Production Spectra of Cosmic-Ray Mesons in the Atmosphere

Recent experimental data on the differential vertical intensities of μ mesons in the atmosphere make it possible not only to improve the original Sands' production spectrum of μ mesons but also to study its dependence on the geomagnetic latitude. It is shown that, for the residual ranges, R^', between 100 g cm^-2 and 6000 g cm^-2, the production spectrum may be approximated by an empirical formula of the type: C(a+R^')^-γ where C and γ are numerical constants practically independent of the geomagnetic latitude. The latitude dependence of the production spectrum is thus expressed through the parameter a which displays a monotonic decrease with increasing latitude. With numerical values of a, C, and γ, compatible with experimental data, the production spectrum of μ mesons is then used as a basis for the derivation of the differential and integral energy spectra of charged π mesons. The latitude dependence of the π-meson spectrum is linked to the geomagnetic cut-off of the primary cosmic radiation, which leads to some crude conclusions on the average multiplicity of π mesons produced in proton collisions with air nuclei. In particular, the dependence of the multiplicity on the primary energies between 2 and 13 Bev is studied in detail and compared with Fermi's statistical theory of π-meson production.