6 FIG. 4: Final three-flavor conversion probabilities for neutrinos, shown in the mass basis. For example, P ( ν$_{1}$ → ν$_{2}$ ) indicates the probability, as a function of energy, that the neutrino originally in eigenstate | ν$_{1}$ 〉 transitions into eigenstate | ν$_{2}$ 〉 by the end of the collective transformations (at 1000 km). The inverted mass hierarchy is assumed. The top panel specifies the labeling convention for the states. (This plot appears in Supplemental Online Material in the Phys. Rev. Lett. version, [52].) 0 200 400 600 800 1000 1200 radius @ km D eigenvalues ¨ n$_{3}$ \ ¨ n$_{2}$ \ ¨ n$_{1}$ \ Inverted, neutrinos 0 10 20 30 40 0.0 0.2 0.4 0.6 0.8 1.0 E$_{n}$ @ MeV D P H n$_{1}$fin$_{1}$ L P H n$_{1}$fin$_{2}$ L P H n$_{1}$fin$_{3}$ L 0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 E$_{n}$ @ MeV D P H n$_{2}$fin$_{1}$ L P H n$_{2}$fin$_{2}$ L P H n$_{2}$fin$_{3}$ L 0 10 20 30 40 0.0 0.2 0.4 0.6 0.8 1.0 E$_{n}$ @ MeV D P H n$_{3}$fin$_{1}$ L P H n$_{3}$fin$_{2}$ L P H n$_{3}$fin$_{3}$ L