  In this paper we present a study of the interaction of low energy electron
antineutrino on nuclei that undergo electron capture. We show that the two
corresponding crossed reactions have a sizeable cross section and are both
suitable for detection of low energy antineutrino. However, only in case very
specific conditions on the Q-value of the decay are met or significant
improvements on the performances of ion storage rings are achieved, these
reactions could be exploited in the future to address the long standing problem
of a direct detection of Cosmological Neutrino Background.
