Enhancing mechanisms of neutrino transitions in a medium of nonperiodic constant-density layers and in the Earth

The enhancement of the transitions ${\nu }_{\mu }\left({\nu }_e\right)\to {\nu }_e\left({\nu }_{\mu ;\tau }\right),$ ${\nu }_2\to {\nu }_e,$ ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_s,$ ${\nu }_e\to {\nu }_s,$ etc. of neutrinos passing through a medium of nonperiodic density distribution, consisting of (i) two layers of different constant densities (e.g., Earth core and mantle), or (ii) three layers of constant density with the first and the third layers having identical densities and widths which differ from those of the second layer (e.g., mantle-core-mantle in the Earth), is studied. We find that, in addition to the known local maxima associated with the MSW effect and the neutrino oscillation length resonance (NOLR), the relevant two-neutrino transition probabilities have new resonance-like absolute maxima. The latter correspond to a new effect of total neutrino conversion and are absolute maxima in any independent variable: the neutrino energy, the layers widths, etc. We find the complete set of such maxima. We prove that the NOLR and the new absolute maxima are caused by a maximal constructive interference between the amplitudes of the neutrino transitions in the different density layers. We show that the strong resonance-like enhancement of the transitions in the Earth of the Earth-core-crossing solar and atmospheric neutrinos is due to the effect of total neutrino conversion.