Abstract
The longitudinal development of the N component of cosmic rays is studied theoretically in the extreme relativistic region. The intergro-differential equations of the N-component cascades are solved analytically for kernel functions which describe multiple meson production in nucleon-nucleon collisions. It is shown that Fermi's and Landau's models are included in the general solutions as two special cases. Some numerical examples for initial conditions of interest are quoted to demonstrate the mathematical procedures involved. In conclusion, a generalization of the discussed kernel functions is proposed in order to incorporate a possible partial elasticity in high-energy nucleon-nucleon collisions.
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