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THE NATURE OF THE NEUTRAL PARTICLE EMITTED IN $\pi$-MESON DECAY
Investigations by a number of authors$^{1,2}$ show that $\mu$-mesons formed in $\pi$-$\mu$ decay, within statistical deviations, have a quite definite range, i.e. are emitted with a quite definite kinetic energy. It has also been established that the angular distribution of $\mu$-mesons formed in decay is isotropic in the laboratory coordinate system. These two circumstances, in combination with the conservation laws, show, first, that the observed $\pi$-mesons at the moment of decay move with very small velocity. Otherwise the range of the $\mu$-mesons would vary strongly depending on the direction of their emission relative to the direction of motion of the $\pi$-meson.
Second, they show that the $\pi$-meson decays into two particles: a $\mu$-meson and some neutral particle emitted in mutually opposite directions. If several neutral particles were produced in the decay of the $\pi$-meson, then the emitted $\mu$-mesons would have different kinetic energies. An analogous question concerning the mechanism of decay of the $\mu$-meson was recently solved by G. B. Zhdanov,$^{3}$ who established that there exists a spectrum of energies of the electrons emitted in the decay of $\mu$-mesons. The existence of such a spectrum indicated the decay of the $\mu$-meson into an electron and several (apparently two) neutrinos.
Thus, it was established that the $\pi$-meson decays into a $\mu$-meson and some neutral particle, but the nature of this neutral particle has until now remained unclear. However, from general considerations one can draw certain conclusions about the mass of the neutral particle. Indeed, applying the conservation laws, one can show that the ratio $(P)$ of the rest mass $(n_0)$ of the neutral particle to the rest mass of the $\mu$-meson is given by the relation
\[ P = \frac{n_0}{m_\mu} = \sqrt{Q^2 - 2QB_\mu + 1}, \]
where
\[ Q = \frac{m_\pi}{m_\mu}, \qquad B_\mu = \frac{1}{\sqrt{1-\beta^2}} \]
for the $\mu$-meson at the moment of its formation. Hence it is clear that, for an exact determination of the mass of the neutral particle, it is necessary to know very accurately the rest masses of the $\pi$- and $\mu$-mesons and the energy with which the $\mu$-meson is emitted. Most measurements give the following values of the masses:
\[ m_\pi = 276 \pm 6m_e, \qquad m_\mu = 210 \pm 4m_e,\ \text{i.e. } Q = 1.315. \]
The mean range of the \(\mu\)-mesons formed in the decay of stopped \(\pi\)-mesons in Ilford-G5 emulsion proved to be \(595 \pm 10_{\mu}\), which corresponds to a meson kinetic energy of \(4.1\) MeV and \(B_{\mu} = 1.038\).
These values lead to a negligibly small rest mass of the neutral particle. The accuracy of the experimental data used for the calculation does not at present make it possible to determine the rest mass of the neutral particle reliably; however, it does make it possible to conclude with confidence that the rest mass of the neutral particle does not exceed several electron masses.
If the rest mass of the neutral particle is taken to be negligibly small, then this particle must possess an energy of \(30.1\) MeV in order to satisfy the conservation laws. Such a particle may be the neutrino (known from \(\beta\)-decay), a light neutral particle distinct from the neutrino, or, finally, the photon.
The author of the work under review\(^4\) made an attempt to detect the formation of photons in events of \(\pi\)-\(\mu\)-decay. Since for photons with energy \(30\) MeV the effective cross section for pair production is seven times greater than the Compton-effect cross section, the absorption of such photons in emulsion must occur mainly through the formation of electron pairs. Therefore, if the neutral particle emitted in the decay is a photon, then an electron pair may with some probability be found on the continuation of the \(\mu\)-meson track.
On electron-sensitive plates of the Ilford-G5 type with an emulsion thickness of \(400\,\mu\), about 400 cases of \(\pi\)-decay were found. The direction of emission of the neutral particle was determined from the mean line of grains in the first \(25\,\mu\) of the \(\mu\)-meson track. However, because of multiple scattering of the \(\mu\)-meson, the direction toward its point of origin, which determines the true direction of emission of the neutral particle, usually does not coincide exactly with the mean line of grains at the beginning of the \(\mu\)-meson track. To take this circumstance into account, the author investigated not only the direction of the mean line of the \(\mu\)-meson track, but also the region of emulsion lying inside a sector with an angle of \(2^\circ\) on each side of the mean line.
Of the 400 detected cases of \(\pi\)-\(\mu\)-decay, only 253 proved suitable for processing. The total examined area of the sectors selected in the manner described was \(1.32\ \text{cm}^2\), and the corresponding total path of the neutral particles in the emulsion was \(38\ \text{cm}\). In all, 35 electron pairs were recorded in this area. This corresponds to a density of pairs of \(26\) pairs/\(\text{cm}^3\). The same density of pairs was observed in any other arbitrarily chosen region of the plate. Assuming that the mean range in emulsion of photons with energy \(30\) MeV is \(66\) mm, the author expected to detect 5.77 electron pairs associated with the \(\pi\)-\(\mu\)-decay events. A pair may be regarded as associated with a decay event if:
1) The point of origin of the pair lies within the solid angle corresponding to the uncertainty in drawing the tangent to the direction of emission of the \(\mu\)-meson.
2) The direction of the electrons of the pair is close to the direction of the tangent to the \(\mu\)-meson track.
3) The energy of the pair is, within the experimental errors, equal to \(30\) MeV.
Of the 36 pairs found, 35 do not satisfy conditions (1) and (2), and one pair does not satisfy condition (3). Thus, instead of 5–6 pairs satisfying all three conditions, not a single one was found. The probability that the neutral particles, if they are photons, would not form a single pair along a path of \(38\ \text{cm}\) (with a mean number of pairs 5.77) is equal to \(e^{-5.77} = 4\cdot 10^{-3}\).
Rejecting this assumption because of its small probability, the author of the paper under review concludes that the neutral particle emitted in the decay of the $\pi$-meson is not a photon.
The same conclusion may be reached by applying the law of conservation of spin to $\pi$-$\mu$-$e$ decay. Assuming that the $\pi$-meson has zero or integral spin$^{5}$, while the $\mu$-meson has half-integral spin$^{6}$, one may conclude that the neutral particle emitted in $\pi$-$\mu$ decay, as well as the “neutrino” produced in the decay of the $\mu$-meson, is a particle with Fermi statistics.
At present there are still no sufficient grounds for identifying the neutral particle arising in $\pi$-$\mu$ decay with the neutrino postulated by Fermi and Pauli to explain the observed features of $\beta$-decay.
A. G.
REFERENCES
- Lattes, Occhialini, Powell, Nature 160, 453 (1947).
- Fowler, Phil. Mag. 41, 169 (1950).
- G. B. Zhdanov, DAN 65, 287 (1949).
- O’Cellaigh, Phil. Mag. 41, 838 (1950).
- Serber, Phys. Rev. 75, 1495 (1949).
- Christy, Kusaka, Phys. Rev. 59, 414 (1941).