The understanding of the basic properties of the ultra - high energy extensive air showers is strongly dependent on the description of the hadronic interactions in a energy range beyond that probed by the LHC. One of the uncertainties present in the modeling of the air showers is the treatment of diffractive interactions, which are dominated by non - perturbative physics and usually described by phenomenological models. These interactions are expect to affect the development of the air showers, since they provide a way of transporting substantial amounts of energy deep in the atmosphere, modifying the global characteristics of the shower profile. In this paper we investigate the impact of the diffractive interactions in the observables that can be measured in hadronic collisions at high energies and ultra - high energy cosmic ray interactions. We consider three distinct phenomenological models for the treatment of diffractive physics and estimate the influence of these interactions on the elasticity, number of secondaries, longitudinal air shower profiles and muon densities for proton - air and iron - air collisions at different primary energies. Our results demonstrate that the diffractive events has a non - negligible effect on the observables and that the distinct approaches for these interactions, present in the phenomenological models, are an important source of theoretical uncertainty for the description of the extensive air showers.
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