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According to the recent experimental data of a GSI--experiment, the rate ofthe number of daughter ions $^{140}{\rm Ce}^{58+}$, produced by a nuclearK--shell electron capture (EC) of the H--like ion ${^{140}}{\rm Pr}^{58+}$, ismodulated in time with a period $T_d=(7.06\pm 8) $seconds. We explain thisphenomenon by neutrino--flavour mixing and show that this can be understoodwithin standard quantum field theory and derive a value for the squared massdifference $\Delta m^2_{21}=m^2_2-m^2_1=(0.763\pm 8) \cdot 10^{-4}\mathrm{eV}^2$. This proves that such processes provide a precise method toinvestigate neutrino--flavour mixing.

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