A parameterisation of the flux and energy spectrum of single and multiple muons in deep water/ice

In this paper parametric formulas are presented to evaluate the flux of atmospheric muons in the range of vertical depth between 1.5 to 5 km of water equivalent (km w.e.) and up to 85^o for the zenith angle. We take into account their arrival in bundles with different muon multiplicities. The energy of muons inside bundles is then computed considering the muon distance from the bundle axis. This parameterisation relies on a full Monte Carlo simulation of primary Cosmic Ray (CR) interactions, shower propagation in the atmosphere and muon transport in deep water [1]. The primary CR flux and interaction models, in the range in which they can produce muons which may reach 1.5 km w.e., suffer from large experimental uncertainties. We used a primary CR flux and an interaction model able to correctly reproduce the flux, the multiplicity distribution, the spatial distance between muons as measured by the underground MACRO experiment.