  We discuss the proposal that the "Darmstadt oscillations" of the orbital
K-shell electron capture decay (EC) rate of the H-like heavy ions are caused by
quantum beats of two coherently excited, closely spaced mass-eigenstates of
decaying H-like heavy ions. We show that such a mechanism to explain the time
modulation of the EC-decay rates of the H-like heavy ions leads to the time
modulation of the beta^+ decay rate of these ions with the same period. Such a
time-dependence of the beta^+ decay rate of the H-like heavy ions contradicts
the experimental data of GSI.
