Precision atomic masses for neutrinoless double-beta-decay and double-electron-capture

As currently understood, the definitive observation of neutrinoless double-beta-decay will imply that neutrinos are their own antiparticles (Majorana particles), while measurements of the decay rate, or limits on the rate, provide information on absolute neutrino mass. Large-scale neutrinoless double-beta-decay detectors, proposed or under development, such as EXO, CUORE, GERDA, MAJORANA, etc. should be sensitive to a linear combination of neutrino masses, the ``effective Majorana mass of the electron neutrino'', below 0.1 eV/c$^{2}$. The signature of neutrinoless double-beta decay is a sharp peak in the total electron-energy spectrum at the Q-value of the decay -- the mass-energy difference between the parent and daughter atoms. Using precision, cryogenic mass spectrometry, with one or two multiply-charged ions in a Penning trap, we have now measured the atomic masses of $^{136}$Xe, $^{130}$Te, $^{130}$Xe, $^{76}$Ge, $^{76}$Se to a fractional precision of 2 x 10$^{-10}$ or better, corresponding to Q-values with uncertainties below 25 eV. This is more than sufficient precision for the proposed large-scale experiments. Progress on mass measurements of $^{74}$Ge and $^{74}$Se, relevant to resonance-enhanced neutrinoless double-electron capture in $^{74}$Se, will also be reported.