Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like ${}^{140}$Pr and ${}^{142}$Pm Ions

We report on time-modulated two-body weak decays observed in the orbital electron capture of hydrogen-like ${}^{140}$Pr${}^{59+}$ and ${}^{142}$Pm${}^{60+}$ ions coasting in an ion storage ring. Using non-destructive single ion, time-resolved Schottky mass spectrometry we found that the expected exponential decay is modulated in time with a modulation period of about 7 seconds for both systems. Tentatively this observation is attributed to the coherent superposition of finite mass eigenstates of the electron neutrinos from the weak decay into a two-body final state.