  Antineutrino induced electron capture is a resonant process that can have a
larg e cross-section for beams of monochromatic antineutrinos. We calculate the
cross-section of this process and investigate an experimental setup where
monochromatic antineutrinos are produced from the bound-beta decay of fully
ionized radioactive atoms in a storage ring. If the energy between the source
and the target is well matched, the cross-sections can be significantly larger
than the cross-sections of commonly used non-resonant processes. The rate that
can be achieved at a small distance between the source and two targets of
$10^3$ kg is up to one interaction per $8 .3\cdot10^{18}$ decaying atoms. For a
source-target distance corresponding to the first atmospheric neutrino osc
illation maximum, the largest rate is one interaction per $3.2\cdot10^{21}$
decaying atoms, provided that extremely stringent monochromaticity conditions
($10^{-7}$ or better) are achieved in future ion beams.
