# Long time deviations from exponential decay in radioactivity

Are there any examples of common substances whose decay is not exponential?

We're used to thinking about radioactivity in terms of half-lives. This is a concept that makes sense only for a decay that is exponential. However, there are plenty of physics articles on the subject of non exponential decay. It seems to be theoretically ubiquitous. For example:

The decay of unstable quantum states is an ubiquitous process in virtually all fields of physics and energy ranges, from particle and nuclear physics to condensed matter, or atomic and molecular science. The exponential decay, by far the most common type, is surrounded by deviations at short and long times$^{1,2}$. The short-time deviations have been much discussed, in particular in connection with the Zeno effect$^{3,4,5}$ and the anti-Zeno effect$^{6,7,8,9}$. Experimental observations of short$^{10,11}$ and long$^{12}$ time deviations are very recent. A difficulty for the experimental verification of long-time deviations has been the weakness of the decaying signal$^{13}$, but also the measurement itself may be responsible, because of the suppression of the initial state reconstruction$^{2,14}$.

1) L. A. Khalfin, Zurn. Eksp. Teor. Fiz. 33, 1371 (1957), English translation: Sov. Phys. JETP 6 1053 (1958).
2) L. Fonda and G. C. Ghirardi, Il Nuovo Cimento 7A, 180 (1972).

10.1103/PhysRevA.74.062102, F. Delgado, J. G. Muga, G. Garcia-Calderon
Suppression of Zeno effect for distant detectors

So are there any examples of deviations from long time decay? If not, then why not? Is the theory wrong or simply impractical? And is there a simple, intuitive explanation for why long decays should not be exponential?

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Possibly useful: arxiv.org/abs/0709.2685 , arxiv.org/abs/quant-ph/0604005v2 . –  Ben Crowell Sep 2 '14 at 2:50