An extended Heitler-Matthews model for the full hadronic cascade in cosmic air showers

The Heitler-Matthews model for hadronic air showers will be extended to all the generations of electromagnetic subshowers in the hadronic cascade. The analysis is outlined in detail for showers initiated by primary protons. For showers initiated by iron primaries the part of the analysis is given for as far as it differs from the analysis for a primary proton. Predictions for shower sizes and the depth of maximum shower size are compared with results of Monte Carlo simulations. The depth of maximum as it follows from the extrapolation of the Heitler-Matthews model restricted to the first generation of electromagnetic subshowers is too small with respect to Monte Carlo predictions. It is shown that the inclusion of all the generations of electromagnetic subshowers leads to smaller predictions for the depth of maximum and to smaller predictions for the elongation rate. The discrepancy between discrete model predictions and Monte Carlo predictions for the depth of maximum can therefore not be explained from the number of generations that is taken into consideration. An alternative explanation will be proposed.