Analytical calculation of muon intensities under deep sea-water

The study of the energy loss of high energy muons through different materials, such as rock and sea-water can cast light on characteristics of lepton interactions. There are less ambiguities for the values of atomic number (Z) and mass number (A) in sea-water than in rock. Muon intensities should be measured as fundamental data and as background data for searching the fluxes of neutrino. The average range energy relation in sea-water is derived. The correction factors due to the range fluctuation is also computed. By applying these results, the intensities deep under sea are converted from a given muon energy spectra at sea-level. The spectra of conventional muons from eta, K decays have sec theta enhancement. The spectrum of prompt muons from charmed particles is almost isotropic. The effect of prompt muons is examined.