High energy cosmic ray physics with underground muons in MACRO. I. Analysis methods and experimental results

In this paper, the first of a two-part work, we present the reconstruction and measurement of muonevents detected underground by the MACRO experiment at Gran Sasso (E{sub {mu}}{ge} 1.3 TeV in atmosphere). The main aim of this work is to discuss the muonmultiplicity distribution as measured in the detector. The data sample analyzed consists of 4.4{times}10{sup 6} muonevents, of which {approximately} 263000 are multiple muons, corresponding to a total live time of 5850 h. In this sample, the observed multiplicities extend above N{sub {mu}}=35, with intermuon separations up to 50 m and beyond. Additional complementing measurements, such as the inclusive muonflux, the angular distribution, and the muonseparation distribution (decoherence), are also included. The physical interpretation of the results presented here is reported in the following companion paper. {copyright} {ital 1997} {ital The American Physical Society}