The Zenith Angle Dependence of Cosmic-Ray Protons

Abstract

The proton spectrum for particles in the momentum band 0.4-1.0 Bev/c and the meson spectrum for particles in the momentum band 0.09-0.34 Bev/c at zenith angles 45\ifmmode^\circ\else\textdegree\fi{} east, vertical, and 45\ifmmode^\circ\else\textdegree\fi{} west have been obtained at 3.3-km elevation and magnetic latitude 48\ifmmode^\circ\else\textdegree\fi{} north. The zenith angle dependence of protons, along with a simplified analysis, is presented as data on the nucleonic cascade. It is found taht the gross zenith angle dependence will fit a ${cos}^{3.2}\ensuremath{\theta}$ distribution at 45 degrees east and west, there being no statistically significant east-west asymmetry. The simplified calculation assumes that a unidirectional component of the primary radiation will (1) suffer exponential absorption along its original path with a path length for removal of 120 g/${\mathrm{cm}}^{2}$ of air and (2) acquire an ultimate distribution at 3.3 km due to scattering fitting a ${cos}^{n}\ensuremath{\omega}$ law, $n$ being an adjustable parameter.It is found that a value of $n$ of 6.5\ifmmode\pm\else\textpm\fi{}0.7 yields a unidirectional distribution which, when integrated over all angles, results in a gross zenith angle dependence agreeing with ${cos}^{3.2}\ensuremath{\theta}$. The ${cos}^{n}\ensuremath{\omega}$ distribution with $n$ equal to 6.5 is quite sharp and leads to the conclusion that the average projected scattering angle per collision is only about 6 degrees.