We report on studies of electron capture decays (EC) of highly ionized nuclei with one or two electrons in their K-orbit (H- and He-like ions) in the Experimental Storage Ring (ESR) of GSI, Darmstadt. These experiments allow for the first time investigating two-body weak decays with a pair of entangled lepton states with quasi mono-energetic massive neutrinos, the properties of which can thus be studied without the inefficient neutrino detection.

In recent experiments we found that the H-like ¹⁴⁰Pr⁵⁸⁺ and ¹⁴²Pm⁶⁰⁺ ions decay 1.49(8) and 1.44(6) times faster than the He-like ¹⁴⁰Pr⁵⁷⁺ and ¹⁴²Pm⁵⁹⁺ ions. This anomaly is explained by spin effects due to the hyperfine structure of the H-like ions. The EC/ß⁺ branching ratios are consistent with expectations from standard weak decay theories within 3%.

Even more surprising is the recently observed time dependence of the electron capture rate of H-like ¹⁴⁰Pr⁵⁸⁺ and ¹⁴²Pm⁶⁰⁺ ions. It is not exponential but time modulated with amplitudes of a = 0.18(3) and 0.22(3), and periods of T = 7.06(8) s and 7.10(22) s, respectively. It corresponds to an energy difference of 8.6×10^-16 eV for a quantum beat type phenomenon. We attribute it to the small recoil energy difference DE of the detected entangled daughter ions induced by the kick of mixed massive neutrinos with masses m₁ and m₂. Using the cm relation DE = Dm²/2M, derived from energy and momentum conservation in the decay of a nucleus with mass M and neutrinos with a mass difference Dm = m₂ – m_1, a squared mass difference Dm² = 2.22(3)×10^–4 eV² is derived. It is 2.9 times larger than reported recently by the KamLAND neutrino oscillation experiment. We have discussed this difference in terms of neutrino mass modification by lepton-W boson loops in the high Coulomb field of the heavy daughter nucleus, but the large difference in Dm² is not understood. A further problem is the small modulation amplitude with an average value <a> = 0.20(2), which would lead to a small neutrino mixing angle q ~ 6^o compared with a value of about 34^o from sun neutrino oscillations. The modulation amplitude may be reduced by the preceding photon decay in H-like ions. In a preliminary analysis of the ß⁺ branch of ¹⁴²Pm we found no modulation with a < 0.03 of this three-body decay with a broad neutrino spectrum in accordance with our theoretical prediction. If verified, this is direct evidence that the modulation is caused by mixed massive neutrinos from quasi-free two-body decays.