Nonadiabatic Level Crossing in Resonant Neutrino Oscillations

Abstract

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 $〈{P}_{{\ensuremath{\nu}}_{e}}〉\ensuremath{\approx}{sin}^{2}{\ensuremath{\theta}}_{0}+{P}_{x}cos2{\ensuremath{\theta}}_{0}$, where ${\ensuremath{\theta}}_{0}$ is the vacuum mixing angle. The probability is averaged over the production as well as the detection positions of the neutrino and ${P}_{x}$ is the Landau-Zener transition probability between adiabatic states. Finally, this result is applied to resonance oscillations within the solar interior.