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It is shown that the fundamental standard hadron cascade diffusion equationin the Mellin transform space is not rigorously correct because of theinconsistent double energy integral evaluation which generates the function$<\eta^{s}>$ with its associated parametizations. To ensure an exact basicworking equation, the Faltung integral representation is introduced which hasthe elasticity distribution function $u(\eta)$ as the only fundamental inputfunction and $<\eta^{s}>$ is just the Mellin transform of $u(\eta)$. ThisFaltung representation eliminates standard phenomenological parameters whichserve only to mislead the physics of cascade. The exact flux transform equationis solved by the method of characteristics, and the hadron flux in real spaceis obtained by the inverse transform in terms of the simple and essentialresidues. Since the essential residues are given by the singularities in theelasticity distribution and particle production transforms that appear in theexponentials, these functions should not be parametized arbitrarily to avoidintroducing non-physical essential residues. This Faltung formulation isapplied to the charged hadron integrated energy spectra of halo events detectedat Mt. Chacaltaya by the Brazil-Japan Collaboration, where the incoming flux atthe atmospheric boundary is a single energetic nucleon.

Faltung formulation of hadron halo event cascade at Mt. Chacaltaya