its momentum is balanced by two equal momenta of the two other π-mesons.
In all seven proposed τ′-decays the energy of the charged π-meson is less than this value (the energy values are 4.3, 6.0, 14.7, 15.2, 22.7, 41.5, 44.5 MeV), which makes the above interpretation of these decays quite plausible.
V. B. Berestetskii \(^{123}\) calculated, under the assumption that the \(\tau\)-meson has unit isotopic spin, the ratio of the probabilities of decay of the \(\tau\)-meson: \(\dfrac{w(\tau)}{w(\tau')}\). He obtained that this ratio, depending on the form of the wave function used, is equal to 4 or 1. The experimentally obtained ratio is close to \(\dfrac{40}{7}\sim 6\).
Possible occurrence of a \(\gamma\)-quantum in \(\tau\)-decay \((\tau \to \pi+\pi+\pi+\gamma)\). Daniel and Pal \(^{10}\) recently reported an interesting case of \(\tau\)-decay which does not fit into the usual decay scheme. A \(\tau\)-meson, produced in a star of type \(9+1n\) (or \(9+0p\)), traveled, before stopping, through 90 emulsion layers, with a range of \(8.7\ \text{cm}\). Two positive secondary particles stopped in the emulsion and gave the characteristic \(\pi \to \mu \to e\)-decay. The third, negative particle left the emulsion. Its mass, determined by the \((\alpha, g)\) method, was \(315 \pm 75\,m_e\), which agrees with the mass of the \(\pi\)-meson. The sum of the kinetic energies of the three charged mesons was \(46 \pm 2.2\ \text{MeV}\), which is considerably less than the decay energy of the \(\tau\)-meson, \(Q\sim 75\ \text{MeV}\). Moreover, the three tracks of the secondary particles prove to be definitely non-coplanar. Thus, this \(\tau\)-meson decay cannot be described by the usual decay scheme \(\tau \to 3\pi+ \sim 75\ \text{MeV}\). It is most plausible to suppose that in this case one more alternative form of \(\tau\)-decay has been observed, in which, along with the three \(\pi\)-mesons, a fourth, neutral particle is emitted, carrying away the excess of energy and momentum. Direct measurements of the mass of the stopped \(\tau\)-meson gave the value \(980 \pm 50\,m_e\), and, consequently, this neutral particle cannot be a \(\pi^0\)-meson. Restricting ourselves to known particles, it is natural to suppose that in this case a \(\gamma\)-quantum was emitted (a neutrino is excluded, since it has half-integer spin):
\[ \tau \to \pi^+ + \pi^+ + \pi^- + \gamma . \]
Starting from the law of conservation of momentum, one can calculate the momentum \(p_4\) carried away by the \(\gamma\)-quantum. It is equal to \(32.1 \pm 2.7\ \text{MeV}/c\), whence for the total decay energy one obtains the value \(Q=46.1+32.1=78.2\pm 4.8\ \text{MeV}\), which agrees well with \(Q\sim 75\ \text{MeV}\). The observed “anomalous” decay of the \(\tau\)-meson is also of interest because, if \(\gamma\)-quanta of high energy can arise also in the decays of other particles, then their occurrence could explain the noticeable number of so-called “anomalous” decays of other unstable particles, when the values of \(Q\) are too small (see III.3.6).
V.1.4. Charge of \(\tau\)-mesons decaying in emulsion. The charge of \(\tau\)-mesons was determined from the charge of the secondary mesons arising in the decay: \(\pi^+\)-mesons, after stopping, underwent \(\pi \to \mu \to e\)-decay; \(\pi^-\)-mesons produced a \(\sigma\)-star or were not detected.
no phenomena at the end of the range. Data on the signs of the charge of secondary particles, obtained for 28 of the 40 known τ-decays, are given in the table.
For nine of the 28 τ-decays considered, the positive sign of the τ-meson charge is established beyond doubt: in six cases two π⁺-mesons and one π⁻-meson are observed in the decay \((+ + -)\), and in three cases both secondary particles whose sign could be established are π⁺-mesons \((+ +)\). The remaining data of the table admit only a statistical analysis. If τ-mesons of both signs are detected in the emulsion with equal probability, then the expected number of observations of π⁺- and π⁻-mesons \((+ -)\) should be twice the number of observations of two π⁺-mesons \((+ +)\), and the number of detected single π⁺-mesons \((+)\) should be twice the number of single π⁻-mesons \((-)\). The data given in the table on the number of \((+ +)\) and \((+ -)\), and \((+)\) and \((-)\) cases agree sufficiently well with their expected number.
| Charge data for τ-mesons | Charge data for τ-mesons |
|---|---|
| Charges of secondary particles | Number of τ-mesons |
| \((+,\ +,\ -)\) | 6 |
| \((+,\ ?)\) | 3 |
| \((+,\ -)\) | 11 |
| \((+)\) | 6 |
| \((-)\) | 2 |
Thus, the data given in the table indicate that all τ-mesons decaying after stopping in emulsion are positively charged, and give no indication of the presence of negatively charged mesons. We note that, in the decay of τ⁻-mesons stopped in emulsion, one might have observed a violation of the coplanarity of the tracks of the three π-mesons, associated with the fact that before decay the τ⁻-meson would have been in a Bohr orbit around a nucleus. The absence of such violations of coplanarity also confirms the conclusion reached.
V.1.5. Positive excess for τ-mesons. In Wilson chambers, 15 τ-mesons decaying in flight were observed¹²⁴. The first observations of such decays were made by Leighton and Wanlass¹²⁵ (1952). Decays of τ-mesons in flight were also observed by Annis and German¹²⁶, Van Lint and Trilling¹²⁷, Gaither¹²⁸, and other authors. The only case of the decay of a τ-meson that stopped in the plate of a Wilson chamber was observed by Alikhanyan and collaborators in 1953. A photograph of the decay in flight of a slow τ-meson in a Wilson chamber, obtained by Gaither, is shown in Fig. 44. Of the total number of 15 τ-mesons decaying in flight in Wilson chambers, 11 are positively and 4 negatively charged¹²⁴. These data indicate the existence of a significant positive excess among τ-mesons arising in nuclear interactions.
V.1.6. Spin and parity of τ-mesons. The energy spectrum of π-mesons emitted in the decay of τ-mesons is substantially
depends on the spin and parity of the \(\tau\)-meson. This problem was studied by Dalitz\({}^{129}\), who indicated simple methods for analyzing experimental data obtained with individual emulsions, when most often the sign of the meson charge cannot be determined. With the advent of emulsion chambers it became possible in many cases to determine the energy and the sign of the charge of all three secondary \(\pi\)-mesons.
Fig. 44. Decay of a slow \(\tau\)-meson in flight in a Wilson chamber\({}^{128}\).
Methods for analyzing the data for this case were indicated by Fabri\({}^{130, 131}\), who also took into account relativistic effects in the spectrum of the secondary particles. If the energy of the negative particle is \(E_-\), and the energies of the two positive \(\pi\)-mesons in increasing order are \(E'_+\) and \(E''_+\), then, according to Fabri, the criterion of the spin and parity of the \(\tau\)-meson may be the distribution of the observed decays over the following three energy intervals:
\[ a)\ E_- > E'_+, E''_+,\qquad b)\ E''_+ > E_- > E'_+,\qquad c)\ E''_+, E'_+ > E_-. \]
In case \(b)\) the energy of the negative meson has a value intermediate between the energies of the positive mesons; in cases \(a)\) or \(c)\) it is greater or less than these energies.
At present, 20 $\tau$-mesons are known for which the signs of the charge and the energies of all secondary particles have been determined. These decays are distributed in the following way among the indicated intervals $a$, $b$, $c$:
| Interval | $a$ | $b$ | $c$ |
|---|---|---|---|
| Number of $\tau$-decays | 7 | 8 | 5 |
In Fig. 45 are shown the distributions of particles over the intervals $a$, $b$, $c$ calculated by Fabri for several combinations of spin and parity. A comparison of this distribution with the distributions calculated by Fabri is given in the following table, where $\chi^2$ is a coefficient characterizing the quadratic deviation of the calculated distribution, shown in Fig. 46, from the distribution given in the preceding table:
Fig. 45. Distribution of the energy of secondary $\pi$-mesons depending on the spin and parity of the $\tau$-meson according to Fabri$^{130,131}$.
| Spin and parity | $0-$ | $1+$ | $1-$ | $2+$ | $3-$ |
|---|---|---|---|---|---|
| $\chi^2$ | 0.7 | 2.9 | 3.1 | 5.7 | 0.3 |
The insufficient number of observed decays does not allow a definite choice to be made among the indicated combinations of spin and parity; however, from this table it is seen that the most probable spin and parity are $(0-)$ or $(3-)$.
V.1.7. Mean lifetime of $\tau$-mesons. On the basis of the data accumulated up to the present time$^{121}$, the mean lifetime of $\tau$-mesons can be estimated from the following considerations. Among 40 decays of $\tau$-mesons in emulsion, not a single decay of a $\tau$-meson in flight was observed. For a $\tau$-meson stopping in emulsion, the time of ionization slowing down can be calculated. The total slowing-down time for all known $\tau$-decays in emulsion is less than $8 \times 10^{-9}$ sec. During this time not a single decay in flight was observed, whence it follows that the mean lifetime of the $\tau$-meson must be greater than $\sim 10^{-8}$ sec. Analysis of data obtained with Wilson chambers also leads to the conclusion of a large lifetime of $\tau$-mesons, in agreement with the value obtained from analysis of their decays in emulsions.
V.2. \(K\)-mesons decaying into one charged particle (emulsion data)
By the present time, about 150 stops in photographic emulsions of charged particles with mass \(\sim 1000\,m_e\) have been described in detail; in their decay one charged particle and one or more neutral particles arise. The first two decays of this type were discovered by O’Ceallaigh in 1951 in a systematic study of the spectrum of electrons arising in the decay of \(\mu\)-mesons \(^{132}\). Table VII gives data known from the literature on \(K\)-decays, summarized at the Padua Conference \(^{124, 138}\).
V.2.1. Nature of the secondary particles. The data obtained up to the present make it possible to assert that the secondary charged particles arising in the decay of \(K\)-mesons are \(\mu\)- and \(\pi\)-mesons and electrons.
a. Evidence for the existence of \(\mu\)-mesons among the secondary particles. Fig. 46 shows a microphotograph of the second \(K\)-decay observed by O’Ceallaigh \(^{132}\) (case \(Br_2\) from Table VII). This photograph is remarkable in that it unambiguously establishes the nature of the secondary particle arising in the decay of the stopped particle \(x\). The secondary particle travels a path of \(1.1\) mm in the emulsion and decays into an electron; it is a \(\mu\)-meson. Three more such \(K\)-decays, in which the secondary particle could be identified from the \(\mu \to e\) decay in the emulsion, were discovered by Amaldi and collaborators \(^{133}\), by the Polytechnic School group \(^{134}\), and by Friedlander et al. \(^{135}\). Along with undoubted cases of the appearance of a secondary \(\mu\)-meson in the decay of \(K\)-particles, fast light mesons emerging from the emulsion were observed. In a considerable number of such decays, the measurements \((g,\ \alpha)\) do not make it possible to distinguish \(\pi\)-mesons from
Fig. 46. Decay of a \(K\)-meson into a \(\mu\)-meson. The heavy meson \(x_2\) reaches the end of its range at point \(P\) and decays, emitting a \(\mu\)-meson with range \(1096\,\mu\). The \(\mu\)-meson stops at point \(Q\) and emits an electron. The track of the \(x\)-meson is shown in two sections. Its mass, measured from grain density and scattering, is \(1125 \pm 230\,m_e\) \(^{132}\).
Table VII
Data on decays of \(K\)-mesons stopped in emulsions \(^{1}\)
| \(K\)-particle | Star | Range (in mm) | Flight time (in \(10^{-9}\) sec) | Mass (in \(m_e\)) \((g, R)\) | Mass (in \(m_e\)) \((a, R)\) | Length (in mm) | \(g^*\) | \(p\beta\) (\(MэВ/c\)) | Mass (in \(m_e\)) |
|---|---|---|---|---|---|---|---|---|---|
| Вк\(_1\) | ? | 9,0 | 0,1068 | — | \(850 \pm 200\) | — | — | — | — |
| Во\(_1\) (*) | \(20 \pm 5\,n\) | 13,7 | 0,1462 | \(950 \pm 100\) | \(955 \pm 140\) | — | — | \(226 \pm 20\) | — |
| Во\(_2\) (*) | \(14 \pm 2\,n\) | 11,3 | 0,1232 | \(1120 \pm 100\) | \(980 \pm 155\) | — | \(0,96 \pm 0,12\) | — | — |
| Во\(_3\) (*) | ? | 5,4 | 0,0744 | \(1115 \pm 100\) | \(1025 \pm 95\) | — | 1 | — | — |
| Во\(_4\) (*) | \(1 \pm 2\,n\) | 32,0 | 0,2618 | \(980 \pm 100\) | \(740 \pm 85\) | — | \(0,93 \pm 0,07\) | — | — |
| Во\(_5\) (*) | \(8 \pm 2\,a\) | 13,3 | 0,1386 | \(865 \pm 100\) | \(1005 \pm 170\) | — | — | — | — |
| Во\(_6\) (*) | \(21 \pm 3\,p\) | 5,0 | 0,0704 | — | \(1050^{+280}_{-200}\) | 25,0 | \(1,045 \pm 0,02\) | \(240 \pm 25\) | — |
| Вг\(_1\) | ? | 4,1 | 0,0622 | \(1380 \pm 180\) | \(1260 \pm 260\) | 2,2 | \(0,97 \pm 0,04\) | \(235 \pm 35\) | \(\mu\;(\pi, e)\) |
| Вг\(_2\) | ? | 5,67 | 0,0782 | \(1125 \pm 150\) | \(1125 \pm 230\) | 1,1 | — | 11,8 | \(\mu\) |
| Вг\(_3\) | ? | 0,53 | 0,0138 | — | \(1000 \pm 2000\) | 5,9 | \(0,96 \pm 0,026\) | \(144 \pm 12\) | \(\mu(e)\) |
| Вг\(_4\) | ? | 2,1 | 0,0368 | — | \(1370 \pm 320\) | 0,17 | 1 | — | — |
| Вг\(_5\) | ? | 1,54 | 0,0286 | \(950 \pm 200\) | \(1220 \pm 400\) | 8,9 | \(1,705 \pm 0,083\) | \(66 \pm 11\) | \(\mu(\pi)\) |
| Вг\(_6\) | ? | 2,55 | 0,0442 | \(1036 \pm 280\) | \(1036 \pm 280\) | 0,1 | 1 | — | — |
| Вг\(_7\) | ? | 0,38 | 0,0114 | — | 1000 | 2,5 | \(1,09 \pm 0,05\) | \(170 \pm 29\) | \(\pi(\mu)\) |
| Вг\(_8\) | ? | 2,55 | 0,0418 | \(900 \pm 200\) | \(1460 \pm 320\) | 7,65 | \(1,14 \pm 0,025\) | \(187 \pm 17\) | \(\pi\) |
| Вг\(_9\) | ? | 0,63 | 0,0168 | — | 1000 | 19,5 | \(1,094 \pm 0,016\) | \(162 \pm 9\) | \(\pi\) |
\(^{1}\) The \(K\)-particles listed in Table VII are designated according to the place where they were found and are provided with a number. For example, Вг\(_{24}\) denotes the 24th \(K\)-particle of the Bristol group, Ко\(_5\) the fifth \(K\)-particle of the Copenhagen group, Рер the particles of the Polytechnic School, etc. Similar designations are used in Table VI.
Continuation of Table VII
| \(K\)-particle | star | range (in mm) | flight time (in \(10^{-9}\) sec) | mass (in \(m_e\)) \((g, R)\) | mass (in \(m_e\)) \((\alpha, R)\) | length (in mm) | \(g^*\) | \(p\beta\) \((\mathrm{MeV}/c)\) | mass (in \(m_e\)) |
|---|---|---|---|---|---|---|---|---|---|
| \(Br_{10}\) | ? | 1,38 | 0,0286 | — | \(1100 \pm 330\) | 0,275 | 1 | — | — |
| \(Br_{11}\) | ? | 0,54 | 0,0153 | — | 1300 | 0,1 | 1 | — | — |
| \(Br_{12}\) | ? | 13,2 | 0,1386 | — | \(1210 \pm 150\) | 0,15 | 1 | — | — |
| \(Br_{13}\) | ? | 0,96 | 0,0224 | — | \(1089 \pm 450\) | 0,2 | 1 | — | — |
| \(Br_{14}\) | ? | 0,44 | 0,0536 | — | \(925 \pm 190\) | 0,5 | \(1,02 \pm ,10\) | \(120 \pm 44\) | \(\mu(e,\pi)\) |
| \(Br_{15}\) | ? | 9,56 | 0,1152 | — | \(1100 \pm 170\) | 4,1 | \(1,028 \pm ,031\) | \(184 \pm 30\) | \(\pi(\mu,e)\) |
| \(Br_{16}\) | ? | 1,7 | 0,0314 | — | 1000 | 2,8 | \(1,030 \pm ,045\) | \(153 \pm 24\) | \(\mu(\pi)\) |
| \(Br_{17}\) | ? | 4,31 | 0,0644 | — | \(1200 \pm 230\) | 6,5 | \(1,15 \pm ,03\) | \(172 \pm 17\) | \(\pi\) |
| \(Br_{18}\) | ? | 1,85 | 0,0342 | — | 1500 | 4,0 | 1 | \(315 \pm 70\) | \(\mu(\pi,e)\) |
| \(Br_{19}\) | ? | 1,02 | 0,0224 | — | \(1000 \pm 2000\) | 2,8 | 1 | \(125 \pm 35\) | \(\mu(\pi,e)\) |
| \(Br_{20}\) | ? | 6,675 | 0,0858 | — | \(990 \pm 150\) | 0,18 | 1 | — | — |
| \(Br_{21}\) | \(1+0\,n\) | 0,35 | 0,0105 | — | — | 18,0 | \(0,93 \pm\) | \(205 \pm 5\) | \(-\mu\) |
| \(Br_{22}(*)\) | \(1-0\,p\) | 28,0 | 0,2384 | — | \(780 \pm 90\) | 6,0 | \(1,09 \pm ,04\) | \(170 \pm 20\) | — |
| \(Br_{23}(*)\) | \(19+3\,n\) | 7,56 | 0,0930 | \(990 \pm 150\) | — | 3,0 | — | — | — |
| \(Br_{24}(*)\) | \(10+0\,p\) | 8,56 | 0,1034 | \(1200 \pm 200\) | \(1400 \pm 200\) | 54,0 | \(1,2 \pm ,1\) | \(119 \pm 9\) | \(203 \pm 8\) |
| \(Br_{25}(*)\) | \(24+3\,p\) | 3,77 | 0,0580 | \(1000 \pm 250\) | \(1150 \pm 250\) | 0,5 | — | — | — |
| \(Br_{26}(*)\) | \(19+24\) | 42,1 | 0,3170 | \(990 \pm 55\) | \(1100 \pm 150\) | — | 1 | 100 | — |
| \(Br_{27}\) | ? | 8 | 0,1000 | — | — | — | — | — | — |
| \(Br_{28}\) | ? | 8 | 0,1000 | — | — | — | — | — | — |
| \(Br_{29}\) | ? | 1,3 | 0,1386 | — | 1000 | — | — | — | — |
| \(Br_{30}(*)\) | ? | 40 | 0,3064 | — | — | Energy 50–60 MeV, estimated from the change in grain density | Energy 50–60 MeV, estimated from the change in grain density | Energy 50–60 MeV, estimated from the change in grain density | Energy 50–60 MeV, estimated from the change in grain density |
Continuation of Table VII
| Primary particles | Primary particles | Primary particles | Primary particles | Primary particles | Primary particles | Secondary particles | Secondary particles | Secondary particles | Secondary particles |
|---|---|---|---|---|---|---|---|---|---|
| \(K\)-particles | star | range (in mm) |
flight time (in \(10^{-9}\) sec) |
mass (in \(m_e\)) \((g, R)\) |
mass (in \(m_e\)) \((a, R)\) |
length (in mm) |
\(g^*\) | \(p\beta\) (MeV/c) |
mass (in \(m_e\)) |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| \(B_{31}\) (*) | \(13+3p\) | 19.09 | 0.1814 | \(900\pm200\) | — | — | 1 | \(145\pm25\) | — |
| \(B_{32}\) (*) | \(27+3p\) | 19.18 | 0.1814 | — | — | — | — | — | — |
| \(B_{33}\) (*) | \(7+5p\) | 4.03 | 0.0602 | \(850\pm200\) | — | — | 1 | \(112\pm20\) | — |
| \(B_{34}\) (*) | \(23+13p\) | — | — | — | — | — | — | — | — |
| \(B_{35}\) (*) | \(15+5p\) | 48.36 | 0.3064 | \(910\pm200\) | — | — | — | — | — |
| \(B_{36}\) (*) | — | — | — | — | — | — | — | — | — |
| \(B_{37}\) (*) | \(4+0n\) | 8 | 0.1000 | — | \(720\pm200\) | Preliminary data | Preliminary data | 67 | Possibly, electron |
| \(B_{33}\) (*) | \(11+4p\) | 18.81 | 0.1746 | \(1200\pm200\) | — | — | — | — | — |
| \(B_{39}\) (*) | ? | 23 | 0.2012 | \(900\pm200\) | — | — | — | — | — |
| \(B_{40}\) (*) | — | — | — | — | — | — | — | — | — |
| \(B_{41}\) (*) | \(19+3n\) | 39.0 | 0.2954 | 950 | — | — | — | — | — |
| \(\mathrm{GeMi}_1\) | ? | 2.0 | 0.3690 | — | \(1270\pm290\) | 3.44 | \(0.94\pm.03\) | \(150\pm27\) | — |
| \(\mathrm{GeMi}_2\) | \(30+8\alpha\) | 5.26 | 0.0744 | \(1050\pm140\) | \(1030\pm165\) | 0.45 | \(1.15\pm.1\) | — | — |
| \(\mathrm{GeMi}_3\) | \(36+6p\) | 1.88 | 0.0342 | \(1170\pm270\) | \(1540\pm380\) | 2.08 | \(1.14\pm.03\) | \(108\pm18\) | \(190\pm32\) |
| \(\mathrm{GeMi}_4\) | ? | \(1.47+\) | 0.0286 | — | \(1360\pm340\) | 2.5 | \(1.06\pm.04\) | \(200\pm33\) | \(300\pm50\) |
| \(\mathrm{GeMi}_5\) | ? | 0.64 | 0.0168 | — | 1000 | — | — | — | — |
| \(\mathrm{GeMi}_6\) | ? | 3.4 | 0.0536 | \(980\pm290\) | \(1010\pm200\) | — | — | — | — |
| \(\mathrm{GeMi}_7\) | ? | 12.57 | 0.1350 | — | \(1100\pm165\) | 0.6 | — | — | — |
| \(\mathrm{GeMi}_8\) (*) | \(4+0n\) | 5.69 | 0.0782 | — | \(1380\pm270\) | — | — | — | — |
| \(\mathrm{GeMi}_9\) (*) | \(7+0p\) | 19.24 | 0.1814 | — | \(1015\pm160\) | 51.0 | \(1.12\pm.012\) | \(135+7\) | — |
Continuation of Table VII
| $K$-particle | star | range (in mm) | flight time (in $10^{-9}$ sec) | mass (in $m_e$), $(g, R)$ | mass (in $m_e$), $(\alpha, R)$ | length (in mm) | $g^{*}$ | $p\beta$ (MeV/$c$) | mass (in $m_e$) |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| GeMi$_{10}$ (*) | ? | 18.5 | 0.1746 | — | $1025\pm200$ | 40.0 | $0.97\pm0.012$ | $150\pm10$ | — |
| GeMi$_{11}$ (*) | $10+7p$ | 18.33 | 0.1746 | — | $900\pm125$ | 53.0 | $0.97\pm0.13$ | $190\pm15$ | — |
| GeMi$_{12}$ (*) | $4+2p$ | 15.85 | 0.1534 | — | $850\pm120$ | 60.0 | $1.21\pm0.025$ | $146\pm10$ | — |
| GeMi$_{13}$ (*) | $16+0p$ | 9.4 | 0.1068 | — | $870\pm165$ | — | — | — | — |
| Bx$_1$ | ? | 3.0 | 0.0490 | — | $800\pm160$ | — | — | — | — |
| Bx$_2$ | ? | 2.0 | 0.0368 | — | $750\pm170$ | — | — | — | — |
| Bx$_3$ | ? | 1.4 | 0.0286 | — | $985\pm255$ | — | — | — | — |
| Bx$_4$ | ? | 20.0 | 0.1880 | — | $1100\pm110$ | 5.0 | 1.09 | $200\pm30$ | — |
| It$_1$ | ? | 5.0 | 0.0704 | — | $1020\pm140$ | 0.2 | $1.12\pm0.11$ | — | — |
| It$_2$ | ? | 0.52 | 0.0138 | — | — | 4.7 | $1.07\pm0.03$ | $172\pm26$ | $280\pm50$ |
| It$_3$ | ? | 0.12 | 0.0051 | — | — | 2.5 | $2.75\pm0.08$ | $24.5\pm25$ | $191\pm30$ |
| It$_4$ | ? | 11.3 | 0.1232 | $1080\pm150$ | $1000^{+260}_{-190}$ | 0.13 | 1 | — | — |
| It$_5$ | ? | 10.4 | 0.1152 | $1030\pm250$ | $1190\pm400$ | 0.34 | $1.15\pm0.14$ | — | — |
| It$_6$ | ? | 1.7 | 0.0314 | — | 1000 | 0.25 | $1.56\pm0.14$ | — | — |
| It$_7$ | ? | 0.44 | 0.0122 | — | — | 0.64 | $1.1\pm0.1$ | $111\pm35$ | $190\pm60$ |
| Ko$_1$ (*) | ? | 1.4 | 0.0286 | — | $1680^{+760}_{-520}$ | 21.0 | $0.93\pm0.02$ | $190\pm20$ | — |
| Ko$_2$ (*) | ? | 0.3 | 0.0097 | — | — | — | — | — | — |
| Ko$_3$ (*) | $12+2p$ | 3.0 | 0.0490 | $1110\pm160$ | $1100\pm300$ | 64.0 | $0.96\pm0.015$ | $223\pm22$ | Possibly, $\pi$ |
| Ko$_5$ (*) | $11+12p$ | 30.0 | 0.2502 | — | $970\pm210$ | 58.0 | $1.02\pm0.02$ | $167\mp8$ | Probably, $\pi$ |
Continuation of Table VII
| \(K\)-particle | Star | Range (mm) | Flight time (in \(10^{-9}\) sec) | Primary particles: mass (in \(m_e\)) \((g, R)\) | Primary particles: mass (in \(m_e\)) \((a, R)\) | Secondary particles: length (mm) | Secondary particles: \(g^*\) | Secondary particles: \(p\beta\) (MeV/\(c\)) | Secondary particles: mass (in \(m_e\)) |
|---|---|---|---|---|---|---|---|---|---|
| \(K_{06}\) (*) | \(6 \pm 1p\) | 5.3 | 0.0744 | \(1000 \pm 40\) | \(880 \pm 160\) | — | — | — | — |
| \(K_{07}\) (*) | \(16 \pm 2n\) | 44 | 0.3276 | — | \(1630 \pm 160\) | 34 | — | — | — |
| \(K_{08}\) (*) | \(23 \pm 9p\) | 15.0 | 0.1534 | — | — | — | — | — | — |
| \(\mathrm{Os}_1\) | \(16 \pm 3p\) | 14.0 | 0.1462 | — | \(1090 \pm 180\) | 2.5 | \(1.05 \pm .03\) | \(126 \pm 21\) | \(200 \pm 20\) |
| \(\mathrm{Mn}_3\) | ? | 3.28 | 0.0512 | \(1000 \pm 150\) | \(1030 \pm 300\) | 9.1 | \(1.010 \pm .05\) | \(124 \pm 12\) | — |
| \(\mathrm{Pd}_1\) | \(29 \pm 4n\) | 0.29 | 0.0168 | — | — | 0.6 | \(1.05 \pm .05\) | \(158 \pm 53\) | — |
| \(\mathrm{Pd}_2\) | \(21 \pm 2n\) | 2.6 | 0.0440 | — | \(1030 \pm 320\) | 0.2 | \(1.03 \pm .2\) | — | — |
| \(\mathrm{Pd}_3\) (*) | \(20 \pm 7n\) | 42.5 | 0.3170 | \(964 \pm 60\) | — | 21.0 | — | \(160 \pm 10\) | \(270 \pm 33\) |
| \(\mathrm{Pd}_4\) (*) | \(15 \pm 1p\) | 19.14 | 0.1814 | \(975 \pm 200\) | \(961 \pm 122\) | 40.0 | — | \(110 \pm 15\) | — |
| \(\mathrm{Pd}_5\) (*) | \(4 \pm 1p\) | 19.31 | 0.1814 | \(1006 \pm 100\) | \(920 \pm 330\) | 37.5 | — | \(70 \pm 16\) | — |
| \(\mathrm{Pd}_6\) (*) | \(14 \pm 11p\) | 17.24 | 0.1676 | \(850 \pm 100\) | \(685 \pm 290\) | 44.4 | — | \(52 \pm 20\) | — |
| \(\mathrm{Pd}_7\) (*) | \(5 \pm 1p\) | 36.5 | 0.2844 | \(943 \pm 60\) | \(948 \pm 100\) | 24.0 | — | \(150 \pm 9\) | \(276 \pm 30\) |
| \(\mathrm{Pd}_8\) (*) | \(15 \pm 7a\) | 26.93 | 0.2262 | \(1180 \pm 140\) | \(895 \pm 225\) | — | — | \(190 \pm 40\) | — |
| \(\mathrm{Pd}_9\) (*) | \(17 \pm 2p\) | 12.0 | 0.1310 | \(1060 \pm 100\) | \(1420 \pm 360\) | 21.0 | — | \(153 \pm 36\) | — |
| \(\mathrm{Pd}_{10}\) (*) | \(10 \pm 5p\) | 25.2 | 0.2262 | \(1100 \pm 160\) | — | 10.0 | — | \(67 \pm 15\) | — |
| \(\mathrm{Pep}_1\) | ? | 1.3 | 0.0256 | \(1150 \pm 300\) | \(970 \pm 300\) | 20.0 | \(0.97 \pm .03\) | \(197 \pm 13\) | \(\mu\) |
| \(\mathrm{Pep}_2\) | \(13 \pm 18p\) | 4.95 | 0.0700 | \(900 \pm 75\) | \(860 \pm 75\) | 0.16 | \(0.85 \pm .2\) | — | — |
| \(\mathrm{Pep}_3\) | \(9 \pm 2p\) | 6.04 | 0.0820 | \(1015 \pm 85\) | \(1090 \pm 130\) | several grains | — | — | — |
| \(\mathrm{Pep}_4\) | \(6 \pm 1p\) | 9.0 | 0.1068 | \(910 \pm 70\) | \(890 \pm 90\) | 0.85 | \(1.0 \pm .1\) | — | — |
| \(\mathrm{Pep}_5\) | ? | 1.52 | 0.0290 | \(800 \pm 250\) | \(1070 \pm 220\) | 0.2 | 1 | — | — |
Continuation of Table VII
| $K$-particle | star | path length (in mm) | flight time (in $10^{-9}$ sec) | mass (in $m_e$), $(g,R)$ | mass (in $m_e$), $(\alpha,R)$ | length (in mm) | $g^{*}$ | $p\beta$ (MeV/$c$) | mass (in $m_e$) |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Pe$_6$ | ? | 1.4 | 0.0286 | $960\pm220$ | $825\pm180$ | 3.4 | $0.975\pm0.05$ | $290\pm60$ | — |
| Pe$_8$ (*) | $28+6p$ | 9.5 | 0.1068 | $980\pm150$ $862\pm60$ |
$920\pm155$ | — | 1 | — | — |
| Pe$_9$ (*) | $2+0p$ | 2.05 | 0.0368 | $950\pm250$ | $1210\pm390$ | — | 1 | — | — |
| Pe$_{10}$ (*) | $11+2p$ | 8.7 | 0.1034 | $990\pm150$ $920\pm60$ |
$1100\pm200$ | — | 1 | — | — |
| Pe$_{11}$ (*) | $29+11p$ | 2.7 | 0.0442 | $950\pm140$ | $1083\pm294$ | — | 1 | — | — |
| Pe$_{12}$ (*) | $13+5p$ | 37.4 | 0.2954 | $960\pm130$ | $850\pm180$ | — | 1 | — | — |
| Pe$_{13}$ (*) | ? | 19.3 | 0.1880 | $880\pm80$ $960\pm130$ |
$1420\pm310$ | 7.18 | $1.03\pm0.03$ | $200\pm20$ | — |
| Pe$_{14}$ (*) | ? | 9.63 | 0.1152 | $1240\pm90$ $1300\pm175$ $1050\pm90$ |
$934\pm165$ | 23.205 | $E=-33.3$ MeV | — | ± |
| Pe$_{15}$ (*) | $21+0p$ | 4.66 | 0.0684 | — | $1005\pm320$ | — | 1 | — | — |
| Pe$_{16}$ (*) | $8+2p$ | 27.8 | 0.2384 | — | $1075\pm190$ | — | $0.96\pm0.09$ | — | — |
| Pe$_{17}$ (*) | $3+6p$ | 14.0 | 0.1462 | — | — | 49 | $1.05\pm0.02$ | $180\pm10$ | — |
| Pe$_{18}$ (*) | ? | 10.3 | 0.1152 | — | $1195\pm260$ | — | 1 | — | — |
| Pe$_{19}$ (*) | $4+0n$ | 0.585 | 0.0153 | — | — | — | $1.14\pm0.11$ | — | — |
| Pe$_{20}$ (*) | ? | 18.0 | 0.1746 | — | — | — | 1 | — | — |
| Pe$_{22}$ (*) | ? | 40.0 | 0.3064 | — | $1120\pm160$ | 20 | $0.98\pm0.02$ | $194\pm34$ | — |
Continuation of Table VII
| Primary particles | Primary particles | Primary particles | Primary particles | Primary particles | Primary particles | Secondary particles | Secondary particles | Secondary particles | Secondary particles |
|---|---|---|---|---|---|---|---|---|---|
| \(K\)-particles | star | range (in mm) |
flight time (in \(10^{-9}\) sec) |
mass (in \(m_e\)) \((g, R)\) |
mass (in \(m_e\)) \((\alpha, R)\) |
length (in mm) |
\(g^*\) | \(p\beta\) (MeV/\(c\)) |
mass (in \(m_e\)) |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| \(\mathrm{Pep}_{23}\ (*)\) | \(7\perp 0n\) | 29,5 | 0,2384 | — | \(1230\pm240\) | 5 | \(1,16\pm,15\) | \(195\pm30\) | — |
| \(\mathrm{Pep}_{24}\ (*)\) | \(19\perp 1p\) | 18,4 | 0,1814 | — | \(1060\pm200\) | — | — | — | — |
| \(\mathrm{Rc}_{1}\ (*)\) | \(16\perp 0n\) | 7,54 | 0,0930 | — | \(660\pm210\) | — | — | — | — |
| \(\mathrm{Rc}_{2}\ (*)\) | \(25\perp 15n\) | 23,8 | 0,2138 | — | \(1020\pm300\) | — | — | — | — |
| \(\mathrm{Rc}_{3}\ (*)\) | \(8\perp 0n\) | 49,5 | 0,3582 | — | \(850\pm125\) | — | \(1,02\pm,06\) | — | — |
| \(\mathrm{Rc}_{4}\ (*)\) | \(6\perp 3p\) | 3,6 | 0,0558 | — | \(1060\pm260\) | — | — | — | — |
| \(\mathrm{Rc}_{5}\ (*)\) | ? | 31,8 | 0,2618 | — | \(950\pm220\) | — | — | — | — |
| \(\mathrm{Rc}_{6}\ (*)\) | \(9\perp 4\) | 40 | 0,3064 | — | \(1030\pm160\) | — | — | — | — |
| \(\mathrm{Rc}_{7}\ (*)\) | ? | 20,2 | 0,1880 | \(980\pm130\) | — | 14,6 | \(E=28\) MeV | \(E=28\) MeV | \(\mu\) |
| \(\mathrm{Ro}_{1}\ (*)\) | \(16\perp 8n\) | 12,1 | 0,1310 | \(1020\pm65\) | \(1040^{+280}_{-140}\) | \(\pi\)-meson: \(E=38,5\) MeV (3—ray \(\sigma\)-star) |
\(\pi\)-meson: \(E=38,5\) MeV (3—ray \(\sigma\)-star) |
\(\pi\)-meson: \(E=38,5\) MeV (3—ray \(\sigma\)-star) |
— |
| \(\mathrm{Ro}_{2}\ (*)\) | ? | 24,6 | 0,2138 | \(935\pm40\) | — | 29,0 | \(1,24\pm0,07\) | — | — |
| \(\mathrm{Ro}_{3}\ (*)\) | \(14\perp 6n\) | 20,2 | 0,01880 | \(860\pm35\) \(980\pm60\) \(950\pm50\) |
\(1020^{+150}_{-120}\) — \(+120\) |
18 | \(1,07\pm,06\) | \(230\pm30\) | — |
| \(\mathrm{Ro}_{4}\ (*)\) | \(6\perp 0p\) | 35,7 | 0,2844 | \(1000\pm40\) \(980\pm330\) \((\alpha, g)\) |
720 \(-90\) |
4,83 | \(E=13,6\pm,3\) MeV | \(E=13,6\pm,3\) MeV | \(\mu\) |
μ-mesons, but in certain most favorable cases with sufficiently long tracks this can be done. Thus, for example, Fig. 47 presents the results of measurements of \((g,\alpha)\) for the decay \(\mathrm{Br}_{24}\) (see Table VII); the length of the track of the secondary particle before leaving the emulsion chamber is \(5.4\ \mathrm{cm}\), and the dependence \((g,p\beta)\) can be checked with sufficient statistical accuracy at several points of the track[^136]. As is seen from Fig. 47, the corresponding experimental points lie well on the curve for μ-mesons and do not agree at all with the curve \((g,p\beta)\) for π-mesons, obtained on the basis of measurements of \((g,\alpha)\) in tracks of shower particles. The mass of the μ-meson obtained from the curve in Fig. 47 is \(203 \pm 8\,m_e\). In addition to the case considered, there are also other analogous cases in which accurate measurements of the mass of the secondary particle make it possible to identify it confidently with a μ-meson (see the decays \(\mathrm{Br}_{21}\), \(\mathrm{Pep}_1\), \(\mathrm{Pep}_{14}\), \(\mathrm{Rc}_7\), \(\mathrm{Ro}_4\) in Table VII).
Fig. 47. Dependence of the grain density \(g^*\) on \(p\beta\) for the secondary particle in the decay of a \(K\)-meson (decay \(\mathrm{Br}_{24}\) from Table VII)[^136].
6. Evidence for the existence of π-mesons among secondary particles. The evidence for the presence of π-mesons among secondary particles is not so indisputable, since up to now no cases of stopping of secondary π-mesons in emulsion have been detected. Therefore all evidence for the production of π-mesons in \(K\)-decays is based on measurements of the mass of secondary particles by scattering and grain density, and on searches for nuclear interactions of secondary particles. In some cases measurements of \((g,\alpha)\) make it possible to separate secondary π-mesons from μ-mesons quite well. Thus, for example, Fig. 48 shows the results of measurements of \((g,\bar{\alpha})\) on three sections of a track \(19.5\ \mathrm{mm}\) long belonging to a secondary particle produced in the decay \(\mathrm{Br}_9\)[^137] (see Table VII). Despite the fact that the ionization is very close to minimum, these measurements make it possible to distinguish the π-meson from the μ-meson fairly well. Similar results were obtained by other investigators[^139],[^140].
It should be noted that very strong evidence for the presence of π-mesons among the fast secondary mesons arising in the decay of \(K\)-particles would be the observation of interaction of these meso-
of them with the nuclei of the emulsion. The total path length traversed by all secondary particles identified, from the measurements \((g,\alpha)\), with \(\pi\)-mesons is close to 22 cm (see the data of Table VII), whereas the mean path length for the interaction of \(\pi\)-mesons with energy \(\sim 100\) MeV in emulsion is \(\sim 25\) cm. Only in 1955 did Rao and Mitra \(^{141}\) discover one case of an undoubted nuclear interaction: the secondary particle which, according to the \((g,\alpha)\)-measurements, is a light meson, produces in flight a star of five strongly ionizing particles.
Fig. 48. Dependence of \(g^*\) on \(p\beta\) for a secondary particle in the decay of a \(K\)-meson (decay \(\mathrm{Br}_9\) from Table VII) \(^{137}\).
V.2.2. Spectrum of secondary \(\mu\)- and \(\pi\)-mesons. Table VII gives 12 \(K\)-decays (\(\mathrm{Br}_2\), \(\mathrm{Br}_{21}\), \(\mathrm{Br}_{24}\), \(\mathrm{GeM}_{13}\), \(\mathrm{H}_3\), \(\mathrm{H}_7\), \(\mathrm{Os}_1\), \(\mathrm{Pd}_8\), \(\mathrm{Pep}_1\), \(\mathrm{Pep}_{14}\), \(\mathrm{Rc}_7\), \(\mathrm{RO}_4\)), in which the secondary particle can be confidently identified with a \(\mu\)-meson either by \(\mu \to e\) decay or by measurements \((g,\alpha)\). In the same table are included data on nine \(K\)-decays for which the secondary particle can be identified with a \(\pi\)-meson with a sufficient degree of confidence. Figure 49 shows the distribution of \(p\beta\) for these two different types of \(K\)-decays. From the graphs it is seen that the values of \(p\beta\) in the case of \(K \to \mu\)-decay are distributed over a wide range of values from 10 to 210 MeV/\(c\). It follows that, if all these \(\mu\)-mesons arose as the result of the decay of a \(K\)-particle of one type, then in such a decay at least two neutral secondary particles also arise. On the basis of these data the Bristol group \(^{137}\) proposed the existence of \(\chi\)-mesons decaying according to the scheme
\[ \chi^{\pm}\to \mu^{\pm} + ? + ?, \]
where \(?\) are neutral particles, about whose nature very little can be said from these experiments.
In contrast to the spectrum of \(\mu\)-mesons, the spectrum of \(\pi\)-mesons (Fig. 49) indicates the existence of a monochromatic line. This points to decay into two particles. Mesons of this type, whose existence was also postulated by the Bristol group \({}^{137}\), were given the name \(\chi\)-mesons. Their decay scheme has the form
\[ \chi^{\pm} \to \pi^{\pm} + \; ? . \]
In constructing the spectra of secondary \(\mu\)- and \(\pi\)-mesons, the most reliable cases from Table VII were used. One may
Fig. 49. Spectra of \(p\beta\) for secondary \(\mu\)- and \(\pi\)-mesons in \(K\)-decays.
also include in the consideration particles whose nature is determined with a lesser degree of certainty, i.e., for example, one may regard all particles with mass less than \(240\,m_e\) as \(\mu\)-mesons, and particles with greater mass as \(\pi\)-mesons. In Table VII, the less probable nature of such particles is indicated in parentheses. For example, the notation \(\mu(\pi)\) means that the mass of the particle is less than \(240\,m_e\), but the statistical accuracy of the measurements does not allow one to exclude completely the assumption that it is a \(\pi\)-meson. The spectra of all secondary \(\mu\)- and \(\pi\)-mesons are given in Fig. 49. They fully support the conclusions drawn from consideration of the most reliably identified particles.
V.2.3. Masses of primary particles. The results of direct measurements of the masses of \(K\)-mesons are given in Table VII,
from which it is seen that the errors of individual mass measurements are too large for one to be able to hope to separate different masses in the interval \(900—1000\,m_e\).
The first measurements of the masses of \(K\)-mesons in photographic emulsions, carried out by the Bristol group for tracks several millimeters long, gave values in the range \(1100—1400\,m_e\) (see Table VII, decays \(\mathrm{Br}_1—\mathrm{Br}_{19}\)). With the appearance of emulsion chambers, considerably longer tracks became accessible to measurement. It then turned out that there is a certain correlation between the track length and the measured mass value: measurements on long tracks, performed with substantially greater statistical accuracy, gave considerably smaller mass values, lying in the range \(800—1000\,m_e\). Table VII gives masses obtained from measurements of \((g, R)^*)\) and \((\alpha, R)\). Table VIII gives the mean weighted mass values of \(x\)- and \(\chi\)-particles, the spectra of the momenta of whose secondary particles were given in Fig. 49.
Table VIII
Mean weighted mass value
| \(g, R\) | \(\alpha, R\) | |
|---|---|---|
| \(M_x\) | \(1035 \pm 25\) | \(1110 \pm 84\) |
| \(M_\chi\) | \(955 \pm 44\) | \(995 \pm 65\) |
It follows from this table that the mean mass values of \(x\)-mesons are somewhat greater than the mean mass value of \(\chi\)-mesons. As always when averaging values that display a large scatter, the indicated small measurement errors cannot be assigned decisive significance. Taking this circumstance into account, it should be said that these mass measurements, considered by themselves, do not give decisive indications of the existence of \(K\)-mesons with a mass different from that of the \(\tau\)-meson, equal to \(965\,m_e\). On this basis Powell\(^{142}\) put forward the hypothesis that the \(\tau\)-, \(x\)-, and \(\chi\)-decays are alternative decays of one and the same particle with mass \(\sim 965\,m_e\).
Some conclusions about the mass of primary \(x\)- and \(\chi\)-particles can be drawn on the basis of the spectra of secondary particles considered.
The spectrum of \(\chi\)-mesons indicates the existence of monochromatic \(\pi\)-mesons. Let us assume that the neutral particle produced in such a decay is a \(\pi^0\)-meson:
\[ \chi = \pi^+ + \pi^0 + Q. \]
Below are given the values of the energy \(E_\pi\), momentum \(p_\pi\), \(Q\), and range \(R_\pi\) of the charged \(\pi\)-meson produced in such a decay,
\[ \text{*) Here \(g\) means any quantity determined by ionization: grain density, gap density, etc.} \]
Assuming that the mass of the \(\chi\)-meson is equal to the mass of the \(\tau\)-meson \((965\,m_e)\):
\[ \chi \to \pi^+ + \pi^0 + Q; \qquad M_\chi = 965\,m_e, \]
\[ Q = 219\ \text{Mev}, \]
\[ E_\pi = 108.5\ \text{Mev}, \]
\[ p_\pi = 205\ \text{Mev}/c, \]
\[ p\beta_\pi = 170\ \text{Mev}/c, \]
\[ R_\pi = 60\ \text{g}/\text{cm}^2\ \text{Pb} = 20\ \text{cm of emulsion}. \]
The mean weighted value \(p\beta\), obtained from all 12 values of \(p\beta\) from which the spectrum in Fig. 49 was constructed, is \(p\beta = 168 \pm 4\ \text{Mev}/c\), which agrees excellently with \(p\beta = 170\ \text{Mev}/c\) given in the table. Thus, the \(p\beta\) spectrum agrees well with the assumption of decay according to the scheme
\[ \chi \to \pi + \pi^0 + \sim 219\ \text{Mev}. \]
Confirmation of this decay scheme is provided by the work mentioned above of Rao and Mitra \(^{141}\), in which a strong nuclear interaction was found for a light meson produced in the decay of a stopped particle whose mass was \(M = 937^{+250}_{-170}m_e\) (constant-sagitta method). The energy of the light meson, measured from scattering and grain density, lies in the range \(104\text{--}115\ \text{Mev}\). If this decay case is interpreted according to the scheme \(\chi^\pm \to \pi^\pm + \pi^0 + Q\), then for \(Q\) we obtain the value \(Q = 222 \pm 12\ \text{Mev}\), and for the mass of the heavy meson \(M = 971 \pm 22\,m_e\), which is in agreement with direct mass measurements.
Remaining within the framework of known neutral particles, one may suppose that in the decay of the \(\chi\)-meson a neutrino or a \(\gamma\)-quantum is produced:
\[ \chi \to \pi + \nu \quad \text{or} \quad \chi \to \pi + \gamma. \]
Starting from the measured value \(p\beta = 168 \pm 4\ \text{Mev}/c\), one can calculate the mass of such a \(\chi\)-meson. It is equal to \(890\,m_e\), which agrees considerably worse with the results of direct mass measurements of the primary particles given in the table.
Thus, the body of data on the mass of the primary particles and on the spectrum of the secondary particles indicates the existence of charged \(K\)-particles with a mass close to that of the \(\tau\)-meson, decaying into \(\pi^\pm\)- and \(\pi^0\)-mesons. In mass and decay scheme these mesons are extremely close to \(\vartheta^0\)-mesons, which decay according to the scheme
\[ \vartheta^0 \to \pi^+ + \pi^- + \sim 214\ \text{Mev}. \]
They have received the designation \(\vartheta^\pm\)-mesons.
Let us turn to consideration of the spectrum of \(\mu\)-mesons arising in \(x\)-decay. The decay parameters are given below:
\[ x \to \mu + \nu + \nu \;(\text{or } \gamma) + Q, \]
calculated on the assumption that \(M = 965\,m_e\):
\[ x \to \mu + \nu + \nu + Q;\quad M_x = 965\,m_e, \]
\[ Q = 385\ \text{MeV}, \]
\[ E_{\mu\max} = 152\ \text{MeV}, \]
\[ p_{\mu\max} = 243\ \text{MeV}/c, \]
\[ p\beta_{\mu\max} = 215\ \text{MeV}/c, \]
\[ R = 104\ \text{g}/\text{cm}^2\ \mathrm{Pb} \simeq 33\ \text{cm of emulsion}. \]
It follows from this table that the \(p\beta\) spectrum for \(\mu\)-mesons should terminate at the value \(p\beta_{\max}=215\ \text{MeV}/c\). From consideration of the \(p\beta\) spectrum for secondary particles identified as \(\mu\)-mesons (Fig. 49 and Table VII), it is seen that only two values of \(p\beta\): \(235 \pm 35\) and \(315 \pm 70\ \text{MeV}/c\), lie beyond the indicated limit. However, these quantities were measured with too large an error for them to be regarded as evidence for the existence of \(p\beta > 215\ \text{MeV}\). Thus, the measured spectrum of secondary particles does not contradict the hypothesis of \(x\)-decay:
\[ x \to \mu + \nu + \nu + \sim 385\ \text{MeV}, \]
in which two light neutral particles—neutrinos or \(\gamma\)-quanta—are produced.
V.2.4. \(\beta\)-decay of \(K\)-mesons. During 1954 evidence was obtained for the production of fast electrons in the decay of charged \(K\)-mesons\(^{143--146}\). These electrons may be identified, first, by measuring scattering and grain density by the \((g,\alpha)\) method; second, by the presence of additional energy losses caused by bremsstrahlung: the probability of bremsstrahlung increases inversely proportionally to the square of the particle rest mass and, in the case of an electron, can easily be detected from a sudden change in the direction of the track not accompanied by a change in grain density. The grain density in the tracks of electrons with energy greater than \(10\text{--}20\ \text{MeV}\) is equal to the grain density “on the plateau”: \(g^* \sim 1\). At the same time, it follows from Figs. 9 and 10 that \(\mu\)- and \(\pi\)-mesons with \(p\beta > 130\ \text{MeV}\) and \(200\ \text{MeV}\), respectively, also produce ionization close to \(g^* \sim 1\). Therefore electrons can be reliably distinguished from \(\mu\)-mesons by the \((g,\alpha)\) method only in the case where the electron momentum is appreciably less than \(100\ \text{MeV}/c\). As for the second selection criterion based on additional losses, it remains valid also at high electron energies.
The first case of electronic decay of a \(K\)-meson was reported by Friedlander et al.\(^{143}\) (see Fig. 50). The \(K\)-particle originated in a four-prong star of the type \(4 + 0n\). Measurements of its mass gave the following results: \(800 \pm 150\,m_e\) \((\alpha, R)\), \(720 \pm 190\,m_e\) (sagitta constant), \(1500 \pm 100\,m_e\) (photometric method).
The secondary particle passes through 11 emulsion layers; the grain density of the track is indistinguishable from \(g_{\text{plate}}\): \(g^* = 1.01 \pm 0.02\); the value of \(p\beta\), measured from scattering, is \(88.5 \pm 6\) MeV/\(c\). On the basis of these data, however, the particle cannot be distinguished with certainty from a \(\mu\)-meson, which at the same grain density has \(p\beta > 100\) MeV/\(c\). At point \(B\) (Fig. 50), at a distance of 2.3 cm from the point of decay, the particle undergoes a sudden deflection (the range length in the emulsion is 2.9 cm), after which it exhibits the properties of a slow electron with energy \(\sim 5\) MeV: the sudden deflection is accompanied by a strong increase in scattering at the same grain density, which with great reliability indicates an energy loss at point \(B\) caused by bremsstrahlung.
Fig. 50. Decay of a \(K\)-meson into an electron\(^{135}\).
An analogous case of \(\beta\)-decay of a \(K\)-meson with a lower electron energy was published by Dahanayake et al.\(^{144}\) from the same laboratory. For the mass of the primary particle the following values were obtained: \(970 \pm 100\,m_e\) \((g, R)\), \(690 \pm 160\,m_e\) \((\alpha, R)\), \(760 \pm 110\,m_e\) (sagitta constant).
The grain density, close to \(g_{\text{plate}}\), and \(p\beta = 49 \pm 4\) MeV in the first four emulsions make it possible, with considerably greater confidence,
than in the preceding case, to exclude from consideration the $\mu$-meson as the secondary particle. Additional evidence for its electronic nature was obtained by measuring the electron energy along the track. These measurements show that, in addition to energy losses due to ionization, the particle loses energy to bremsstrahlung.
Two more cases of $\beta$-decay of $K$-mesons (the total electron path length $\sim 0.8$ shower unit) were observed by O’Sileem$^{139}$. Thus, the existence of $\beta$-decay in $K$-mesons has received convincing evidence. The spread of the values of $p\beta$ shows that in this case there is a decay into no fewer than three particles, two of which are neutral:
\[ K \to e + ? + ? . \]
V.3. Masses of fast charged mesons produced in high-energy nuclear disintegrations
The measurements of the masses of heavy unstable particles considered above were performed for slow particles stopping in single emulsions or in nuclear-emulsion chambers. Daniel and Perkins$^{147}$ and Fowler and Perkins$^{148}$ measured the masses of shower particles arising in nuclear disintegrations with energies exceeding $50$ MeV. Since shower particles, as a rule, have high energy and do not stop in the emulsion, the method of measuring the grain density and the scattering angle was used to determine their masses (see 1.3.6). In these works the dependence of the yield of heavy particles on the energy of the nuclear disintegration was also investigated.
The mass measurements were carried out in work$^{147}$ by means of single plates and continued in work$^{148}$ by means of nuclear-emulsion chambers. In both works the masses of shower particles were measured for which the grain density in the tracks lies within $\sim (1.1—2.2)g_{\text{plate}}$, which corresponds to a velocity $0.5 < \beta < 0.85$.
In the latter work$^{148}$ the mass measurements were carried out for shower particles from stars containing no fewer than three shower particles ($n_s > 3$); the tracks made an angle $<5^\circ$ with the plane of the emulsion; their length lay between $4$ and $14$ cm.
The results of the mass measurement obtained in work$^{147}$ are shown in Fig. 51, which gives the mass spectrum for 350 shower particles. From consideration of the measured mass spectrum it is seen that among 325 shower particles, in addition to 164 protons, 129 $\pi$-mesons and 11 deuterons and tritons, there is a group of 20 particles whose mass lies between the mass of the $\pi$-meson and the mass of the proton, in the interval $(900—1400)m_e$. The distribution drawn in Fig. 51 by a solid line was obtained under the assumption that all these 20 particles are particles with a mass close to $1210m_e$. Thus, the resulting distribu-
…indicates the existence of a group of shower particles whose mass is greater than the mass of the $\tau$-meson. If one attempts to explain these particles by a single value of the mass, one must assume the existence of particles with mass $\sim 1200\,m_e$. This result, however, is in sharp contradiction with all the most reliable measurements of the masses of slow $K$-mesons stopping in emulsion.
Figure 51 also gives the mass distributions for tracks of artificially produced $\pi$-mesons and protons, measured by the same method ($g^*, \bar{\alpha}$). As can be seen from the figure, for the masses of artificial $\pi$-mesons approximately the same distribution is obtained as for $\pi$-mesons from cosmic-ray showers.
Fig. 51. Mass spectrum of shower particles and calibration $\pi$-mesons and protons. Shower particles were selected from stars with $n_s>1$, produced by particles with energy $10$–$50$ Bev[^147].
$\pi$-mesons from cosmic-ray showers. The distribution of the measured masses of artificial protons also coincides with the mass distribution of shower protons and shows no irregularity in the region $900$–$1400\,m_e$, which would indicate possible systematic errors of the mass-measurement method.
The results of Fowler and Perkins[^148] for shower particles observed in photographic-emulsion chambers are shown in Fig. 52. Comparison of these curves with those given above shows a significant improvement in the resolving power of the method, achieved by using longer tracks in the photographic-emulsion chamber. Thus, for example, the half-width of the proton line in measurements performed in single emulsions is close to $300\,m_e$, whereas in measurements performed with a photographic-emulsion chamber it does not exceed $150\,m_e$.
In these improved measurements, \(K\)-particles whose mass is greater than the mass of the \(\tau\)-meson were again detected. The authors believe that the group of particles with masses in the interval \((900—1400)m_e\) observed in the previous measurements split in these measurements into two groups: particles with a mass of about \(970m_e\), and nine particles whose mean mass is \(\sim 1450m_e\). The total range of these 9 particles in the emulsion is \(\sim 70\) cm, and their flight time is \(\sim 3 \times 10^{-9}\) sec. One nuclear interaction caused by such a particle was observed.
Results close to these were obtained by Rosendorff, Shalem, and Ekutiel\({}^{149}\), who measured the mass of 55 shower particles with track lengths from 5 to 34 mm and grain densities in the range \(1.05—1.50\,g_{\text{plate}}\). Twenty of them turned out to be \(\pi\)-mesons. From the obtained
[In the figure: vertical axis—“Number of tracks”; horizontal axis—“Mass,” “Logarithm of mass”; marked positions include \(970m_e\), \(1450m_e\), “Proton,” and “Deuteron.”]
Fig. 52. Mass spectrum of shower particles according to data obtained with an emulsion chamber\({}^{148}\).
mass distribution for the remaining particles, it follows that there are particles with a mass greater than the mass of the \(\tau\)-meson and close to \(\sim 1200m_e\).
The existence of an intense group of particles with mass \(\sim 1200—1450m_e\), detected in these experiments, is not confirmed, however, either by experiments with Wilson chambers or by measurements of the masses of \(K\)-mesons that stopped in the emulsion. One might suppose that these particles are very short-lived and decay in flight when their velocity is large. Such decays were not observed; but if, in this case, a heavy meson with mass \(\sim 900—1000m_e\) of the \(\tau\)-, \(\chi\)-, \(\chi\)-, or \(\vartheta\)-meson type arises as the secondary particle, then such decays would be difficult to detect. Thus, at present the question of the nature of these particles remains open: if these particles really exist, nothing is known about their decay scheme. If these particles do not exist and the corresponding maxima in the spectra of Figs. 51 and 52 are caused by unknown fluctuations in the proton mass distributions, it would be very important to determine the causes of such fluctuations.
V.4. \(S\)-Particles
Let us consider the data on charged \(K\)-particles stopping in the plates of a Wilson chamber or of a mass spectrometer. The mean range of these particles in the plates is of the order of tens of \(\mathrm{g/cm^2}\), whereas the mean range of \(K\)-particles stopping in emulsion chambers, as is seen from Table VII, does not exceed \(15\)—\(20\ \mathrm{g/cm^2}\). Thus, both methods register heavy unstable particles in close or overlapping intervals of ranges, and it is natural to assume that the \(S\)-particles observed in Wilson chambers and the \(K\)-mesons stopping in emulsion chambers are one and the same particles. Therefore, the data obtained by both methods complement one another. At the same time, because of the presence of a large number of plates in the Wilson chamber, one may hope to observe the stopping of secondary particles with large momentum, which usually leave the emulsion long before being brought to rest. A typical photograph of the decay of \(S\)-particles was given in Fig. 19.
V.4.1. Data of the Alikhanian group.
Mass measurements of a large number of \(K\)-particles stopping in the plates of a mass spectrometer or a Wilson chamber connected with a mass spectrometer were carried out by Alikhanian and co-workers (for diagrams of the installations see Figs. 20, 21). The mass spectrum obtained in the 1952 work\(^{566}\) on an old-type apparatus (Fig. 20) is shown in Fig. 53. The spectrum consists of two lines of approximately equal intensity, corresponding to mass values \(\sim 580\,m_e\) and \(\sim 950\,m_e\). The half-width of the first line is \(\sim 70\), and that of the second \(\sim 110\,m_e\). Measurements of the range of \(S\)-particles and of their ionization, performed with the aid of a proportional counter installed in the mass spectrometer, also indicated the presence, in the interval \(500\)—\(1000\,m_e\), of two groups of particles\(^{69,150,151}\). A detailed description of these measurements is contained in the review by A. I. Alikhanov\(^{68}\).
Fig. 53. Mass measurements of \(S\)-particles according to the data of Alikhanian and co-workers\(^{56}\) by the range–momentum method.
After the system of lower filters of the mass spectrometer was replaced by a multiplate Wilson chamber\(^{55b}\), photographs were obtained of the decay, in the chamber plates, of particles whose masses are close to the values given above\(^{152,153}\). In one case\(^{152}\) it was found that
positively charged particle with momentum \(p = 2.16 \cdot 10^8\ \mathrm{eV}/c\) and with ionization increasing toward the end of its range comes to rest in the third plate. From the stopping point two tracks emerge, one of which reaches the fourth plate, where it undergoes multiplication; moreover, the two tracks emerging from the fourth plate end in the fifth plate. The mass of the stopped primary particle, determined from the momentum \(p\) and range \(R\), is \(525 \pm 50\,m_e\); the authors regard the secondary particles as electrons. In two other analogous decays, also accompanied by the emission of two
Fig. 54. Decay of an \(S\)-particle with mass \(525 \pm 50\,m_e\), according to Alikhanian and collaborators \({}^{152}\).
charged particles from the plate where the decay occurred, the masses of the unstable particles are
\[ \begin{array}{cc} 510 \pm 80\ \text{(from momentum} & 500 \pm 150\ \text{(from ionization} \\ \text{and range)} & \text{and range)} \\[6pt] 650 \pm 150\ \text{(from momentum} & 700 \pm 250\,m_e\ \text{(from ionization} \\ \text{and range)} & \text{and range)} \end{array} \]
Two cases of similar decays are shown in Fig. 54.
In addition to these three stops, two further stops of particles with mass \(500\text{–}600\,m_e\) were observed, accompanied by the emission of two electrons \({}^{152}\). Along with these five stops, four stops of positive particles were recorded, accompanied by the emission of only one electron. The stop of the last particle, with mass \(650 \pm 100\,m_e\), was accompanied by the emission of a very slow meson, which underwent strong scattering in the chamber gas. The data obtained on the properties of the secondary particles are insufficient for establishing the decay scheme, and as one of the proposed decay schemes the authors indicate decay into \(\pi^\pm\)- and \(\pi^0\)-mesons.
The analysis of the decays of heavy mesons that stopped in the plates of a Wilson chamber was continued in work \(^{153}\), in which 3 stops in copper plates of slow negatively charged particles with masses \(940 \pm 90\,m_e\) and \(\sim 1000\,m_e\) are described. In the first of these three cases emission of a secondary particle was observed, which, apparently, is a \(\mu\)- or \(\pi\)-meson, although the authors note that it is impossible completely to exclude an electron as the secondary particle. This secondary particle passes through one copper plate and apparently stops in the lead plate situated above it. In the two other cases the secondary particles emitted at stopping were most likely mesons. It is significant that in all three cases of stopping of negatively charged mesons no formation of stars was found, although such stars should have been seen in the Wilson chamber. This agrees with emulsion data showing that the stars from the capture of \(K\)-mesons are weak “evaporation stars,” sometimes accompanied by the emission of \(\pi\)-mesons. In observing this phenomenon in a multiplate chamber, the “evaporation” particles will be absorbed in the plate, while the \(\pi\)-meson may in some cases leave it.
In addition to the cases mentioned, this work reports the stopping of a positive particle with mass \(1520 \pm 150\,m_e\). The secondary particle undergoes weak scattering, and its range in lead is \(2.6 < R < 4.36\) cm. If it is a \(\pi\)-meson, then its energy is \(70 < E < 100\) MeV.
Thus, in the works considered from the Alagez group, the existence has been established of particles of both signs with mass \(\sim 950\,m_e\), passing through the whole apparatus and decaying after stopping in the plates of a Wilson chamber. The lifetime of these particles is greater than \(5 \cdot 10^{-9}\) sec, and it is natural to identify them with the long-lived \(K\)-mesons discovered in emulsions. In the Alagez laboratory, measurements of the masses of \(S\)-particles were also carried out by M. S. Kozodaev and A. I. Filippov \(^{153}\). To determine the momentum of the \(S\)-particles these authors used a magnetic Wilson chamber, and to determine the range—in the 1950–1951 measurements, lead plates shifted by rows of counters, and in the 1951–1952 measurements, a multiplate Wilson chamber placed under the magnetic chamber. In all, nine positive and two negative particles were recorded; the mass spectrum obtained can be explained by the presence of \(S\)-particles with a single value of the mass, close to \(1000\,m_e\).
In the works of Alikhanian and collaborators the existence was also found of a second group of long-lived particles with mass \(500\text{–}600\,m_e\). The intensity of these particles is comparable with the intensity of particles of mass \(\sim 950\,m_e\). The presence of a considerable number of particles with mass \(\sim 600\,m_e\) among the very soft component (range less than 12 mm Al) was reported in their recent work by Hinoki et al. \(^{156}\). The remaining experiments with Wilson chambers controlled by penetrating-
... with showers, and with emulsions, did not confirm the presence of a noticeable number of such particles, although individual mass measurements gave values close to \(500\text{--}600\,m_e\). Thus, for example, one of the shower particles whose masses were measured in the work of Daniel and Perkins has a mass of \(520\pm60\,m_e\) (see the mass spectrum in Fig. 51), and the mass of one of the \(K\)-mesons stopping in emulsion and forming a \(\sigma K\)-star is, according to measurements of scattering and range, \(540^{+290}_{-170}\,m_e\). The reason for the discrepancy between the data of the Alagez group and the data of other groups is at present unclear. Among the possible reasons one should first of all point to the difference in the methods of selecting particles. Thus, for example, \(K\)-mesons detected in emulsions have until now been sought chiefly by phenomena at the end of the range, and have more rarely been traced from stars. \(K\)-mesons observed in Wilson chambers were selected from penetrating showers. Meanwhile, the Alagez group registers all stopped particles, irrespective of their origin or mode of decay.
Fig. 55. Measurements of the masses of \(S\)-particles (according to data of the École Polytechnique group) by the range–momentum method \({}^{156}\).
V.4.2. Mass of charged \(K\)-mesons according to measurements by the École Polytechnique and M.I.T. groups. To determine the mass of \(S\)-particles, the École Polytechnique group measured their momenta with the aid of a second, magnetic chamber, placed above a multiplate Wilson chamber \({}^{154}\) (for the arrangement of the apparatus see Fig. 15). They succeeded in measuring the masses of 22 \(S\)-particles. The results of these measurements are presented in Fig. 55, where ...
also the results of mass measurements of the “supporting” protons. The weighted mean value of the proton mass is \(1833 \pm 25\,m_e\); the mean value of the mass of the \(S\)-particles is
\[ M = 928 \pm 13\,m_e \]
and is in good agreement with the data of the Alagez group.
Although the value of the mass does not coincide with the values of the masses of the \(\tau\)-, \(x\)-, and \(\chi\)-mesons given in Table VIII, the discrepancies do not exceed the limits of the measurement errors. Thus, with the accuracy achieved, these mass measurements do not make it possible to assert that there exist \(K\)-particles with a mass different from the masses of the \(\tau\)-, \(x\)-, and \(\chi\)-mesons.
The M.T.I. group\(^{155}\) estimated the mass of decaying particles from their range and scattering in plates. For these estimates, 16 particles were selected which were identified as \(K\)-particles from the properties of the secondary particles, whose range exceeded the thickness of two lead plates. Such measurements are, in principle, analogous to measurements of the masses of particles stopping in an emulsion by scattering and range, but they have a considerably lower resolving power, since the number of angle measurements is equal to the number of plates crossed by the secondary particle, which severely limits the statistical accuracy of the measurements. The mean value of the mass of the \(K\)-particles obtained by this method is \(1200^{+270}_{-200}\,m_e\) and is only an estimate of the mass value. It is not excluded that among the 16 \(S\)-particles there are charged hyperons. This could explain the overestimated value of the mass of the \(K\)-particles in comparison with the data from photoemulsions and with the data of the Alagez group and of the Polytechnic School group.
V.4.3. Secondary particles in \(S\)-decays. Decay schemes. The M.T.I.\(^{156}\) and Polytechnic School\(^{154}\) groups recorded 67 and 45 \(S\)-decays, respectively, and measured the ranges of secondary particles in the chamber plates. In order to exclude decays of \(\tau\)-mesons or \(\pi \to \mu \to e\)- and \(\mu \to e\)-decays, it was sufficient to consider only secondary particles with a range greater than \(\sim 20\ \mathrm{g/cm^2}\) Pb.
In the majority of cases, the secondary particles arising in the 112 decays considered leave the chamber or enter its unilluminated region, possessing minimum ionizing power. For such secondary particles it was possible only to indicate a lower limit of the range. Twenty-three secondary particles stopped in the chamber plates, having a range \(>20\ \mathrm{g/cm^2}\) Pb. In this case it was possible to establish more or less accurately the limits within which their ranges lay. The range spectra obtained are shown in Fig. 56, \(a\) (M.T.I. data) and 56, \(b\) (P. Sh. data).
From these spectra it is seen that the ranges of the secondary particles form two groups: 1) ranges \(<60\ \mathrm{g/cm^2}\) Pb and 2) ranges close to \(100\ \mathrm{g/cm^2}\) Pb.
On some photographs of \(S\)-decays, the occurrence of small electron showers was discovered, whose direction is approximately opposite to the direction of emission of the secondary charged particle. In most decays the electron cascade is formed not in the plate where the decay occurred, but in one of the adjacent ones; moreover, the points of decay and of the beginning of the cascade are not connected by the track of an ionizing particle, which indicates their origin from \(\gamma\)-quanta. A photograph of one such decay was given in Fig. 19. In the range spectra of Fig. 56, decays accompanied by electron cascades are marked with the symbol “\(\gamma\)”. All of them are associated with secondary particles with range \(\leqslant 60\ \mathrm{g/cm^2}\ \mathrm{Pb}\). In addition to the five electron cascades noted, seven more cascades were observed\(^{157}\), for which it was possible to determine only the lower limit of the range of the secondary particle: in all cases it proved to be less than \(60\ \mathrm{g/cm^2}\ \mathrm{Pb}\).
Fig. 56. Range spectrum of secondary particles in \(S\)-decays according to data of the M.T.I. group (a) and P. Sh. (b).
The data obtained on the presence of a group of ranges \(\leqslant 60\ \mathrm{g/cm^2}\ \mathrm{Pb}\) and of electron cascades associated with such ranges constitute an extremely strong argument in favor of the view that the corresponding group of \(S\)-particles is identical with \(\chi^{\pm}\)- or \(\vartheta^{\pm}\)-mesons, decaying according to the scheme
\[ \chi^{\pm} = \vartheta^{\pm} \to \pi^{\pm} + \pi_{+}^{0} \sim 220\ \mathrm{Mev}. \]
Indeed, the ionization range of the \(\pi^{\pm}\)-mesons arising in such decays is \(60\ \mathrm{g/cm^2}\ \mathrm{Pb}\) (see V.2.3); the presence of nuclear interactions leads to the appearance of smaller ranges, which is clearly manifested in the spectrum (Fig. 56). The \(\gamma\)-quanta arising in the decay of \(\pi^{0}\)-mesons with energy \(\sim 110\ \mathrm{Mev}\) have energy \(\sim 120\ \mathrm{Mev}\). Such \(\gamma\)-rays form, in thin copper or lead plates, cascades of several electrons. The direction of the electron cascades confirms the decay scheme and contradicts the supposition of the direct production of \(\gamma\)-quanta in a decay of the type
\[ S^{\pm} \to \pi^{\pm} + \gamma . \]
Indeed, in this case the direction of the cascade would have had to be opposite to the direction of emission of the secondary particle. The angles observed by the M.T.I. group between these two directions are, for the decays they considered, \(180, 180,\)
180, 170, 166, 163, 157, 151, 147, 127, 123, and 112°, which, within the limits of limited statistics, is consistent with the assumption that the $\gamma$ quanta did not arise directly in the $S$ decay, but were formed from the decay of $\pi^0$ mesons.
Let us turn to the conclusions that follow from the presence of a monochromatic group of secondary particles with a range $\sim 100\ \mathrm{g/cm^2}$ Pb. The absence of nuclear interactions, the scattering of these particles in the chamber plates, and also their ionizing ability indicate that these particles are $\mu$ mesons. The mean value of the momentum of these monochromatic $\mu$ mesons is $230 \pm 5\ \mathrm{Mev}$ according to M. T. I. and $225 \pm 6\ \mathrm{Mev}$ according to P. Sh. Direct measurements of masses for primary particles producing secondaries with a range $\sim 100\ \mathrm{g/cm^2}$ Pb were possible in only one case^[156], for which the mass value obtained was: $874 \pm 57\,m_e$. In four cases it was possible to measure the masses of particles for which the range of the secondary particles was greater than $60\ \mathrm{g/cm^2}$ Pb. These masses are $872 \pm 76$, $933 \pm 54$, $902 \pm 76$, and $917 \pm 58\,m_e$. The weighted mean value from these five measurements is $(906 \pm 30)\,m_e$.
Knowing the mean momentum of the secondary $\mu$ mesons $(225—230\ \mathrm{Mev}/c)$ and assuming a decay scheme, one can calculate the mass of the primary particle. The results of these calculations are given in Table IX.
Table IX
| Assumed decay scheme | $K \to \mu + \nu$ (or $\gamma$) | $K \to \mu + \pi^0$ | $K \to \pi + \nu$ (or $\gamma$) | $K \to \pi + \pi^0$ |
|---|---|---|---|---|
| Mass of the primary particle $(m_e)$ | $941 \pm 11$ (P. Sh.) $950 \pm 15$ (M. T. I.) |
$1012 \pm 12$ | $1090 \pm 13$ | $1150 \pm 14$ |
It follows from the table that the best agreement with the direct mass measurements is given by the decay scheme $K \to \mu + \nu$, which at the same time is also in the best agreement with the properties of the secondary particles investigated in the experiment. Thus, the data considered indicate the existence of a new particle with mass $\sim 930—960\,m_e$, whose decay scheme is analogous to the decay scheme of charged $\pi$ mesons.
In concluding the review of studies of $S$ decays with the aid of the multiplate Wilson chamber, it should be noted that the obtained data showed absolutely no manifestation of the presence of $\chi$ mesons, whose existence followed convincingly from experiments with emulsions. A possible explanation of this may be that the lifetime of $\chi$ mesons is too short: they decay in Wilson chambers in flight and do not “survive” until the $S$ decay. The data on in-flight decays of $K$ mesons registered in magnetic Wilson chambers so far support such an assumption.
V.5. New methods for selecting \(K\)-particles and direct measurements of their lifetimes
In Chapter I it was indicated that attempts to develop new methods for selecting \(V^0\)-particles have so far not led to an increase in their yield. Attempts to implement new methods for selecting \(K\)-particles stopped in plates proved more successful. The secondary particles arising in the decay of stopped \(K\)-particles in most cases have energies considerably exceeding the energy of secondary particles in \(\tau\)-, \(\pi\)-, and even \(\mu\)-decays. Therefore, the registration of fast secondary particles makes it possible to select \(K\)-decays. This selection method was used in the work of Mazetti and Keuffel \(^{157}\).
Fig. 57. Apparatus for measuring the mean lifetime of \(K\)-mesons. \(G_1\), \(G_2\), \(G_3\) are rows of Geiger–Müller counters. All elements of the apparatus have an approximately square shape, with the exception of \(S\), whose dimensions are \(27 \times 61\ \mathrm{cm}^2\). Two Cherenkov counters \(C\) are arranged one after the other \(^{157}\).
In the work of Barker and Binnie \(^{158,159}\) another method of selecting \(K\)-particles was used. \(K\)-particles stopped in given filters have velocities smaller than the lighter particles stopped in the same filters, and still more so than those passing through them. Therefore, by including in the selection system a threshold anticoincidence counter that does not operate when a slow \(K\)-particle passes through it, one can select \(K\)-particles.
The arrangement of the Mazetti and Keuffel apparatus is shown in Fig. 57. It consists of a liquid scintillation counter, two directional Cherenkov counters \(C\), three rows of counters \(G_1\), \(G_2\), \(G_3\) connected into a hodoscope, and absorbers made of lead and aluminum. This apparatus, and the associated radio-engineering circuit, select events of the following type. A charged unstable particle, produced in a 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. It then 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 (with an efficiency of \(\sim 90\%\)). At the same time the counter remains insensitive to shower particles traversing it in the opposite direction, from top to bottom (efficiency \(\sim 0.4\%\)). The time interval between the triggering of counters \(S\) and \(C\) was measured with the aid of a time-measurement circuit
Fig. 58. Distribution of time shifts in the decay of \(K\)-mesons. Counter arrangement as in Fig. 57. Duration of the experiment 231 hours, total intensity 19.8 per hour of experiment. Cherenkov counters displaced by 50 cm. Normalized to the duration of the main experiment \(^{157}\).
of the “chronotron” type \(^{160}\). A hodoscopic system of Geiger–Müller counters made it possible to exclude from consideration delays associated with the passage of shower particles through the apparatus.
The threshold value of the velocity of a particle causing the triggering of the Cherenkov counter, equal to \(0.76c\), corresponds to electrons, \(\mu\)-mesons, and \(\pi\)-mesons with energies greater than 250 keV, 50 MeV, and 70 MeV, respectively.
In the presence of such a threshold the system obviously will not register charged \(\pi\)-mesons arising in \(\tau\)-decay. As for the decays of \(K\)-particles into light mesons or into electrons, decays of the type \(K_{\mu}\), \(K_{\pi}\), or \(K_{e}\) will certainly be registered
HEAVY UNSTABLE PARTICLES
by the system, while the decays of \(x\)-mesons will be recorded in those cases when the \(\mu\)-meson acquires a sufficiently large energy in the decay.
The results of the measurements are shown in Fig. 58. Along the abscissa is plotted the time in \(10^{-9}\) sec, and along the ordinate the number of decays occurring in a time interval of \(3.1 \cdot 10^9\) sec. The “bell-shaped” part of the curve, with wings extending on both sides, is due to fluctuations in the time of appearance of pulses in counters \(S\) and \(C\) and to accidental pulses from shower particles. These shifts, which form the background of the measurements, were measured separately, and the corresponding data are shown in Fig. 58 by a dashed line. The straight portion in Fig. 58 corresponds to exponential decay. Analyzing this portion of the decay curve under the assumption of a single decay time, the authors obtained for the mean lifetime of \(K\)-particles the value:
\[ \tau_k = (8.7 \pm 1.0)\cdot 10^{-9}\ \text{sec}. \]
Fig. 59. Barker and Binnie apparatus for selecting \(K\)-mesons and measuring their lifetime \(^{158}\).
(Labels in the figure: white surfaces; lead; PM—photomultiplier; Wilson chamber; \(S_1\), \(C_1\), \(S_2\), \(G\), \(C_2\); scale \(0\)–\(10\) cm.)
In the work of Barker and Binnie, simultaneously with the measurement of the lifetime of charged \(K\)-particles, the tracks of these particles in a Wilson chamber were photographed \(^{159}\) (altitude 2850 m, Pic-de-Midi). The experimental apparatus included (Fig. 59; the time-measurement circuit is not shown in the figure) a multiplate Wilson chamber, in which there was also a Cherenkov counter \(C_2\) with a photomultiplier. The system of control counters located above the chamber consisted of a Cherenkov counter \(C_1\), two liquid scintillation counters, and two rows \(G\) of Geiger–Müller counters. The Cherenkov counters operated only from
passage” of a fast particle. The counter system above the chamber selected coincidences of pulses from the counters \(S_1, S_2, C\), not accompanied by a pulse from the Cherenkov counter \(C_1\) (coincidences \(H = S_1 + S_2 + C - C_1\)). These coincidences \(H\), obviously, 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 threshold of the Cherenkov counter was chosen so that \(\pi\)- and \(\mu\)-mesons passing through the system would trigger the counter \(C_1\) and would not be registered by the system, whereas heavier particles, if their velocity was below the critical one, would not be detected by the counter \(C_1\) and would give coincidences \(H\).
Expansion of the chamber was controlled by the coincidence \(H + C_2\), occurring within the resolving time \(5 \cdot 10^{-6}\) sec. The critical velocity 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 \(\mu\)- and \(\pi\)-mesons with energies close to the counter-triggering energies in the work of Mazetti and Keuffel. Thus, the system considered was specially adjusted to select single slow heavy particles, with mass exceeding \(300m_e\), which, after stopping in the multiplate Wilson chamber, emitted fast charged particles or the products of their annihilation. Such a method of selecting heavy particles in work with a Wilson chamber is of great interest, since earlier installations selected penetrating showers containing heavy unstable particles. The only exception in this respect was the mass spectrometer of Alikhanian and his collaborators, which also registered single particles.
The results of this experiment may be summarized as follows. In 2000 hours of operation eight particles were observed that stopped in the lead plates in a well-illuminated part of the Wilson chamber and emitted secondary charged particles that entered the counter \(C_2\). The secondary particles do not multiply and do not scatter appreciably in the lead plates, whence it follows that they are not electrons. Measurements of the magnitude of the momentum in the counter \(C_2\) agree with the assumption that these secondary particles are monochromatic \(\mu\)-mesons from \(K_\mu\)-decay.
To determine the lifetime of \(K\)-particles, the time interval between the triggering of the counters \(C_1\) and \(C_2\) was measured. After introducing corrections for the flight time of the primary and secondary particles, from the eight obtained lifetimes one can, by a statistical method, obtain the “most probable” 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
\[ T_k = (15.8^{+8.7}_{-4.0}) \cdot 10^{-9}\ \text{sec}. \]
If one includes in the consideration 5 additional decays, discovered in poorly illuminated parts of the chamber, then
\[ T_k=\left(11.0^{+4.0}_{-2.4}\right)\cdot 10^{-9}\ \text{sec}. \]
Both of these values, within the limits of the experimental error, agree with the results of the preceding work \(^{157}\) and with estimates of the mean lifetime of the principal part of the \(K\)-particles from their flight time in Wilson chambers.
VI. CHARGED \(V^\pm\)-PARTICLES
VI.1. Masses of the primary particles
The principal investigations of charged particles observed from decays in flight in Wilson chambers (\(V^\pm\)-particles) were carried out
Fig. 60. \(V^\pm\)-decay of one of the shower particles in a Wilson chamber \(^{161}\).
by both Manchester groups (Jungfrau-Joch and Pic-du-Midi) \(^{161,162}\), the M.I.T. group \(^{163}\), the Indiana group \(^{164}\), and the group of the Polytechnic School \(^{51,165}\).
Two typical examples of the decay of charged \(V\)-particles are shown in Figs. 60 and 61. The particle in Fig. 60 is one of the shower particles produced in a nuclear interaction in a lead plate above the chamber. In Fig. 61 the particle has a low velocity, and its track is sufficiently large to estimate, from
Fig. 61. \(V^{+}\)-decay of a slow particle in a Wilson magnetic chamber \(^{161}\).
its momentum and ionization, its mass, which lies in the range \(920\text{--}1440\,m_e\).
York, Leighton, and Björnerud \(^{43}\) analyzed 103 decays of charged \(V\)-particles (the arrangement of the apparatus is shown in Fig. 12). For 17 decays they were able to determine the mass of slow \(V^{\pm}\)-particles from their momentum and ionization. The resulting mass spectrum is given in Fig. 62, from which it is evident that the measured values of the masses are grouped around \(1000\,m_e\). Examination of the data of the Jungfraujoch group \(^{161}\) leads to the same conclusion. Among the 44 charged \(V\)-particles observed by this group in 1952–1954, 11 slow \(V^{\pm}\)-particles were found whose masses lie in the range
from 600 to 2500 \(m_e\) and are grouped around \(\sim 1000\,m_e\). The mass measurements carried out by other investigators lead to the same conclusions.
From all these measurements, made in Wilson cloud chambers, it follows that, taking into account the existing measurement errors, most of the observed masses can be explained by the presence of particles with a single value, or with close values, of the mass in the interval \(900\)—\(1000\,m_e\).
VI.2. Secondary particles in \(V^{\pm}\)-decays
In a small number of decays the conditions for observing the secondary particles were sufficiently favorable for a direct determination of their mass. Thus, for example, in Fig. 62 there is shown
Fig. 62. Masses of primary and secondary particles in \(V^{\pm}\)-decays. The unshaded portion corresponds to the masses of the primaries, the shaded portion to the masses of the secondary particles. The spectrum was constructed for 10 positive and 7 negative primary particles.
the mass spectrum of secondary particles, measured by the Pasadena group (the shaded part of the spectrum). From this spectrum it is seen that in all cases, with the exception of two*), the secondary particles are light (\(\mu\)- or \(\pi\)-) mesons. It is of interest to compare this mass spectrum of light mesons arising in \(V^{\pm}\)-decays with the mass spectrum of \(\pi\)-mesons arising in \(V_1^0\)-decays, measured on the same apparatus of the Pasadena group (Fig. 24). This comparison clearly shows the presence not only of \(\pi\)-, but also of \(\mu\)-mesons among the secondary particles in \(V^{\pm}\)-decays.
*) In these two cases the secondary particles are positively charged and their mass is close to the proton mass. These decays were interpreted as hyperon decays \(V^{+}\to \pi^0+p\).
The properties of secondary charged particles were also studied by the Polytechnic School group \(^{165}\), which observed 66 \(V^+\)-decays and 40 \(V^-\)-decays in the upper magnetic chamber of its setup (see Fig. 15). Of the secondary particles produced in these decays, 15 negative and 12 positive particles penetrated into the lower multiplate chamber. Analysis of their passage through the plates showed that the positive particles do not undergo nuclear interactions in the plates and, apparently, are \(\mu\)-mesons. In two cases, when these particles stop in the plates of the lower chamber, the estimate of the mass from range and ionization confirms that they are \(\mu\)-mesons. Eight of the fifteen negative secondary particles undergo nuclear interactions in the plates and, apparently, are \(\pi\)-mesons.
VI.3. Positive excess and lifetime of \(V^{\pm}\)-mesons
Table X gives the number of \(V^+\)- and \(V^-\)-mesons registered in Wilson magnetic chambers of various sizes.
Table X
| Group | Vertical chamber size (cm) | \(V^+\) | \(V^-\) |
|---|---|---|---|
| Manchester (Pic-du-Midi) | \(\sim 20\) | 5 | 14 |
| Pasadena (upper chamber) | 20 | 14 | 28 |
| Indiana | 55 | 13 | 18 |
| Manchester (Jungfraujoch) | 50 | 29 | 13 |
| Polytechnic School | 68 | 66 | 40 |
| 127 | 113 |
The table reveals a correlation between the positive excess
\[ \delta=\frac{V^+}{V^-} \]
and the vertical sizes of the chambers: the quantity \(\delta\) changes from \(\sim 1/2\) to \(\sim 2\) in passing from small chambers to large ones. This may be regarded as an indication of the existence of at least two types of charged \(V\)-particles with different lifetimes. The relatively long-lived \(V\)-mesons that “survive” in large chambers must be predominantly positively charged.
Direct confirmation of such a hypothesis is provided by the distribution of decay points in the large chamber of the Indiana group, shown in Fig. 63 for 13 \(V^+\)- and 18 \(V^-\)-decays. The first decays
are distributed almost uniformly along the chamber, whereas negative decays are grouped in its upper part. Naturally, as an extreme measure one may provisionally identify the reported positive particles with the positive \(K_\mu^+\)-particles of the École Polytechnique group. This is also confirmed by estimates of the lifetime of \(K_\mu\)-particles carried out by the P. Sh. group, which showed that the mean lifetime of \(K_\mu\)-particles is large and, in any case, greater than \(5\times 10^{-9}\) sec. \(^{165}\) In work \(^{166}\), on the basis of an analysis of the relative number of \(V^\pm\)- and \(S\)-particles in its apparatus, the P. Sh. group came to the conclusion that the mean lifetime of \(K_\mu\)-particles is close to \(2.8\times 10^{-8}\) sec. For the remaining \(V^\pm\)-particles, not belonging to the group of \(K_\mu\)-particles and considered as a homogeneous group of particles (\(\chi\)- and \(\vartheta^\pm\)-mesons), an estimate of the mean lifetime gives \(\sim 2.4\cdot 10^{-9}\) sec.
Fig. 63. Distribution of decay points of \(V^\pm\)-mesons in the large chamber of the Indian group \(^{164}\).
In addition to these two groups of particles with different lifetimes, one should note a group of still shorter-lived particles singled out by York, Bjørnerud, and Leighton. According to their estimate, the mean lifetime of the main part of the \(V^\pm\)-particles whose decay is observed in the lower chamber lies in the range
\(10^{-11}<\tau<10^{-10}\) sec. The nature of these particles has not been established, but among them two charged hyperons were found, producing protons in their decay, and the authors believe that the greater part of the particles of this group, among which a large positive excess is observed, are charged hyperons.
VI.4. Distribution of the momenta \(p_t\) and \(p^*\) for secondary particles
The data presented above indicate the existence of at least two types of charged \(V\)-particles, but they are insufficient for deciding the question of their number and decay schemes. Additional information may be obtained as a result of a dynamical analysis of \(V^\pm\)-decays; however, this analysis also does not solve the problem completely. Indeed, it was shown above that \(K\)-particles stopping in emulsion or multilayer chambers are a mixture of particles with close masses but entirely different decay schemes.
decay. In addition, among the \(V^\pm\)-particles there is a noticeable fraction of charged hyperons. Therefore one should not expect that the distribution of transverse momenta, with the existing accuracy of their measurements, will give a well-resolved momentum spectrum and make it possible easily to distinguish the various decay schemes.
In view of the presumed presence of long-lived \(V^+\)-particles identical with \(K_\mu^+\)-mesons, let us consider the \(p_t\)-distributions separately for
Fig. 61. Distribution of transverse momenta \(p_t\) for \(V^\pm\)-decays.
\(V^+\)- and \(V^-\)-particles. They are shown in Fig. 64 and are constructed from the data of papers \(^{161,162,43,164}\). The measurements of the Indiana group \(^{164}\) are the most accurate: the mean error is \(\Delta p_t \simeq 5\%\). From the histograms shown it is evident that the \(p_t\)-distributions are different for positive and negative secondary particles. For positive particles the maximum of the distribution is shifted toward larger momenta and lies in the region \(\sim 200\text{--}250\ \mathrm{MeV}/c\). The most accurately measured \(p_t\)-distribution agrees well with the theoretical distribution for the decay \(K_\mu \to \mu + \nu\) at the value \(p^* \sim 220\ \mathrm{MeV}/c\) (solid curve) and does not agree with the assumption of decay into a \(\mu\)-meson and two particles of zero mass (dashed curve). This analysis thus shows that a significant part of the \(V^+\)-decays proceeds according to the scheme \(K_\mu \to \mu + \nu\). At the same time, decays of \(V^-\)-mesons,
as is evident from Fig. 64, cannot be explained by such a scheme. These conclusions are confirmed still more clearly by the distribution of momenta \(p^*\) in the center-of-mass system for such \(V^\pm\)-decays, when the velocity of the primary particle and the momentum and mass of the secondary particle are measured. A corresponding analysis of the data known in mid-1954 was carried out by Sowerby\(^{167}\). The distribution of \(p^*\) obtained by him is shown in Fig. 65, separately for \(V^+\)- and \(V^-\)-decays. The shaded part of the histograms corresponds to particles which, by direct mass measurements, were identified as \(K\)-mesons. The distributions for particles of different sign differ strongly: for
Fig. 65. Distribution of the momenta of secondary particles in the system of the decaying \(V^\pm\)-particle\(^{167}\).
\(V^+\)-particles there is a maximum near \(p^* \sim 220\ \mathrm{MeV}/c\), absent for \(V^-\)-particles. It is natural to identify this maximum with the decay \(K_\mu \to \mu + \nu\), and to ascribe the broad momentum distribution to secondary particles arising in the decay of \(\chi\)-mesons. In the unshaded part of the distribution for \(V^-\)-particles there is a maximum in the region \(\sim 180\ \mathrm{MeV}/c\). It is possible that it is caused by the presence among the \(V^-\)-particles of negatively charged hyperons (see IV.4; IV.5).
It follows from the data presented that the results of the investigation of \(V^\pm\)-particles in Wilson cloud chambers confirm the conclusions drawn in the study of \(K\)-decays and hyperon decays in emulsion chambers and multi-plate Wilson chambers.
VII. GENERATION OF HYPERONS AND \(K\)-MESONS AND THEIR INTERACTION WITH NUCLEI
VII.1. Frequency of observation of particles in Wilson cloud chambers
In most existing methods of selecting unstable particles, particles produced in penetrating showers of high energy are recorded. Regarding the cross section for the formation of such showers
It is known that it is close to the geometric cross section of the nuclei in which the showers are generated. Therefore, by estimating the frequency of appearance of heavy unstable particles in penetrating showers, one can obtain an idea of the production cross section of these particles. The number of penetrating showers per one \(V\)-particle that is of interest to us may vary within broad limits, depending on the experimental conditions of observation (particle-selection scheme, chamber dimensions, position of the generating layer of matter relative to the chamber, altitude of the observation site, etc.). For mountain altitudes (\(\sim 3\)—\(4\) km), this quantity, according to various authors who worked with magnetic or multiplate Wilson chambers, lies in the range of 25—150 penetrating showers per one \(V\)-particle. To pass from this purely experimental quantity to the true number of penetrating showers per one \(V\)-particle is rather difficult, since for this purpose it is necessary to introduce large and not always sufficiently well-founded corrections for absorption of particles in the generating material, for their decay before entering the chamber, for differences in the registration efficiency of \(V\)-decays of different types and different energies, etc. These corrections change the above quantities by several times. Thus, for example, Deutschman \({}^{100}\) observed 46 \(V^{0}\)-particles among 1150 penetrating showers. After the indicated corrections were introduced, this quantity increased to 153 \(V^{0}\)-particles for the same number of penetrating showers; i.e., the ratio of the number of \(V^{0}\)-particles to the number of penetrating showers is \(\sigma = 1/(8 \pm 2)\).
Knowing the average number of shower particles in the registered penetrating showers, one can estimate the fraction of \(V\)-particles among shower particles. This quantity, according to various authors \({}^{168,169,43}\), is close to \(3\%\).
The relative number of charged \(V^{\pm}\)-particles among \(V\)-particles depends on the registration conditions, in particular on the vertical dimensions of the chambers used, and is approximately 3—6 times smaller than the observed number of \(V^{0}\)-particles.
VII.2. Frequency of observation of heavy unstable particles in emulsions and multiplate Wilson chambers
The data relating to emulsions were obtained as a result of a systematic examination of a considerable volume of emulsion chambers exposed at an altitude of \(\sim 25\) km for \(\sim 8\) hours by the Sardinian expedition of 1953. The Milan, Padua, Paris, and Rome groups \({}^{121}\) examined 118.5 cm\(^3\) of emulsion and found, among 5052 \(\pi\)-mesons stopped in the emulsion, nine \(\tau\)-mesons, three \(\tau'\)-mesons, and 25 \(K\)-mesons, which gives:
\[
N_{\tau}/N_{\pi} = 9/5052 = 1.8 \cdot 10^{-3},
\]
\[
N_{\tau}/N_{K} = 9/25,
\]
\[
N_{\tau}/N_{\tau'} = 9/3.
\]
The absolute intensity of \(\tau\)- and \(K\)-mesons, calculated from these data and referred to \(1\ \text{cm}^3\) of emulsion per day, is equal to:
\[ n_{\tau}=2.3\cdot 10^{-1}\ \text{cm}^{-3}\ \text{day}^{-1}, \]
\[ n_{\tau+k}=8.7\cdot 10^{-1}\ \text{cm}^{-3}\ \text{day}^{-1}. \]
It is interesting to compare the latter value with the intensity of heavy mesons at mountain altitudes. According to Fowler et al.\(^{170}\), in \(1\ \text{cm}^3\) of photographic emulsion placed under \(30\ \text{cm}\) of lead at an altitude of \(3\ \text{km}\), \(1.2\times 10^{-2}\) heavy mesons are registered per day, i.e., the intensity increases approximately 70-fold between altitudes of 3 and 25 km.
Data on the relative frequency of occurrence of \(K\)-mesons and charged hyperons in emulsion were obtained by Bonetti et al.\(^{171}\), who, in a systematic examination of all particles producing single charged secondary particles in the emulsion, observed 14 \(K\)-mesons and four charged hyperons.
Data on the frequency of observation of \(S\)-particles in multiplate chambers can be obtained from the work of Bridge et al. According to these authors’ estimate, the ratio of the number of \(S\)-particles stopped in the plates to the number of stopped \(\pi\)-mesons (altitude \(3250\ \text{m}\)) is close to \(1/70\). This is in rough agreement with the frequency of observation of \(K\)-mesons in emulsions (stratosphere) cited above, where one \(K\)-meson corresponds to \(\sim 200\) stopped \(\pi\)-mesons.
VII.3. The nature of the particles generating heavy unstable particles
In measurements in photographic emulsion, in some cases it is possible to establish whether the star in which the heavy unstable particle arose was produced by an \(\alpha\)-particle, a singly charged particle, or a neutral particle. The data obtained from consideration of the tables of the Padua Conference are given in Table XI.
Table XI
| Primary particle that produced the disintegration | Particles produced in the nuclear disintegration | \(\tau\) | \(K\) | \(Y\) | \(\tau+K+Y\) |
|---|---|---|---|---|---|
| \(\alpha\)-particle | Particles produced in the nuclear disintegration | 3 | 3 | 1 | 7 |
| Singly charged | Particles produced in the nuclear disintegration | 8 | 37 | 8 | 53 |
| Neutral | Particles produced in the nuclear disintegration | 9 | 22 | 11 | 42 |
It follows from this table that nuclear disintegrations in the stratosphere, in which \(\tau\)-mesons, \(K\)-mesons, and charged
hyperons, are created approximately in equal numbers by singly charged and neutral particles.^53 ^42
Let us now consider the data obtained with Wilson chambers and relating to altitudes up to 4 km.
If a \(V\)-particle originated in the upper block of material located above the chamber, then it is, as a rule, impossible to establish whether it was charged or neutral. This can be done only for particles born in plates located in Wilson chambers, when the track of the charged primary particle in the chamber can be seen. An analysis of the corresponding data shows that, in contrast to emulsions, the majority of both \(V^\pm\)- and \(V^0\)-particles arising in the chamber plates are formed by charged “primary” particles.
Thus, for example, according to the data of the M. T. I. group, of 24 \(V^0\)-particles that arose in a multiplate Wilson chamber, 22 particles arose in nuclear interactions caused by charged primary particles, and only two \(V^0\)-particles arose from neutral particles. Similar data of the Pasadena group, relating to \(V\)-particles produced in a lead plate between chambers (see Fig. 12), are given in Table XII.
Table XII
Number of \(V\)-particles produced by a charged or neutral particle in lead between chambers
| Nature of the primary particle | \(V^\pm\) | \(V^0\) | \(R = V^\pm/V^0\) |
|---|---|---|---|
| Charged, accompanied by other shower particles, or unaccompanied | 38 | 104 | \(0.36 \pm 0.07\) |
| Neutral primary | 5 | 14 | \(0.36 \pm 0.18\) |
| All particles | 43 | 118 | \(0.36 \pm 0.05\) |
Two conclusions follow from this table. First, regardless of whether the nuclear interaction (penetrating shower) was caused by a charged or by a neutral particle, there is a remarkable parallelism in the formation of charged and neutral \(V\)-particles: in this experiment, to within the statistical errors, the ratio \(V^\pm/V\) is close to the mean value 0.36. Second, it follows from the table that the overwhelming number of \(V\)-particles (132 out of 161) emerging from the plate located between the chambers is created by charged primary particles.
It is known that protons and neutrons of high energy are present in cosmic radiation at mountain altitudes in approximately equal quanti-
quality. Proceeding from the fact of the charge independence of nuclear forces, it is natural to assume that neutrons and protons of high energies are equally effective with respect to the production of \(V\)-particles. Therefore, in order to explain the predominant role of charged particles in the production of \(V\)-particles in the plates of the Wilson chamber, it is necessary to assume that a considerable fraction of them is produced by charged particles other than protons. Such particles are charged \(\pi\)-mesons, produced in high-energy nuclear interactions in the upper lead block located above the Wilson chamber or in the plates of the chamber.
VII.4. Spectrum and angular distribution of \(V^{0}\)-particles
In Fig. 66 the energy spectrum is given of 21 \(\Lambda^{0}\)-particles produced in penetrating showers with energy \(5 \div 50\) Bev. This spectrum was measured by Geiter at Pic-du-Midi \(^{167}\). The generator of \(\Lambda^{0}\)-particles was a 4-cm lead plate placed inside a magnetic Wilson chamber. A noteworthy property of this distribution is the relatively small number of \(\Lambda^{0}\)-particles with large energy.
Fig. 66. Kinetic energy of neutral hyperons arising in showers with energy \(\sim 5—10\) Bev \(^{167}\).
Fig. 67. Angular distribution of the directions of emission of neutral hyperons with respect to the direction of the primary particle \(^{167}\).
A similar result was obtained by the Princeton group, which investigated the energy spectrum of \(V^{0}\)-particles.
In Fig. 67 is shown the angular distribution of the directions of emission of \(\Lambda^{0}\)-particles with respect to the primary particle, obtained by Geiter \(^{167}\).
It should be noted that both the energy spectrum and the angular distribution show a similarity to the corresponding distributions of “gray” protons in high-energy nuclear disintegrations.
VII.5. Pair production of hyperons and \(K\)-mesons
The data on hyperons and \(K\)-mesons obtained in the study of cosmic radiation were confirmed by experiments at the Brookhaven cosmotron[^172]. Thus, for example, when a diffusion chamber was bombarded with a neutron beam, among 20,000 photographs there were registered 3 \(\Lambda^0\)-decays and 2 unambiguous decays of charged \(V\)-particles. When nuclear emulsions were irradiated with a proton beam scattered from a beryllium target, charged \(K\)-particles and \(\tau\)-mesons were observed.
Fig. 68. Formation of a neutral hyperon \(\Lambda^0\) and a \(\vartheta^0\)-meson in the collision of a \(\pi\)-meson with energy \(1.37\ \text{Bev}\) with a proton[^173]. Tracks \(1a\) and \(2a\) belong, respectively, to the proton and \(\pi\)-meson arising in the decay of the \(\Lambda^0\)-particle. Tracks \(1b\) and \(2b\) belong to the \(\pi\)-mesons arising in the decay of the \(\vartheta^0\)-meson.
The most important result obtained in the very first period of operation of the Brookhaven cosmotron was the proof of pair production of hyperons and \(K\)-mesons in the interaction of fast \(\pi\)-mesons with protons[^173]. It was shown that these interactions occur according to the schemes:
\[ \pi^- + p \to \Lambda^0 + \vartheta^0, \]
\[ \pi^- + p \to Y^- + K^+. \]
The phenomenon of pair production of hyperons and \(K\)-mesons was discovered upon irradiating, with \(\pi\)-mesons of energy \(1.3\ \text{Bev}\), a diffusion chamber filled with hydrogen at a pressure of \(\sim 18\ \text{atm}\). The discovery of pair production was soon confirmed by numerous examples of pair production found in cosmic radiation by means of nuclear emulsions and Wilson chambers.
In papers \(^{173}\), 4 photographs are presented which directly or indirectly indicate the formation of pairs of \(\Lambda^0\)- and \(\vartheta^0\)-particles, and one photograph testifying to the formation of a pair \(Y^-\), \(K^+\). The evidence that one of the neutral particles in the first photographs is the neutral hyperon \(\Lambda^0\) is based on the fact that the mass of the positive secondary particles, determined from momentum and ionization, is close to the proton mass, while the value of \(Q\), calculated under the assumption of \((p,\pi^-)\)-decay, is close to \(\sim 37\) MeV. The evidence for the occurrence of \(K^0\)-mesons in the same \(\pi^- — p\) collision is of a somewhat less definite character. Thus, for example, in two cases \(K^0\)-mesons were not observed, and the presence of these particles is established from the application of the laws of conservation of energy and momentum. The most illustrative is the photograph shown in Fig. 68, depicting a case in which the whole phenomenon—the formation of a \(\Lambda^0\) hyperon and a \(K^0\) meson and their decays—occurred in the gas of a diffusion chamber. The values of \(Q\) obtained for the \(\Lambda^0\)- and \(\vartheta^0\)-particles are, respectively, \(27 \pm 11\) and \(233 \pm 41\) MeV, which within the limits of error agrees with the known values of \(Q\) for these particles.
Fig. 69. Pair production of a neutral hyperon (secondary particles 3 and 4) and a meson (secondary particles 1 and 2) in cosmic radiation \(^{174}\).
A case of the simultaneous production of \(\Lambda^0\)- and \(\vartheta^0\)-mesons in cosmic radiation was observed by Thompson et al. \(^{174}\). This photograph is shown in Fig. 69, where two \(V^0\)-decays are visible. The strongly ionizing particle 3 is a proton, and particle 4 is a \(\pi\)-meson. The value calculated on the basis of momentum measurements, \(Q(p,\pi^-) = 37 \pm 4\) MeV, and thus the decay \((3,4)\) can with certainty be ascribed to a \(\Lambda^0\)-particle. The nature of particles 2 and 3, producing ionization close to minimum, cannot be established exactly; however, if it is assumed that they are \(\pi\)-mesons, then \(Q(\pi,\pi) = 223 \pm 10\) MeV, which is in good agreement with \(Q = 214\) MeV for \(\vartheta^0\)-decay.
The absence in the photograph of other tracks leads the authors to the conclusion that the \(\Lambda^0\)- and \(\vartheta^0\)-particles arose as a result of the collision of a primary particle with a nucleon at the periphery of a nucleus, and the analysis
decay dynamics shows that in such a case the mass of this primary particle must be close to the mass of the $\pi$-meson. Numerous cases of pair production of charged hyperons and $K$-mesons are noted in Table VI, which summarizes the data on charged hyperons. In several cases the paired particle was a $\tau$-meson. This fact speaks in favor of Powell’s hypothesis on the identity of $\tau$-mesons with certain types of $K$-mesons.
VII.6. Nuclear interactions of $K$-mesons and hyperons
For a long time it was not possible to detect nuclear interactions of $K$-mesons. Friedlander et al. $^{175}$ carried out careful, but unsuccessful, searches for stars produced in individual emulsion layers by stopped negative $K$-mesons ($\sigma K^-$-stars). It followed from this work that if $K$-stars do exist, their number is considerably smaller than the number of stopped and decayed $K^+$-mesons.
At present, more than 120 stoppings of $K^+$-mesons in emulsion are known and no more than 20 $\sigma K^-$-stars. One of the first observations of a star produced by a heavy meson in emulsion was the work of P. I. Lukirskii et al. $^{176}$. At the Padua conference, data were considered on sixteen $\sigma K^-$-stars in emulsion. Since the masses of all known $K$-particles are very close to one another, if they do not coincide, it is impossible to determine to which of the known types of $K$-particles the particle that formed the $\sigma K$-star belongs. This circumstance, as well as the small number of observed stars, leads to the fact that the study of the elementary act of interaction of $K$-mesons with nucleons is still at its very initial stage.
Fig. 70. Distribution of stars formed by capture of a $K^-$-meson ($\sigma K^-$-stars) according to the number of prongs $^{138}$.
In Fig. 70 the distribution of $\sigma K$-stars according to the number of prongs is given. In this distribution there are no stars with a number of prongs greater than five; the majority of stars contain two or three prongs. Consideration of the character of the tracks shows that these stars are either weak “evaporation” stars, or evaporation stars accompanied by the emission of a $\pi$-meson whose energy does not exceed 50 MeV. In one case a charged hyperon with an energy of about 60 MeV, decaying in flight, is emitted in a $\sigma K$-star. A similar case, observed in De-Stébler’s multiplate Wilson chamber $^{177}$, is shown in Fig. 71. A $K$-meson, stopped in the third plate from above, produced a star in which a light ...
meson and a slow neutral hyperon \(\Lambda^0\), which decayed in the same plate. This author also found two more \(K\)-stars accompanying the emission of a \(\Lambda^0\)-particle.
The \(\sigma K\)-stars known at the present time can be tentatively explained by the following possible types of interactions of \(K\)-mesons with nucleons:
a) Interaction of a \(K\)-meson with two nucleons
\[ K^- + N + p \to n + N + Q \]
(\(N\) is a neutron (\(n\)) or a proton (\(p\))), similar to the interaction of a \(\pi^-\)-meson with a pair of nucleons. As a result of such an interaction, the rest energy of the \(K\)-meson, close to \(Q \sim 500\) MeV, is distributed between the two nucleons of the nucleus, which leads to the appearance of a typical evaporation star, which may sometimes be accompanied by the emission of one, and considerably more rarely two, \(\pi\)-mesons.
Fig. 71. \(\sigma K^-\)-star in a multiplate chamber \(^{177}\).
b) Interaction of a \(K\)-meson with one nucleon
\[ K^- + p \to n + N^0 + Q \]
(\(N^0\) is a neutral particle). This “weak” interaction is analogous to the interaction of a \(\mu^-\)-meson with a proton, as a result of which the greater part of the rest energy of the \(\mu^-\)-meson is carried off by a neutrino. The result of such a capture is a weak evaporation star, whose energy is considerably less than 500 MeV and, depending on the type of neutral particle, lies approximately in the range \(20\)–\(200\) MeV.
c) Cases analogous to the De-Staebler \(\sigma K\)-star may be explained by interactions of the type
\[ K^- + n \to \Lambda^0 + \pi^-, \]
\[ K^- + p \to \Lambda^0 + \pi^0, \]
inverse to the interaction of \(\pi\)-mesons with nucleons, leading to the pair production of \(K\)-mesons and hyperons.
Data on the nuclear interactions of hyperons are still more scanty than the data on \(\sigma K\)-stars considered above. By the beginning of 1955 it was
five stars have been found that were produced by the capture of charged hyperons that had stopped in the emulsion \(^{178}\). An example of such a star is shown in Fig. 72. Four of these stars are typical evaporation stars with 1, 2, 3, and 6 prongs. The last star is formed by the tracks of a proton and a \(\pi\)-meson. In no case does the visible energy of the stars exceed \(\sim 100\) MeV. Thus, from the properties of these stars
Fig. 72. Star formed by the capture of a charged hyperon that had stopped in the emulsion. \(1\)—track of the stopped hyperon \(^{178}\).
first of all it follows that the excitation energy of the nucleus, imparted to it upon capture of the hyperon, is small and does not exceed the excitation energy from capture of a \(\pi^-\)-meson.
VII.7. Unstable nuclear fragments
At the present time the generally accepted point of view is that the types of hyperons that have been discovered are nucleons in an excited state. Passing to the ground state, i.e., transforming into a proton or neutron, they emit \(\pi\)-mesons. This point of view is confirmed by two experimental facts. First, as follows from experiments performed on the cosmotron, hyperons arise even when the initial kinetic energy of the colliding particles is insufficient to provide the rest mass of the hyperon. Second, in the reverse process, when a stopped hyperon interacts with a nucleus, the energy released is also small and does not exceed the rest energy of the \(\pi\)-meson. If hyperons really are nucleons in an excited state, then one may expect the existence of nuclei in which at least one of the nucleons is replaced by a hyperon. Convincing evidence for the existence of such a new type of nuclear excitation was first adduced by Danysz and Pniewski\(^{179}\). A characteristic feature of such nuclei (“unstable nuclear fragments”) is that they, like the other heavy unstable particles, are formed in nuclear disintegrations of high energy and possess, on the nuclear time scale, an extremely long lifetime, comparable with the lifetime of hyperons. At the Padua conference data on 17 decays of such nuclei were summarized\(^{180}\). Their lifetimes lie in the range \(\sim 10^{-12}—10^{-10}\) sec; moreover, the length of their tracks in the emulsion ranges from 2 microns to 13 mm.
A characteristic case of the decay of an unstable nuclear fragment is shown in Fig. 73. This case is of special interest also because, simultaneously with the fragment under consideration, a \(\tau\)-meson also appeared in the star. The fragment \(f\) traverses in the emulsion a path equal to 17.3 mm and, after stopping, decays into a short-range particle \(a\) and a fast particle \(b\), leaving the emulsion. The short track \(a\) merges with the end of the track of the fragment itself, while the track \(b\) is, to within \(\sim 2^\circ\), opposite to the track \(a\). Thus, from the geometry of the decay it follows that the fragment \(f\) decayed into two particles \(a\) and \(b\). A count of the number of \(\delta\)-rays along the track \(f\) shows that it was formed by a singly charged particle. For the mass of this particle the following values were obtained:
\[
M_f = 4830 \pm 1400\, m_e\,(\bar a, R),
\]
\[
M_f = 5300 \pm 900\,(g_*, R).
\]
Thus, the particle \(f\), for which \(Z=1\) and \(A=3\), is the tritium nucleus \(\mathrm{H}_1^3\). Measurements of the ionization and scattering of particle \(b\) show that it is a light meson. From the law of conservation of charge it follows that this light meson is negatively charged, while the short-range particle \(a\) carries a double positive charge, i.e., is an \(\alpha\)-particle. The decay scheme of the heavy unstable fragment can therefore be written in the following form:
\[ \mathrm{H}_1^{3*}\to \mathrm{He}_2^3+\pi^-+Q. \]
The amount of energy \(Q\) released in this decay is \(42.0\pm 4.2\) MeV. An analogous decay of an excited tritium nucleus was found earlier by Bonetti et al.\(^{181}\), who obtained the value \(Q=41.7\pm 1.0\) MeV. These values of the energy \(Q\) are close to the decay energy of the neutral hyperon (\(\sim 37\) MeV). Therefore the decays considered can be explained by the assumption that in both excited tritium nuclei one of the neutrons was replaced by a neutral hyperon.
Fig. 73. Decay of a heavy nuclear fragment (excited \(\mathrm{H}_1^3\) nucleus) into a \(\pi^-\)-meson and an \(\alpha\)-particle.
Almost all the data obtained on heavy unstable fragments (many of them have charge considerably greater than 1) agree with the assumption that these fragments are formed by the replacement of one of the neutrons by a neutral hyperon. One of the observed cases of decay of a neutral fragment (a two-prong fork)\(^{182}\) agrees
with the assumption that this splitting is the decay of an excited “dineutron” into a π-meson and a deuteron, with the value \(Q = 89 \pm 10\) MeV. This case also admits another interpretation: it may be an example of the decay of a fragment that is a compound of a nucleon and a charged hyperon.
Knowing the nature of the fragment, and the mass and energy of the particles arising in its decay, one can determine the binding energy of the neutral hyperon in the fragment. Such estimates, made for several cases admitting measurement, show that the binding energy of a neutral hyperon in a nuclear fragment is several times smaller than the binding energy of a neutron in the corresponding stable fragment.
Summary table of masses and decay schemes of heavy unstable particles
Table XIII summarizes the most reliable data on the masses and decay schemes of heavy unstable particles presented in the review. In some cases several possible values of decay parameters are given, with references to the corresponding works.
The data considered on charged hyperons require the existence of at least three types of charged hyperons: the positively charged hyperon \(Y^+\) (also denoted \(\Sigma^+\)), to which two alternative decay schemes should be assigned \((Y^+ \to p + \pi^0\) and \(Y^+ \to n + \pi^+)\), the negatively charged hyperon \(Y^-\), decaying into a neutron and a π-meson (also denoted \(\Sigma^-\)), and a heavier hyperon, whose decay produces a neutral hyperon and a negatively charged π-meson. The latter type of hyperon, which forms the so-called cascade decays, is also denoted \(\Xi^-\).
The most reliably established decay schemes of \(K\)-mesons are the decay schemes of \(\tau\)-, \(\vartheta^\pm\)-, \(\vartheta^0\)- and \(K_\mu\)-mesons. As is seen from the table, within the errors of the measurements the masses of these mesons almost coincide. As indicated above, the \(\vartheta^0\)-meson may be regarded as the neutral analogue of the \(\vartheta^\pm\)-meson, just as the \(\pi^0\)-meson is the neutral analogue of the \(\pi^\pm\)-meson. It was shown that there is a significant probability that the \(\tau\)-meson has spin and parity \((0-)\), i.e. is, like the π-meson, a pseudoscalar particle. In this case one may expect that, like the ordinary π-meson, it will also decay into a μ-meson and a neutrino. It is therefore possible that the decay of the \(K_\mu\)-meson is a competing branch of the decay of the \(\tau\)-meson. If this is so, then the masses of these mesons should coincide, and measurements of the mean lifetimes of \(\tau\)- and \(K_\mu\)-mesons should give identical values. From the data in the table it is seen that the masses of \(\tau\)- and \(K_\mu\)-mesons are close to one another. The same should also be said of the mean lifetimes. For
Table XIII
| Designations | Decay scheme | Decay energy in MeV | Mass in \(m_e\) | Mean lifetime in sec | Spin |
|---|---|---|---|---|---|
| 1. Hyperons | 1. Hyperons | 1. Hyperons | 1. Hyperons | 1. Hyperons | 1. Hyperons |
| \(\Lambda^0\) | \(\Lambda^0 \to p+\pi^-\) | \(37.2\pm0.3\) | \(2182\pm1\) | \((3.7^{+0.8}_{-0.6})\cdot10^{-10}\) | Half-integer |
| \(Y^+(\Sigma^+)\) | \(Y^+ \to p+\pi^0\) | \(116\pm0.7\) | \(2333\pm1.5\) | \((2.9^{+4.8}_{-1.1})\cdot10^{-10}\) | " " |
| \(Y^\pm(\Sigma^\pm)\) | \(Y^\pm \to n+\pi^\pm\) | \(110\pm10\) | \(2333\pm20\) | \(10^{-11}<\tau<3\cdot10^{-10}\) | " " |
| \(Y^-(\Xi^-)\) | \(Y^- \to \Lambda^0+\pi^-\) | \(\begin{cases}67\pm12\\65\pm5\end{cases}\) | \(\begin{cases}2600\pm24\\2582\pm10\end{cases}\) | \(\sim10^{-10}\) | " " |
| 2. \(K\)-mesons | 2. \(K\)-mesons | 2. \(K\)-mesons | 2. \(K\)-mesons | 2. \(K\)-mesons | 2. \(K\)-mesons |
| \(\tau;\ {}^{965.5}_{0}K_{3\pi}\) | \(\tau^\pm \to \pi^\pm+\pi^+ +\pi^-\) | \(74.4\pm0.3\) | \(965.5\pm0.7\) | \(>10^{-8}\) | Integer |
| \(\tau';\ {}^{975}_{2\pi^0}K_\pi\) | \(\tau^\pm \to \pi^\pm+\pi^0+\pi^0\) | — | \(975\pm44\) | \(>10^{-9}\) | " |
| \(\vartheta^0;\ {}^{971}_{0}K^0_{2\pi}\) | \(\vartheta^0 \to \pi^+ + \pi^-\) | \(214\pm5\) | \(971\pm10\) | \((1.5^{+0.4}_{-0.3})\cdot10^{-10}\) | " |
| \(\chi;\ \vartheta^\pm;\ {}_{\pi^0}K^\pm_\pi\) | \(\vartheta^\pm \to \pi^\pm+\pi^0\) | — | \(952\pm11\) | \(>10^{-9}\) | " |
| \(x;\ {}^{1060}_{??}K_\mu\) | \(x \to \mu+\nu+\gamma\) or \(\mu+\nu+\nu\) | — | \(1060\pm35\) | \(>10^{-9}\) | — |
| \(K_\mu,\ \chi K_\mu\) | \(K_\mu \to \mu+\nu\) | — | \(\begin{cases}950\pm15\\941\pm11\\928\pm13\end{cases}\) | \(\sim2.8\cdot10^{-8}\) | Integer |
| \(K_e\) | \(K_e \to e+\gamma+\nu\) | — | \(\sim1000\) | — | — |
| \({}^{1450}K\) | ? | — | \(\sim1200\text{—}1450\) | ? | — |
| \({}^{550}K\) | ? | — | \(\sim500\text{—}600\) | \(>\sim5\cdot10^{-9}\) | — |
final conclusions, however, require more accurate measurements of these quantities.
For the mass of the \(x\)-meson the table gives the value \(1060\pm35\,m_e\), obtained by weighting measurements made by the ionization–range method, according to cloud-chamber data. It should be noted that the evidence that the mass of the \(x\)-meson exceeds \(1000\,m_e\) is not sufficiently convincing. Indeed, the indicated accuracy \((\pm35\,m_e)\) is misleading, since it was obtained in weighting
values of masses with a scatter not covered by the standard deviations, while the data on the spectrum of secondary $\mu$-mesons in $\chi$-decay also do not give reliable indications that the mass of the $\chi$-meson is greater than $1000\,m_e$. Thus, it may be asserted that the mass measurements for all $K$-mesons stopping in emulsion are consistent with the assumption of a single mass value, close to the mass of the $\tau$-meson, i.e., to $965\,m_e$. This is the basis for the hypothesis that $\tau$-, $\chi$-, $\gamma$-, and $K$-decays are alternative decays of particles of one type. As has already been indicated, to test this hypothesis it would be necessary to verify that all these decays correspond to the same lifetime of the particle and that the relative frequency of occurrence of these particles does not depend on the conditions of their observation. Apparently, this problem will be solved at accelerators when it becomes possible to obtain a beam of charged $K$-mesons.
The question of the existence of mesons with a mass of about $1450\,m_e$ (${}^{1450}K$) also cannot be regarded as settled until the reliability of mass measurements by the ionization–scattering method has been definitively confirmed or rejected. This problem can be solved when shower particles for which mass measurements give values close to $1450\,m_e$ are traced until they stop in an emulsion chamber and their mass is measured by one of the usual methods, in which one of the parameters is the residual range of the particle.
For one and the same particle, several commonly used designations are given in the table. Thus, for example, the $\tau$-meson is denoted by ${}^{965.5}_{0}K_{3}$, which means a $K$-meson with mass $965.5\,m_e$, giving, upon decay, 3 charged particles and not forming neutral secondary particles.
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