Multiple Scattering of $\mu$-Mesons

Determination of the energy of a fast particle from the magnitude of the multiple Coulomb scattering which it undergoes in a photographic emulsion has in recent years become one of the most widely used methods in cosmic-ray physics. In this connection, the experimental—

A further check was made of Williams’ formula (1939), which gives the dependence between the mean square angle of multiple scattering \(\sqrt{\overline{\vartheta^{2}}}\) and the particle energy. In the paper reviewed here\(^1\), cosmic-ray \(\mu\)-mesons were used as fast particles. It is known that their nuclear interaction is extraordinarily small, and its contribution to multiple scattering may be completely neglected.\(^2\) The experimental arrangement is shown in the figure. The scatterer, a lead plate \(2.5\ \mathrm{cm}\) thick, was placed in the middle of a Wilson chamber \(30\ \mathrm{cm}\) in diameter. The chamber was controlled by a telescope consisting of rows 1–4 of Geiger counters (see figure). Mesons were registered by the method of delayed coincidences: expansion of the chamber occurred when a pulse in row 4 coincided with pulses in rows 1, 2, and 3, delayed by \(1.5\ \mu\mathrm{sec}\). In this way \(\mu\)-mesons were selected which had passed through absorber \(A\) (\(130\ \mathrm{g}/\mathrm{cm}^{2}\) of lead), stopped in absorber \(B\) (\(7.5\ \mathrm{cm}\) of graphite), and emitted a decay electron registered by row 4. The energy of such mesons lies between \(172\) and \(196\ \mathrm{MeV}\) (\(184 \pm 12\ \mathrm{MeV}\)). Altogether, 72 cases of passage of \(\mu\)-mesons through the system were photographed. The measured values of the projection of the mean scattering angle onto a plane are well described by a Gaussian distribution and give, for the mean scattering angle, the value \(\sqrt{\overline{\vartheta^{2}}}=3.68 \pm 0.4^\circ\). Williams’ formula for this case gives \(\sqrt{\overline{\vartheta^{2}}}=5.7^\circ\). Thus the measured value is 65% of the theoretical one. The author points out that this result confirms the work of L. A. Kulchitskii and G. D. Latyshev\(^3\) and of Sinka.\(^4\) In paper 3, scattering in thin lead foil was measured for \(\mu\)-mesons and electrons with energy \(2.5\ \mathrm{MeV}\). The value obtained for \(\sqrt{\overline{\vartheta^{2}}}\) proved to be 89% of the theoretical value. In paper 4, the scattering in lead of \(\mu\)-mesons with energy \(55\)–\(155\ \mathrm{MeV}\) was measured, and the measured value of \(\sqrt{\overline{\vartheta^{2}}}\) was equal to 47% of the value given by Williams’ formula. It is possible that the observed discrepancy is explained by the fact that Williams’ theory, based on the Born approximation, ceases to be valid for heavy elements.\(^5\) This is all the more probable since the author’s measurements for iron (\(Z=26\)) are in agreement with Williams’ formula.

A. Weisenberg

References Cited

1. A. V. Grewe, Proc. Phys. Soc. 64, 660 (1951).
2. E. Amaldi and G. Fidecaro, Helv. Phys. Acta 93, 23 (1950).
3. L. A. Kulchitskii and G. D. Latyshev, Phys. Rev. 61, 254 (1944).
4. M. S. Sinka, Phys. Rev. 68, 153 (1948).
5. Parzen, Phys. Rev. 80, 261 (1950).