We study three-flavor collective neutrino transformations in the dense-neutrino region above the neutrino sphere of a supernova core. We find that two-flavor conversions driven by the atmospheric mass difference and the 13-mixing angle capture the full effect if one neglects the second-order difference between the ${\nu }_{\mu }$ and ${\nu }_{\tau }$ refractive index. Including this “mu-tau matter term” provides a resonance at a density of $\rho \approx 3\times {10}^7\mathrm{g}{\mathrm{cm}}^{-3}$ that typically causes significant modifications of the overall ${\nu }_e$ and ${\overline{\nu }}_e$ survival probabilities. This effect is surprisingly sensitive to deviations from maximal 23-mixing, being different for each octant.

• Received 17 December 2007

DOI:https://doi.org/10.1103/PhysRevD.77.065024