Os-184 has been excluded as a promising candidate for the search of neutrinoless double-electron capture. High-precision mass measurements with the Penning-trap mass spectrometer TRIGA-TRAP resulted in a marginal resonant enhancement with = -8.89(58) keV excess energy to the 1322.152(22) keV 0+ excited state in W-184. State-of-the-art energy density functional calculations are applied for the evaluation of the nuclear matrix elements to the excited states predicting a strong suppression due to

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... he large deformation of mother and daughter states. The half-life of the transition in Os-184 exceeds T_1/2 > 1.3 10^29 years for an effective neutrino mass of 1 eV.