  According to the recent experimental data of a GSI--experiment, the rate of
the number of daughter ions $^{140}{\rm Ce}^{58+}$, produced by a nuclear
K--shell electron capture (EC) of the H--like ion ${^{140}}{\rm Pr}^{58+}$, 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 $\Delta m^2_{21}=m^2_2-m^2_1=(0.763\pm 8) \cdot 10^{-4}
\mathrm{eV}^2$. This proves that such processes provide a precise method to
investigate neutrino--flavour mixing.
