The Energy Spectrum of Electrons in the Atmosphere Arising from the Disintegration of Mesotrons

The energy spectrum of electrons at the altitude of 14,618 feet originating from the decay of mesotrons is calculated by means of the cascade theory of showers. It is assumed that the mesotron decays into a neutrino and an electron, which are emitted with equal probability in all directions in the reference frame of the mesotron. The diffusion equations for the showers are derived with the boundary conditions that there are no incoming electrons or photons. By approximations similar to those used in the shower theory, it is possible to calculate the electron spectrum in the lower atmosphere, provided the mesotron spectrum is known. If we assume a mesotron spectrum in accordance with experiment, the theoretical calculations for the electron spectrum can be compared with new observations on the intensity of the soft component for energies higher than 5×${10}^7$ ev. The calculations are in satisfactory agreement with experimental results found by D. Hall and later by W. Hazen.