Can the "Darmstadt oscillations" be treated as two closely spaced mass-eigenstates of the H-like mother ions ?

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.