Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Mathematics

Scientific paper

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Cosmic Rays, Distribution (Property), Electrons, Energy Spectra, Gamma Rays, Compton Effect, Laplace Transformation, Mathematical Models, Monte Carlo Method, Simulation

Scientific paper

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

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