Production Spectra of Cosmic-Ray Mesons in the Atmosphere

Abstract

Recent experimental data on the differential vertical intensities of $\ensuremath{\mu}$ mesons in the atmosphere make it possible not only to improve the original Sands' production spectrum of $\ensuremath{\mu}$ mesons but also to study its dependence on the geomagnetic latitude. It is shown that, for the residual ranges, ${R}^{\ensuremath{'}}$, between 100 g ${\mathrm{cm}}^{\ensuremath{-}2}$ and 6000 g ${\mathrm{cm}}^{\ensuremath{-}2}$, the production spectrum may be approximated by an empirical formula of the type: $C{(a+{R}^{\ensuremath{'}})}^{\ensuremath{-}\ensuremath{\gamma}}$ where $C$ and $\ensuremath{\gamma}$ 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 $\ensuremath{\gamma}$, compatible with experimental data, the production spectrum of $\ensuremath{\mu}$ mesons is then used as a basis for the derivation of the differential and integral energy spectra of charged $\ensuremath{\pi}$ mesons. The latitude dependence of the $\ensuremath{\pi}$-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 $\ensuremath{\pi}$ 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 $\ensuremath{\pi}$-meson production.