Calculations of average characteristics of EAS components and Monte Carlo calculations of their fluctuations using different models of nuclear interactions. I. Methodology—Lateral structure and transition curve of electrons

Properties of extensive air showers are computed by two methods based on eight plausible models of ultra-high-energy interactions of nucleons and pions with air nuclei. The first method is the numerical solution of the diffusion equations describing the one-dimensional nuclear cascade, from which the average properties of nucleon-initiated showers of given energy are deduced. The second method is Monte Carlo simulation of the three-dimensional nuclear cascades from a sample of which typical shower properties and the extent of their fluctuations are estimated.1. For showers of size < 106, the deduced shower absorption lengths are consistent with experimental results only for models involving nucleon pair production.2. The accuracy of experimental results on the depth of the shower maximum at different primary energies (105–1010 GeV) available at present is insufficient to select any particular model.3. Monte Carlo size distributions for a given primary energy indicate that with the primary energy spectrum known at present, showers of a given size originate from primaries of a relatively narrow range.4. The electron lateral structure parameter, α, fluctuates considerably for showers of primary energy < 106 GeV; the spread decreases with the primary energy.5. The average value of α increases with primary energy up to 106 GeV and saturates at ~ 1.2 for showers of larger sizes.