Profiles of energetic muons in the atmosphere

The production spectrum of high-energy muons as a function depth in the atmosphere is relevant for understanding properties event rates deep detectors. For given atmospheric profile, cascades heavy nuclei develop at higher altitude than proton showers, giving rise to larger separation depth. type primary cosmic ray, seasonal variations muon reflect fact that temperatures correspond lower densities and relative increase ratio decay re-interaction parent mesons. In this paper, we present generalization Elbert formula tracks meson along trajectory cosmic-ray nucleus. convolution with changing profile provides dependence sizes bundles on temperature mass. We consider applications IceCube also multiple events compact underground detectors MINOS NOvA Near Detector.