Oscillations in the decay law: A possible quantum mechanical explanation of the anomaly in the experiment at the GSI facility

Abstract: We study the deviations from the usual exponential decay law for quantum mechanical systems. We show that simple and physically motivated deviations from the Breit-Wigner energy distribution of the unstable state are sufficient to generate peculiar deviations from the exponential decay law. Denoting with $p(t)$ the survival probability, its derivative $h(t)$ shows typically an oscillating behavior on top of the usual exponential function. We argue that this can be a viable explanation of the observed experimental results at GSI Darmstadt, where the function $h(t)$ has been experimentally measured for electron capture decays of Hydrogen-like ions. Moreover, if our interpretation is correct, we predict that by measuring $h(t)$ at times close to the initial one, the number of decays per second rapidly drops to zero.