Hidden evidence of non-exponential nuclear decay

The framework to describe natural phenomena at their basics being quantum mechanics, there exist a large number of common global phenomena occurring in different branches of natural sciences. One such global phenomenon is spontaneous quantum decay. However, its long time behaviour is experimentally poorly known. Here we show, that by combining two genuine quantum mechanical results, it is possible to infer on this large time behaviour, directly from data. Specifically, we find evidence for non-exponential behaviour of alpha decay of 8Be at large times from experiments. PACS numbers: 23.60.+e, 03.65.Ta, 03.65.Nk The decay law in quantum mechanics is necessarily non-exponential [1] and deviates from a simple exponential form at small and large times (for reviews see [2, 3, 4]). Recently, some experimental facts regarding the short time behaviour have confirmed the expectations [5]. Till today this is not the case for the long time evolution. Although this long tail of the survival probability of an unstable quantum state is more often than not, not directly observable [6, 7, 8] (indeed, we are not aware of any such successful experiment), the information about resonance time evolution, in general, and the long time behaviour, in specific, should as a matter of principle be encoded in the resonant scattering data A+ a → resonance → B + b. Since energy is a dual variable to time, we can imagine that the survival amplitude AΨ(t) = 〈Ψ|e |Ψ〉 = 〈Ψ|Ψ(t)〉 (1) (related to the survival probability, PΨ(t) = |AΨ(t)| /|AΨ(0)| ) can be written as a Fourier transform of an energy dependent quantity which can be