Nonexponential decay in autoionization near threshold

A general upper bound is obtained for the nonexponential contribution to the time-dependent occupation amplitude $G\left(t\right)\mathrm{}$ for an autoionizing state just above the continuum threshold in the limit of narrow widths. This upper bound is shown to be inconsistent with some recently published results predicting new observable nonexponential effects in ${\mathrm{}\left|G\right(t\left)\right|}^2$, but is consistent with earlier long-accepted theory. It is also shown how some nonexponential contibutions to the decay might, in principle, still occur as a consequence of close proximity between the autoionizing state and the ionic threshold, although these contributions now have a different form than those recently proposed.