Computer simulations of cosmic-ray air showers III. Fluctuations in shower development

Abstract
Detailed studies are made of the fluctuations of a wide range of parameters in computer-simulated extensive air showers in attempts to design experiments which will be sensitive to the mass number of primary cosmic rays of energy 10$^{17}$-10$^{18}$ eV. The computational procedures depend heavily on the Monte Carlo technique and the model for the high-energy interactions of nucleons and pions is simple, involving pionization only. The magnitudes of the fluctuations of the electron size, muon sizes and depths of cascade maximum development are determined as a function of the energy and mass of the primary particle. The origin of the fluctuations is identified for showers initiated by primary protons of various energies from studies of the correlations between observable parameters of the showers and measures of the stage of longitudinal development of the electron cascade. The correlation between the different components of air showers and between these components and the longitudinal cascade development are evaluated for over 50 parameters in the showers. Measurable parameters depending little on the longitudinal development of a shower (and hence being good measures of the primary particle energy) and those depending strongly on the cascade development (being indications of the nature of the primary particle) are identified.

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