Penetrating Showers in Light and Heavy Elements

Abstract

A large cloud chamber fitted with one thick "producer plate" of light materials and with eight \textonequarter{}-in. lead plates was operated at Echo Lake, Colorado (altitude 3260 m) to record penetrating showers originating in three light elements (Li, C, Al) and in lead. The average primary energies, estimated with the "$F$-plot" method of Duller and Walker, were between 20 and 25 Bev. From a comparison of the shower rates in the producer plates and in the top lead plate, upper and lower limits for the transparencies of the light elements are obtained, the latter if correction is made for the differences in the primary energies. More reliable values, however, are derived from a direct comparison of the rates in the three light elements. This yields a value of $\ensuremath{\lambda}=(2.55\ifmmode\pm\else\textpm\fi{}0.25)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm for the mean free path in nuclear matter, and accordingly transparencies of (15\ifmmode\pm\else\textpm\fi{}7) percent, (12\ifmmode\pm\else\textpm\fi{}4) percent, and (6\ifmmode\pm\else\textpm\fi{}3) percent, respectively for Li, C, and Al. It is shown that second-generation effects are not negligible even in light nuclei, and that they can account for the observed differences in the average multiplicities of showers initiated in the four elements studied. At a primary energy of 25 Bev, the average multiplicity of a nucleon-nucleon collision is about 3.4. The contribution of the $\ensuremath{\pi}$ mesons to the intranuclear cascade is very small. This agrees well with the observed mean free path for shower production in the lead plates by secondary particles, which varies from (380\ifmmode\pm\else\textpm\fi{}35) g/${\mathrm{cm}}^{2}$ for secondaries from light elements to (475\ifmmode\pm\else\textpm\fi{}70) g/${\mathrm{cm}}^{2}$ for secondaries from lead. Since nuclear scattering in the lead plates was observed for secondaries from the light elements and from lead with mean free paths of (370\ifmmode\pm\else\textpm\fi{}35) g/${\mathrm{cm}}^{2}$ and (300\ifmmode\pm\else\textpm\fi{}36) g/${\mathrm{cm}}^{2}$ respectively, the total interaction mean free path in lead, comprising both scattering and secondary showers, is very nearly the same for secondaries emerging from light and heavy elements---about (190\ifmmode\pm\else\textpm\fi{}25) g/${\mathrm{cm}}^{2}$---and is also close to the geometrical value.