The nuclear method to discover Majorana neutrinos is the neutrinoless \beta \beta decay. We propose to study the inverse process accompanied by a photon emission, the neutrinoless radiative double electron capture. Chances for such a decay are estimated. These favour studies of 0+ 0+ nuclear transitions of small energy release in high Z atoms.
PACS numbers: 13.15.+g, 23.40.Bw
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