Statistical properties of cosmic-ray showers at ground level determined from photomultiplier-tube background registrations

Abstract

The fluctuations of cosmic-ray particles resulting from extensive air showers at ground level are well described by the two-parameter Poisson-driven Yule-Furry and negative-binomial counting probability distributions. The background signal from a single photomultiplier tube has been used to experimentally verify these results with remarkable precision, in spite of the simplicity of the underlying pure-birth stochastic process. Counting distributions from three different photomultiplier-tube detectors operated in the dark are presented, together with the theoretical predictions. Probability distributions of interevent times have also been obtained and these are found to be consistent with the observed clustering properties at the detector output. Our approach is expected to be of importance in quantum optics where cosmic-ray-shower particles can pose a significant limitation on the detection of squeezed light.