$Q$ value and half-life of double-electron capture in ${}^{184}$Os

${}^{184}$Os 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 result in a marginal resonant enhancement with $\Delta =-8.89\left(58\right)$ keV excess energy to the 1322.152(22) keV $0^{+}$ excited state in ${}^{184}$W. 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 exceeds $T_{1/2}{(}^{184}\mathrm{Os})\ge 1.3\times {10}^{29}$ yr for an effective neutrino mass of 1 eV.

Figure 1

Time-of-flight ion cyclotron resonance of ${}^{184}$Os${}^{+}$ with about 450 ions. The data points show the mean time-of-flight values as function of the excitation frequency. The solid line is a fit of the theoretical line shape [23] to the data points.

Figure 2

The data points show the 32 cyclotron-frequency ratio measurements recorded to determine the double-electron capture $Q$ value of ${}^{184}$Os. The thick line represents the weighted-mean value and the gray area its 1 $\sigma$-uncertainty.

Figure 3

Deformation amplitudes for the three first $0^{+}$ excited states of ${}^{184}$W (a) and the ground state of ${}^{184}$Os (b) calculated with EDF Gogny D1M. (c) Intensity of the Fermi component of the $0\nu \epsilon \epsilon$ NME as a function of the quadrupole deformations $\beta$ and ${\beta }^{\prime }$ of the ${}^{184}$Os and ${}^{184}$W nuclei, respectively.