Production Spectra of Cosmic-Ray Mesons in the Atmosphere

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