Universality in the longitudinal development of Cosmic Ray showers

Abstract

In this work we derive the result that the shape of the longitudinal development of individual very high energy showers, not too far from maximum, has in most cases a simple, smooth shape that resembles a gaussian with a small distortion, so that the post–maximum width of the shower profile is broader than the pre–maximum width. The distortion becomes smaller for larger shower energies. These results are independent from the nature of the primary particle (photon, electron, proton or nucleus) and are related to the fact that the spectra of the particles (e± and γ) that form the dominant component of a shower, have spectra that in good approximation depends only on the shower age. The longitudinal profiles of the showers are therefore reasonably well characterized by only few parameters: the position and size at maximum: tmax and Nmax, the width σ and the asymmetry a. Information about the nature of the primary particles (and the properties of hadronic interactions) can be extracted from statistical studies of the distributions of the shape parameters. Studies of tmax (the position of the shower maximum) are the most sensitive, but also the distributions of the shower width and asymmetry can give valuable information.