  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.
