Nonadiabatic level crossing in resonant and nonresonant neutrino oscillations

We study neutrino oscillations and the level-crossing probability PLSZ=exp(-γₙFₙπ/2) (LSZ stands for Landau-St\"uckelberg-Zener) in power-law-like potential profiles A(r)∝rⁿ. After showing that the resonance point coincides only for a linear profile with the point of maximal violation of adiabaticity, we point out that the ``adiabaticity'' parameter γₙ can be calculated at an arbitrary point if the correction function Fₙ is rescaled appropriately. We present a new representation for the level-crossing probability, PLSZ=exp(-κₙGₙ), which allows a simple numerical evaluation of PLSZ in both the resonant and nonresonant cases, and where Gₙ contains the full dependence of PLSZ on the mixing angle ϑ. As an application we consider the case n=-3 important for oscillations of supernova neutrinos.