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_νₑ〉≈sin²θ₀+Pₓcos2θ₀, where θ₀ is the vacuum mixing angle. The probability is averaged over the production as well as the detection positions of the neutrino and Pₓ is the Landau-Zener transition probability between adiabatic states. Finally, this result is applied to resonance oscillations within the solar interior.
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Stephen Parke (1986) studied this question.
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