LIFETIME OF THE POSITIVELY CHARGED $\pi$-MESON

In UPhN[^1] it was reported that the lifetime had been determined for negatively charged $\pi$-mesons (the mass of the $\pi$-meson is equal to 276 electron masses), obtained at the Berkeley synchrocyclotron by bombarding a carbon target with $\alpha$-particles of kinetic energy 380 MeV. The lifetime obtained in these measurements is

\[ \tau = \left(1.11^{+0.31}_{-0.22}\right)\cdot 10^{-8}\ \text{sec.}, \]

which is almost 200 times less than the lifetime of $\mu$-mesons, which constitute the principal part of the penetrating component of cosmic rays $(2.15\cdot 10^{-6}\ \text{sec.})$. Soon after this experiment, carried out by Richardson,[^2] $\pi$-mesons were produced by bombarding targets with fast protons. The maximum energy of the protons used for this purpose was 345 MeV. Owing to the considerable separation of this proton energy from the energy threshold for $\pi$-meson production, the yield of the latter increased by approximately a factor of 10 and their energy increased appreciably. This made possible a more thorough repetition of Richardson’s experiment in order to refine the value of $\tau$ obtained by him. Such a refinement was carried out in the work under review.[^3]

The arrangement of the experiment is shown in Fig. 1. A beam of protons falls on a carbon target placed in the chamber of the cyclotron. In this process $\pi$-mesons of various kinetic energies are produced, flying out in different directions. Three helical channels, made of copper and arranged one below another (see Fig. 1), separate three beams of positively charged $\pi$-mesons flying out of the target in a direction opposite to the direction of the proton beam. Fig. 2 shows a general view of the device with the three channels; the cover over the first channel has been removed. In Fig. 1 the position is shown of the holders for the photographic plates registering the $\pi$-mesons. Since the mesons move in the magnetic field of the cyclotron $(H = 14{,}295\ \text{oersted})$, their trajectories are helical lines, and the photographic plates are reached by $\pi$-mesons that have made—

...making, respectively, \(1/2\), \(3/2\), and \(5/2\) revolutions along the helical line. The channels focus mesons whose energies lie between 8 and 15 MeV. The time

Fig. 1. Diagram of the trajectories of mesons in the apparatus for measuring the lifetime.

Labels in the figure: lead screen; upper channel; lower channels; position of the photographic-plate holders; cyclotron beam; carbon target.

Fig. 2. Photograph of the apparatus for measuring the lifetime of mesons. The cover over the first channel has been removed.

during which a \(\pi\)-meson makes one complete revolution in the channel does not depend on its energy and is equal to

\[ T = 0.6945 \times 10^{-8}\ \text{sec}. \]

The intensity of the meson beams measured at the end of the three channels is less than the intensity of the beams at the beginning of the channels for the following reasons:

1) Part of the mesons, owing to the initial divergence of the beam, will leave the solid angle determined by the geometry of the channel and be absorbed by the walls.

2) Some of the mesons will decay while traveling. The attenuation of the intensity caused by the first reason depends on purely geometrical factors and can be taken into account. The observed additional decrease in intensity occurs because of decay, and, if the time of motion of the mesons through the channels is known, the lifetime of the $\pi$-meson can be determined from the magnitude of this decrease. The mesons were detected with photographic plates; moreover, unlike Richardson’s experiment, the lifetime was determined for positively charged $\pi$-mesons, which were identified by the $(\pi-\mu)$ decay that they undergo after stopping in the plate.

The experimentally observed quantity in the work described was the number of tracks of positively charged $\pi$-mesons incident per unit area of the photographic plate (the meson density). The authors obtained:

\[ \frac{\text{meson density after } 3/2 \text{ revolutions}} {\text{meson density after } 1/2 \text{ revolution}} = 0.248 \pm 0.014; \]

\[ \frac{\text{meson density after } 5/2 \text{ revolutions}} {\text{meson density after } 1/2 \text{ revolution}} = 0.0954 \pm 0.0052. \]

Measurements made with $\alpha$-particle sources instead of a carbon target showed that, if the $\pi$-mesons were stable, this ratio would be $0.333$ and $0.200$, respectively.

Using these data, knowing the time $T$ in which the meson makes one complete revolution in the magnetic field, and after an analysis of the errors, the authors obtain for the mean lifetime of the positively charged $\pi$-meson the value

\[ \tau = \left(1.97^{+0.14}_{-0.17}\right)\cdot 10^{-8}\ \text{sec}, \]

which is almost twice as large as the value of $\tau$ obtained by Richardson. Further measurements should clarify whether this discrepancy is the result of experimental inaccuracies allowed by Richardson, or whether positively and negatively charged mesons in fact have different lifetimes.

A. V.

References

1. UFN, vol. 37, issue 4, p. 500, 1949.
2. I. Richardson, Phys. Rev. 74, 1720 (1948).
3. E. Merthell and W. Panofsky, Phys. Rev. 77, 465 (1950).