Oscillations in the electron-capture (EC) decay rate observed in storage-ring experiments are reconsidered in connection with the neutrino mass difference. Taking into account that - according to Relativity Theory - time is slowed down in the reference frame of the orbiting charged particles as compared to the neutral particles (neutrinos) moving on a rectilinear path after the EC decay, we derive a value of $Delta m^{2}_{21}=(0.768pm0.012)cdot10^{-4} eV^{2}$ for the neutrino mass-squared difference which fully agrees with that observed in other neutrino-oscillation experiments. To further check the connection between EC-decay oscillations and $Delta m^{2}_{21}$ we suggest experiments with different orbital speeds, i.e., different values of the Lorentz factor.
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