  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 the 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.
