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

TL;DR

This paper proposes a quantum mechanical explanation for observed oscillations in decay rates, suggesting that deviations from standard energy distributions can cause these effects, which match experimental results at GSI Darmstadt.

Contribution

It introduces a simple model of energy distribution deviations that accounts for oscillations in decay laws, explaining experimental anomalies observed at GSI.

Findings

Oscillations in decay probability derivative $h(t)$ can arise from energy distribution deviations.

The model explains the GSI experimental results showing oscillating decay rates.

Predicted rapid drop in decay rate near initial times if the model is correct.

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.