We investigate neutrino flavor oscillations in vacuum within a general
    conformal coupling model. We first examine the flavor oscillations within the
    plane-wave description of neutrinos, and then we extend our analysis to the
    wavepacket-based formalism. In both cases, we derive the general formulas for
    the flavor transition probability in arbitrary static and spherically symmetric
    spacetimes. We thoroughly discuss and assess in both cases the different
    possible ways — dictated by the presence of the conformal coupling — of
    computing the flavor transition probability. We show that the conformal
    invariance of the Dirac equation implies that the effect of conformal coupling
    on neutrino flavor oscillations modifies the oscillation length, but preserves
    the coherence length and unitarity. A detailed application to two-flavor
    neutrinos is then made and a numerical analysis is conducted within the
    well-known chameleon conformal coupling model.

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