Universality of electron–positron distributions in extensive air showers

Using a large set of simulated extensive air showers, we investigate universality features of electron and positron distributions in very-high-energy cosmic-ray air showers. Most particle distributions depend only on the depth of the shower maximum and the number of particles in the cascade at this depth. We provide multi-dimensional parameterizations for the electron–positron distributions in terms of particle energy, vertical and horizontal momentum angle, lateral distance, and time distribution of the shower front. These parameterizations can be used to obtain realistic electron–positron distributions in extensive air showers for data analysis and simulations of Cherenkov radiation, fluorescence signal, and radio emission.