New Enhancement Mechanism of the Transitions in the Earth of the Solar   and Atmospheric Neutrinos Crossing the Earth Core
  It is shown that the $\nu_2 \to \nu_{e}$ and $\nu_{\mu} \to \nu_{e}$ ($\nu_e \to \nu_{\mu (\tau)}$) transitions respectively of the solar and atmospheric neutrinos in the Earth in the case of $\nu_e - \nu_{\mu (\tau)}$ mixing in vacuum, are strongly enhanced by a new type of resonance when the neutrinos cross the Earth core. The resonance is operative at small mixing angles but differs from the MSW one. It is in many respects similar to the electron paramagnetic resonance taking place in a specific configuration of two magnetic fields. The conditions for existence of the new resonance include, in particular, specific constraints on the neutrino oscillation lengths in the Earth mantle and in the Earth core, thus the resonance is a ``neutrino oscillation length resonance''. It leads also to enhancement of the $\nu_2 \to \nu_e$ and $\nu_e \to \nu_s$ transitions in the case of $\nu_e - \nu_s$ mixing and of the $\bar{\nu}_{\mu} \to \bar{\nu}_{s}$ (or $\nu_{\mu} \to \nu_{s}$) transitions at small mixing angles. The presence of the neutrino oscillation length resonance in the transitions of solar and atmospheric neutrinos traversing the Earth core has important implications for current and future solar and atmospheric neutrino experiments, and more specifically, for the interpretation of the results of the Super-Kamiokande experiment. 
S. T. Petcov