Kinematics and Quantum Field Theory of the Neutrino Oscillations Observed in the Time-modulated Orbital Electron Capture Decay in an Ion Storage Ring

According to the recent experimental data of a GSI–experiment, the rate of the number of daughter ions ${}^{140}{\mathrm{C}\mathrm{e}}^{58+}$, produced by a nuclear K–shell electron capture (EC) of the H–like ion ${}^{140}{\mathrm{P}\mathrm{r}}^{58+}$, is modulated in time with a period $T_d=(7.06\pm 8)$seconds. We explain this phenomenon by neutrino–flavour mixing and show that this can be understood within standard quantum field theory and derive a value for the squared mass difference $\Delta m^2_{21}=m^2_2-m^2_1=(0.763\pm 8) \cdot 10^{-4} $\mathrm{e}\mathrm{V}$^2$. This proves that such processes provide a precise method to investigate neutrino–flavour mixing.