NUCLEAR DISINTEGRATIONS INDUCED BY $\mu$-MESONS

As is known, as early as 1947, almost simultaneously with the discovery of $\pi$-mesons, experiments were carried out on the nuclear capture of stopped $\mu$-mesons; the results of these experiments sharply contradicted the prevailing notions concerning the strong nuclear interaction of $\mu$-mesons. For further study of the nuclear interactions of $\mu$-mesons it was natural to proceed to experiments at great depths, where all nuclear-active particles (nucleons, $\pi$-mesons) are practically entirely absorbed and can no longer create any appreciable “background” of nuclear processes.

Direct indications of nuclear disintegrations under the action of fast $\mu$-mesons (mean energy $\sim 10^{10}$ eV) were first obtained in 1950 by the photographic-plate method1 at depths down to 60 m water equivalent. A significant fraction of the “stars” in these experiments could be explained by the direct interaction of a relativistic $\mu$-meson with a nucleus, while the rest by nucleons and, in part, photons in equilibrium with the $\mu$-mesons. The presence of a certain number of nucleons, as well as of $\pi$-mesons stopped in the photoemulsion, proved possible to connect with the emission of these nuclear-active particles in “stars” produced directly by $\mu$-mesons. The authors also give an approximate quantitative explanation of the observed value of the effective cross section for the generation of “stars” by $\mu$-mesons ($\sim 10^{-29}\text{ cm}^2$), starting from the decomposition of the electromagnetic field of a moving $\mu$-meson into a spectrum of virtual photons and from the value of the effective cross section for the generation of $\pi$-mesons by photons. In this case the whole process is regarded as the virtual conversion of a $\pi$-meson born by a virtual $\gamma$-quantum in the same beam.

Fig. 1.

In the recently published work of Cocconi and Tongiorgi2 the same process involving fast $\mu$-mesons is studied by an entirely different method. Using a system of neutron counters with a special coincidence-selection system, the authors recorded (with an efficiency of $\sim 5\%$) the production of groups of neutrons in a thick layer of material (Pb or Al), and this considerably increased the statistical accuracy of the observations in comparison with the photographic-plate method (where only a thin layer of photoemulsion is used).

The arrangement (front view) is shown in Fig. 1: 12 neutron counters HC were connected in parallel and sent pulses to a special radio circuit with nine channels. Each channel operated in the presence of a definite number ($m$) of pulses following one another with a time interval not exceeding 160 $\mu$sec*). Such a system made it possible to record the production of groups of neutrons with good statistics at a small number of random coincidences ($\sim 10$ “useful” events per hour at a depth of 20 m H$_2$O for $m=2$, with a “background” of random coincidences of 0.1% even at a depth of 1 m H$_2$O). When the whole apparatus was lowered into the water of a lake to a dis-

*) This time corresponds to the mean slowing-down time of neutrons with energies of the order of several MeV.

to various depths down to 60.5 m*) the authors obtained the curves shown in Fig. 2 for the dependence of the number of coincidences of various multiplicities \(F(m)\) on the depth of observation. The absorption curves are given here only for the case when the neutrons were produced in a 10-cm lead block; however, analogous results were also obtained for a filter of 10 cm Al. The corresponding absorption curves are also given in Fig. 2 for the nuclear-active component (the \(N\)-component), having a range of \(\sim 160\ \mathrm{g/cm^2}\) of \(H_2O\), and for single \(\mu\)-mesons, whose range is \(\sim 4000\ \mathrm{g/cm^2}\) (for 10 m \(H_2O\)). A joint analysis of all the curves shows that the groups of neutrons registered by the apparatus at a depth of several meters of water decrease in number in parallel with the absorption of the \(N\)-component, but, beginning at approximately a depth of 10 m \(H_2O\), they are already entirely due to fast \(\mu\)-mesons.

Fig. 2.

In addition, the paper gives curves for the distribution of the number of coincidences by multiplicity \(m\) both for different thicknesses of lead \(\Sigma\) in air and for thick filters (10 cm Pb and 10 cm Al) at great depths. In this connection it turned out that, for the case \(\Sigma = 10\) cm Pb, the distribution \(F(m)\) at all depths has approximately the same form, smoothly decreasing with increasing \(m\) and corresponding to a mean multiplicity of the process of 16–20 neutrons in one event. This fact means that the phenomenon observed at great depths can in no way be reduced to the “trivial” effects of neutron production by reactions of the type \((\gamma, n)\) or to the capture of stopped \(\mu\)-mesons by nuclei (although coincidences of small multiplicity, \(m = 1–2\), in the overwhelming majority of cases are due precisely to these “trivial” processes). With a decrease in the thickness of the lead filter \(\Sigma\), as also in the transition from lead to aluminum, the mean multiplicity of neutron generation sharply decreases; this finds a natural explanation³ in the fact that, for nuclear disintegrations under the action of \(\mu\)-mesons leading to neutron generation, the nuclear-cascade process both outside the nucleus and inside it plays the same role as for ordinary disintegrations.

In order to determine the effective cross section for nuclear disintegrations caused by \(\mu\)-mesons, it is necessary to subtract from the total effect registered at a depth of 20 m \(H_2O\) the “background” associated with the reaction \((\gamma, n)\) and with the capture of slow mesons (this “background” amounts

* The zero point was obtained in the laboratory with the apparatus surrounded on all sides by paraffin of thickness 15 cm.

respectively, \(1.5\cdot 10^{-28}\ \text{cm}^2/\text{nucleon}\) and \(1.3\cdot 10^{-28}\ \text{cm}^2/\text{nucleon}\), calculated per one \(\mu\)-meson; the effective cross section obtained is
\(\sigma_\mu = 1.7\cdot 10^{-29}\ \text{cm}^2/\text{nucleon}\). Introducing also a certain correction that takes into account, in the nuclear component, \(\mu\)-mesons born outside the apparatus (in water), the authors obtain the final result
\(\sigma_\mu=(1\pm0.5)\cdot 10^{-29}\ \text{cm}^2/\text{nucleon}\); this refers to a mean \(\mu\)-meson energy equal to \(6\cdot 10^9\ \text{eV}\).

A detailed analysis of all the experimental material presented above was made in the theoretical paper of Hayakawa\(^3\). The author also arrives at the conclusion that the mechanism of the process consists in an intranuclear conversion of \(\pi\)-mesons produced by virtual photons of the electromagnetic field of a fast \(\mu\)-meson. Thus there is no need to introduce into consideration a purely nuclear interaction of \(\mu\)-mesons with a comparatively large effective cross section*) or to assume the existence of any as yet unknown particles in the penetrating component of cosmic rays underground.

It should be added that the presence of an intranuclear cascade process in the present case apparently may also lead to the production of showers of \(\pi\)-mesons observed at great depths\(^1\). In addition, a natural consequence of the process under consideration should be both appreciable anomalous scattering of sufficiently fast \(\mu\)-mesons and the presence of additional (besides ionization and radiation) energy losses, which must be taken into account in analyzing the absorption curve of cosmic rays at great depths. The processes of anomalous scattering of penetrating particles and of the production of penetrating showers (in lead) were recently observed\(^4\) at a depth of \(6\ \text{m}\ \mathrm{H_2O}\) with the aid of a hodoscopic apparatus. However, the effective cross sections of both processes proved to be approximately an order of magnitude larger than might be expected, which makes one doubt the reliability of the data obtained.

G. B. Zhdanov

Cited Literature

1. E. P. George, J. Evans, Proc. Phys. Soc. A 63, 1248 (1950).
2. G. Cocconi, V. Cocconi-Tongiorgi, Phys. Rev. 84, 29 (1951).
3. S. Hayakawa, Phys. Rev. 84, 37 (1951).
4. E. P. George, P. T. Trent, Proc. Phys. Soc. A 64, 1134 (1951).