Hidden evidence of nonexponential 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 behavior is experimentally poorly known. Here we show, that by combining two genuine quantum mechanical results, it is possible to infer on this large time behavior, directly from data. Specifically, we find evidence for nonexponential behavior of alpha decay of ${}^8\mathrm{Be}$ at large times from experiments.

Figure 1

D-wave phase shifts (upper half) in $\alpha$-$\alpha$ elastic scattering from Ref. 15, polynomial fit to these data (solid line) and the derivative of phase shift (lower half) calculated from the fit showing all established ${}^8\mathrm{Be}\left(2^{+}\right)$ levels, as a function of the excitation energy $E_{\mathrm{ex}}=E_{\mathrm{cm}}-E_{{}^8\mathrm{Be}\left(\text{ground}\text{state}\right)}$ and plotted here in arbitrary units (arb. units). The negative region in derivative of phase shift (lower half) between 5 and $15\mathrm{MeV}$, due to the slowly falling phase shift is not obvious in the plot due to the scale of the vertical axis.

Figure 2

D-wave phase shift (upper half) and its derivative (lower half) in $\alpha$-$\alpha$ elastic scattering as a function of $E_{\mathrm{cm}}-E_{\text{threshold}}$, in the region of the first $2^{+}$ level of ${}^8\mathrm{Be}$. The dashed line shows the fit mentioned in the text. The inset displays the accuracy of the fit near the threshold energy region which is crucial for the large time behavior of the decay law.

Figure 3

Survival probability $P\left(t\right)$ of the decay ${}^8\mathrm{Be}\left(2^{+}\right)\to \alpha +\alpha$, as a function of the number of lifetimes after decay. $P\left(t\right)$ is evaluated numerically using $d{\delta }_l∕d{E}_{\mathrm{cm}}$ of Fig. 2 as the spectral density. The dashed line ($e^{-\Gamma t}$) shows that the decay law for the ${}^8\mathrm{Be}\left(2^{+}\right)$ state (solid line) is exponential up to about 30 lifetimes after which it proceeds as $t^{-6.36}$. ${ϵ}_R$ and $\Gamma$ are the resonance mass and width, respectively.