Non-adiabatic Level Crossing in Resonant Neutrino Oscillations

Analytic results are presented for the probability of detecting an electron neutrino after passage through a resonant oscillation region. If the electron neutrino is produced far above the resonance density, this probability is simply given by $⟨P_{{\nu }_e}⟩\approx {\sin }^2{\theta }_0+P_{\text{x}}\cos 2{\theta }_0$, where ${\theta }_0$ is the vacuum mixing angle. The probability is averaged over the production as well as the detection positions of the neutrino and $P_{\text{x}}$ is the Landau-Zener transition probability between adiabatic states. Finally, this result is applied to resonance oscillations within the solar interior.