  By using an exact analytical approach to the time evolution of decay we
investigate the tunneling decay of ultracold single atoms, to discuss the
conditions for deviations of the exponential decay law. We find that $R$, given
by the ratio of the energy of the decaying fragment $\mathcal{E}_r$ to its
corresponding width $\Gamma_r$, is the relevant quantity in this study. When
$R$ is less than $0.3$ the decay of the atom goes to a good approximation for
the first few lifetimes as $\exp(-\Gamma_rt/2\hbar)t^{-3/2}$. We also find that
for values of $R \sim 1$, the nonexponential behavior occurs in a
post-exponential regime that goes as $t^{-3}$ after around a dozen of
lifetimes. The above conditions depend on suitable designed potential
parameters and suggest that for values $R \lesssim 1$, the experimental
verification of nonexponential decay might be possible.
