An extended universality of electron distributions in cosmic ray showers of high energies and its application

• It was shown that lateral distributions of shower electrons can be described by one function.
• Also their angular distributions depend on a combination of angle and energy.
• A new method of shower reconstruction from its optical images is proposed.

It is shown that the shape of any electron distribution in a high energy air shower is the same in all such showers, if taken at the same age, independently of the primary energy, mass and thus, of the interaction model. A universal behaviour has been also found within a single shower, such that the lateral distributions of electrons with fixed energies, at various shower ages, can be described by a single function of only one variable. The angular distributions of electrons with a fixed energy can be represented, at a given lateral distance, by a function of the product θ·Eαθ·Eα only, which is explained by a model of small angle electron scattering with simplified energy losses. These results have been obtained by Monte Carlo simulations of the extensive air showers. The electron universality can be used as a method for determining the longitudinal profile of any single shower from its optical images measured by the fluorescence light technique, which is particularly useful with showers observed with large fraction of the Cherenkov light.