Enhancing Mechanisms of Neutrino Transitions in a Medium of Nonperiodic Constant - Density Layers and in the Earth

The extrema of the probabilities of transitions $\nu_{\mu} (\nu_e) \to \nu_e (\nu_{\mu;\tau}), \nu_{2} \to \nu_e$, etc. of neutrinos passing through a medium consisting of i) two layers of different constant densities or ii) three layers of constant density of which the first and the third are identical but differ in density from the second (e.g., mantle-core-mantle in the Earth), are analyzed. We show that in addition to the MSW and neutrino oscillation length resonance (NOLR) local maxima previously discussed, there exist new resonance-like absolute maxima of interference nature. The latter correspond to a new effect of total neutrino conversion. The conditions for existence of the new maxima are fulfilled, in particular, for the Earth-core-crossing solar and atmospheric neutrinos. We prove that the NOLR and the new resonance-like enhancement are caused by a maximal constructive interference between the amplitudes of the neutrino transitions in the different density layers. The strong resonance-like enhancement of the transitions in the Earth of the Earth-core-crossing solar and atmospheric neutrinos is due to the new effect of total neutrino conversion.