Nonadiabatic level crossing in resonant and nonresonant neutrino oscillations

Abstract

We study neutrino oscillations and the level-crossing probability ${P}_{\mathrm{LSZ}}=\mathrm{exp}(\ensuremath{-}{\ensuremath{\gamma}}_{n}{\mathcal{F}}_{n}\ensuremath{\pi}/2)$ (LSZ stands for Landau-St\"uckelberg-Zener) in power-law-like potential profiles $A(r)\ensuremath{\propto}{r}^{n}.$ 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 ${\ensuremath{\gamma}}_{n}$ can be calculated at an arbitrary point if the correction function ${\mathcal{F}}_{n}$ is rescaled appropriately. We present a new representation for the level-crossing probability, ${P}_{\mathrm{LSZ}}=\mathrm{exp}(\ensuremath{-}{\ensuremath{\kappa}}_{n}{\mathcal{G}}_{n}),$ which allows a simple numerical evaluation of ${P}_{\mathrm{LSZ}}$ in both the resonant and nonresonant cases, and where ${\mathcal{G}}_{n}$ contains the full dependence of ${P}_{\mathrm{LSZ}}$ on the mixing angle $\ensuremath{\vartheta}.$ As an application we consider the case $n=\ensuremath{-}3$ important for oscillations of supernova neutrinos.