Neutrino oscillations and the effect of the finite lifetime of the neutrino source

We consider a neutrino source at rest and discuss a condition for the existence of neutrino oscillations which derives from the finite lifetime $\tau_S$ of the neutrino source particle. This condition is present if the neutrino source is a free particle such that its wave function is non-stationary. For a Gaussian wave function and with some simplifying assumptions, we study the modification of the usual oscillation probability stemming from $\tau_S$. In the present accelerator experiments the effect of $\tau_S$ can be neglected. We discuss some experimental situations where the source lifetime becomes relevant in the oscillation formula.