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The neutrino oscillation probability in vacuum can be computed using scattering theory methods developed earlier in the context of collider physics, considering
Feynman diagrams that combine neutrino production and detection processes as a single quantum amplitude. Initial-state particles in the neutrino source and the
detector are treated as wave packets. Our approach offers simple and transparent framework to discuss decoherence effects in neutrino oscillations,
and the effects of the finite lifetime of the neutrino source. The latter are particularly relevant for oscillation experiments using neutrinos from pion decays in flight.