A MC generator incorporating the new features of hadronic multiproduction, observed at the CERN collider with the European hybrid spectrometer, has been developed using considerations based on the dual parton model. This semi-empirical model is especially efficient at reproducing the complex characteristics of semi-inclusive data under the principle of scaling in the central region for relative rapidity density against z, and violation of KNO scaling. Extended to include p-A collisions, such as a triple-Gaussian random generator, it has been inserted in a cosmic-ray cascade simulation.

From a Monte Carlo simulation study of cosmic ray air showers around the knee of the primary energy spectrum it is shown that, despite a strong radial dependence of the lateral shower age parameter, the lateral density distribution of electrons in cosmic ray EAS displays universality when expressed in terms of local age parameters. The nature of the radial variation of local age is found to depend on the choice of the effective Moliere radius, particularly for radial distances below about 400 m. The possible use of shower age parameters in a multi-parameter study of EAS for extracting information about the nature of the shower initiating particles, has been re-examined.

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After performing extensive simulations with the code CoRSiKa, we have obtained an analytical description fitting with surprising accuracy the numerical densities up to distances larger than 5 km from the shower axis. This was achieved by using the hypergeometric formalism in place of the traditional NKG approach. The difficulty of cascade theory (validity limited to 3.5 Moliere radii), underlined with reason by the particle data group, is solved here, after overcoming the constraints of approximation B, to show that the distribution of lateral profiles at large distances is also correlated with the age parameter. This is an important step for a coherent interpretation of hybrid events recorded with both surface array and fluorescence telescopes, even with other information coming from Cerenkov or radio emission. A set of hypergeometric Gaussian functions, with a consistent relation between age parameter and total size, is proposed in the ultra-high-energy range (above 1 EeV) for electrons, muons and vertical equivalent muons.

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