Summary

In this chapter, I have shown that the flavor conversion of a neutrino can be greatly enhanced when it propagates through an oscillatory matter profile when certain resonance conditions are satisfied. This derivation is done from the perspective of Rabi oscillations and is much more physically intuitive than the original derivation by J. Kneller et al. in references ^{1 2}. I have shown that, although there can exist an infinite number of Rabi modes that approximately satisfy the resonance condition, only a few of them need to be considered for a real system. I have also derived a criterion when an off-resonance Rabi mode may significantly affect the resonance. Using this criterion I have shown that only a few of the infinite set of off-resonance Rabi modes may contribute to neutrino flavor conversions. Although I have assumed small perturbations on top of a constant matter profile, this approach can be applied to a matter profile with perturbations on top of a smoothly varying background density as have been done by K. Patton et al. in reference ³. This result may be applicable to the regions in a star where the matter density fluctuates. There can also exist a turbulent matter distribution behind the shock in a core-collapse supernova where this result may be applicable. However, the large neutrino fluxes inside a supernova core may have an even larger impact on neutrino oscillations which I will consider in the next chapter.

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