Nuclear Size from Cosmic-Ray Interactions

The total path length of 3625 penetrating charged secondaries of average energy 4 Bev has been measured in three plate assemblies of Al, Cu, and Pb inside a big square cloud chamber. The total number of nuclear interactions observed were divided into two groups, (i) nuclear disintegrations (high-energy transfers) and (ii) nuclear scatterings (elastic), and the total cross section and the cross section for nuclear disintegrations alone have been determined. It has been found that the equivalent square-well radii of Al, Cu, and Pb found from the latter cross sections agree well with $1.19A^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm whereas the radii corresponding to the total cross sections follow $1.34A^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm. The results thus indicate the same matter distribution in Al, Cu, and Pb nuclei as that determined from high-energy electron scattering, mu-mesonic x-ray data, and highenergy neutron absorption data. Moreover, each nucleus appears to be surrounded by an equivalent spherical shell of thickness $0.15A^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm which chiefly accounts for the elastic nuclear scatterings. The existence of this shell is presumably the effect of the finite range of nuclear forces.