(Oscillating) non-exponential decays of unstable states

We discuss deviations from the exponential decay law which originate when going beyond the Breit-Wigner distribution for an unstable state. In particular, we concentrate on an oscillating behavior, reminiscent of the Rabi-oscillations, in the short-time region. We propose that these oscillations can explain the GSI experiment, which measured superimposed oscillations on top of the exponential law for hydrogen-like nuclides decaying via electron-capture (the so-called GSI anomaly). Moreover, we discuss the possibility, that the deviations from the Breit-Wigner distribution in the case of the GSI anomaly are (predominantly) caused by the interaction of the unstable state with the measurement apparatus. The consequences of this scenario, such as the non-existence of oscillations in an analogous experiment performed at the Berkeley Lab, are investigated.