Abstract
In this paper a new semi-analytical model is used to describe the evolution of air showers in the atmosphere. The model is based on the interpretation of the shower as a branching processes which can be well described by generating functions. The method as introduced has a very general use and in this paper it is applied to study the evolution of the number of muons in the shower. The mean and the variance of the total number of muons in the shower are calculated within the new semi-analytical model. The results are compared to previous semi-analytical models and to Monte Carlo simulation of the air showers.
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