The Energy Distribution in Cosmic-Ray Showers

The track length distribution $f\left(E\right)\mathrm{dE}$ in a shower is defined as the total distance traveled by all electrons while in the energy interval $\mathrm{dE}$. It is representative for the average energy distribution in a shower. The present paper obtains by numerical methods the complete functions for both electrons as well as for photons in showers of high primary energy. Calculations have been made for air and for lead, down to energies of about 4 Mev. Close approximations to the actual cross sections have been used for all energies and all physically significant processes have been included—radiation, pair production, energy loss through collision, Compton effect, and knock-on electrons. As a special result of importance we mention the high number of low-energy photons that accompany a shower, a quantity that has here been evaluated for the first time.