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The two-particle wave function of neutrino and recoil nucleus is found as asolution of an initial value problem in the far zone for a time longer than theelectron capture decay lifetime of a hydrogenlike ion. The neutrino-recoilentanglement arising in such a process is a consequence of the momentumconservation and is closely related to the wave packet structure of the state.Because of neutrino mixing, the joint wave packet involves the coherentsuperposition of the neutrino mass eigenstate packets. This is the new physicalrealization of the Einstein-Podolsky-Rosen thought experiment, which has noanalogue in quantum optics and quantum informatics. A class of possibleexperiments for the registration of a neutrino and a recoil nucleus isproposed. It is shown that due to spatial correlations neutrino oscillationscan be observed in the coincidence experiment with the recoil.

Spatial entanglement and massive neutrino oscillations produced by orbital electron capture decay