Background: The observation of neutrinoless double-$\beta$ transitions would indicate physics beyond the standard model as the lepton number conservation is violated. For a complete degeneracy in the energy of the initial and final states, the neutrinoless double-electron capture is resonantly enhanced. This shortens the half-life to similar orders of magnitude as the neutrinoless double-$\beta$ decay and expands the set of nuclei for the search of neutrinoless double-$\beta$ transitions as the observation of either process would be equally likely.

Purpose: To clearly identify transitions that are resonantly enhanced, among other parameters the total energy of the decay, $Q_{\varepsilon \varepsilon }$, needs to be measured very precisely. Of the 12 initially identified candidates, the last remaining decay without a precise $Q_{\varepsilon \varepsilon }$ was ${}^{190}\mathrm{Pt}\left(0\nu \varepsilon \varepsilon \right){}^{190}\mathrm{Os}$.

Method: The $Q_{\varepsilon \varepsilon }$ value was determined with the Penning trap mass spectrometer LEBIT by measuring the ratio of the cyclotron frequencies of ${}^{190}\mathrm{Pt}^{+}$ and ${}^{190}\mathrm{Os}^{+}$ in a 9.4-T superconducting magnet.

Result: The $Q_{\varepsilon \varepsilon }$ value was determined to be 1401.57(47) keV with an uncertainty reduction of an order of magnitude compared to its previously known value. The absolute value is shifted by 17.17(623) keV relative to the previously accepted one. Furthermore, the mass value of ${}^{190}\mathrm{Pt}$ was found to be shifted by more than three standard deviations. In addition we improved the mass values for ${}^{186,190}\mathrm{Os}$ and ${}^{194}\mathrm{Pt}$.

Conclusion: Transitions to the two nuclear excited states of ${}^{190}\mathrm{Os}$ with 1326.9(5) and 1387.00(2) keV energy were identified to be resonantly enhanced within a $1\sigma$ uncertainty. The significantly reduced uncertainty of $Q_{\varepsilon \varepsilon }$ confirmed the potential for a resonantly enhanced transition.

• Received 8 April 2016

DOI:https://doi.org/10.1103/PhysRevC.94.015502