Stefan Grimm Karlsruhe

Analytic investigation of extended Heitler-Matthews model

\textbf{Analytic investigation of extended Heitler-Matthews model} Many features of extensive air showers are qualitatively well described by the Heitler cascade model and its extensions. The core of a shower is given by hadrons that interact with air nuclei. After each interaction some of these hadrons decay and feed the electromagnetic shower component. The most important parameters of such hadronic interactions are inelasticity, multiplicity, and the ratio of charged vs.\ neutral particles. However, in analytic considerations approximations are needed to include the characteristics of hadron production. We discuss extensions of the simple cascade model by analytic description of air showers by cascade models which include also the elasticity, and derive the number of produced muons. In a second step we apply this model to calculate the shower center of gravity which can be related to the shower maximum. \textbf{Stefan Grimm, Darko Veberi\v{c} and Ralph Engel}