Atmospheric neutrinos and ν-mass hierarchy

We discuss the possibility for matter effects in the three-neutrino oscillations of the atmospheric νe(ν¯e) and νμ(ν¯μ), driven by one neutrino mass squared difference, |Δm312|≫Δm212, to be observable under appropriate conditions. We derive predictions for the Nadir angle (θn) dependence of the ratio Nμ/Ne of the rates of the μ-like and e-like multi-GeV events which is particularly sensitive to the Earth matter effects in the atmospheric neutrino oscillations, and thus to the values of sin2θ13 and sin2θ23, and also to the type of neutrino mass spectrum.