Abstract
Analyses of observable supernova neutrino oscillation effects require the calculation of the electron (anti)neutrino survival probability ${P}_{\mathrm{ee}}$ along a given supernova matter density profile. We propose a simple analytical prescription for ${P}_{\mathrm{ee}},$ based on a double-exponential form for the crossing probability and on the concept of maximum violation of adiabaticity. In the case of two-flavor transitions, the prescription is shown to reproduce accurately, in the whole neutrino oscillation parameter space, the results of exact numerical calculations for generic (realistic or power-law) profiles. The analytical approach is then generalized to cover three-flavor transitions with (direct or inverse) mass spectrum hierarchy, and to incorporate Earth matter effects. Compact analytical expressions, explicitly showing the symmetry properties of ${P}_{\mathrm{ee}},$ are provided for practical calculations.
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