Octupolar-Excitation Penning-Trap Mass Spectrometry forQ-Value Measurement of Double-Electron Capture inEr164

The theory of octupolar-excitation ion-cyclotron-resonance mass spectrometry is presented which predicts an increase of up to several orders of magnitude in resolving power under certain conditions. The new method has been applied for a direct Penning-trap mass-ratio determination of the $^{164}\mathrm{Er}\mathrm{\text{\ensuremath{-}}}^{164}\mathrm{Dy}$ mass doublet. $^{164}\mathrm{Er}$ is a candidate for the search for neutrinoless double-electron capture. However, the measured ${Q}_{ϵϵ}$ value of 25.07(12) keV results in a half-life of ${10}^{30}$ years for a 1 eV Majorana-neutrino mass.