Atmospheric proton and neutron spectra at energies above 1 GeV

Laboratory for Theoretical Physics, Irkutsk State University, Gagarin boulevard 20, RU-664003 Irkutsk, RussiaAbstract. We discuss an effective numerical method forsolving the transport equations for cosmic ray nucleons inthe atmosphere. It is demonstrated that the nucleon attenua-tion lengths are strongly energy and depth dependent due tothe non-power-lawbehavior of the primary spectrum, growthof the total inelastic cross sections with energy, and scalingviolation in the nucleon-nucleus interactions. The numericalresults are compared with the available experimental data.1 IntroductionMeasurements of the fluxes of secondary cosmic-ray protonsand neutrons can furnish valuable information about primarycosmic rays and about the nuclear interactions at high ener-gies. In order to extract this information from experimentaldata, it is necessary, among other things, to be able to calcu-late the nucleon attenuation lengths, which are functionals ofthe primary spectrum and which also depend, in general, onenergy and atmospheric depth.In this paper we discuss some results obtained by using asimple but rather efficient and physically evident numerica lmethod for solving transport equations describing the propa-gation of cosmic-ray protons and neutrons through the atmo-sphere (Naumov and Sinegovskaya, 2000). The method isapplicable at sufficiently high energies and demands severa lapproximations which are quite traditional for high-energyatmospheric cascade calculations. Namely, we use the one-dimensional (1D) approach, in which all secondary particlesin the cascade are supposed collinear with the projectiles.The processes of generation of NN pairs in meson-nucleuscollisions aredisregarded,but thecorrespondingcontributionis typically small and can be taken into account as a correc-tion (Vall et al., 1986). Besides, we apply the standard su-perposition model for the collisions of cosmic-ray nuclei andneglect the geomagnetic effects and proton ionization energyCorrespondence to: T. S. Sinegovskaya (tanya@api.isu.runnet.ru)losses. These approximations confine the range of applica-bility of the method. However, it remains rather broad in or-der to describe all currentlyavailable data on the high-energynucleons in the atmosphere and at sea level. In particular, itcovers completely the depth-energy area relevant to calcu-lations of atmospheric muon and neutrino fluxes at energiesabove several GeV, – one of the most important fields of ap-plication of the method.We compare our calculations with the experimental dataand with the results of a more sophisticated approach byFiorentini et al. (2001)based on an updatedversion of CORTcode which was designed for applications to low and inter-mediate energy atmospheric cascade calculations and whichtakes into account essentially all significant effects (Nau mov,1984; Bugaev and Naumov, 1985a,b; Bugaev et al., 1998).2 The Z factor methodWithin the aboveassumptions, the problemof calculating thedifferential energy spectra of protons D