A Nucleonic Cascade Theory and an Analysis of Extensive Air Showers

Abstract

A model of extremely high-energy nuclear collisions which describes Landau's model ap­ proximately or satisfies the constancy of transverse momenta of secondary particles as special cases is applied to the nucleonic cascade process in the atmosphere. The model contains some free parameters which specify the dynamical character of the nuclear collisions. The fact that the diffusion equation is solved analytically in a rather simple form on certain assump­ tions makes it easy to find the best values of the parameters by comparing with experimental information if available. Applications to extensive air showers are presented. The main results obtained are as follows. (i) If the energy spectrum of secondary charged pions at a high-energy collision is well approximated by a power law spectrum E-ndE, 2;;::; n;;::; 1.5 is consistant with the lateral distribution of high-energy muons far underground. Oi) Any model in which the energy spectrum, the inelasticity, the ratio of charged-to neutral pions are independent of an incident energy in a wide range of 101~~1O17 eV seems unable to ex­ plain the altitude variation of the electron component. (iii) The lateral distribution of the electron component is insensitive to the energy spectrum of neutral pions at a high-energy collisions and also to the primary energy. Further discussions on our model and the solution of the diffusion equation are given.