A rigorous evaluation of the time evolution amplitude $G(t)$ for an isolated autoionizing state has yielded the result ${{|G(t)|}^{2}}_{t\ensuremath{\rightarrow}\ensuremath{\infty}}={e}^{\ensuremath{-}\frac{\ensuremath{\Gamma}t}{\ensuremath{\hbar}}+\frac{{\ensuremath{\hbar}}^{2}}{{\ensuremath{\pi}}^{2}(4{E}^{2}+{\ensuremath{\Gamma}}^{2}){t}^{2}}}$ where $E$ is the energy above the ionization threshold and $\ensuremath{\Gamma}$ the width. For states with lifetimes in the region ${10}^{\ensuremath{-}8}$-${10}^{\ensuremath{-}11}$ sec near the ionization threshold, the nonexponential decay corrections are sufficiently large to suggest that perhaps it is possible to test the validity of the fundamental exponential "law" within the realm of atomic physics.A rigorous evaluation of the time evolution amplitude $G(t)$ for an isolated autoionizing state has yielded the result ${{|G(t)|}^{2}}_{t\ensuremath{\rightarrow}\ensuremath{\infty}}={e}^{\ensuremath{-}\frac{\ensuremath{\Gamma}t}{\ensuremath{\hbar}}+\frac{{\ensuremath{\hbar}}^{2}}{{\ensuremath{\pi}}^{2}(4{E}^{2}+{\ensuremath{\Gamma}}^{2}){t}^{2}}}$ where $E$ is the energy above the ionization threshold and $\ensuremath{\Gamma}$ the width. For states with lifetimes in the region ${10}^{\ensuremath{-}8}$-${10}^{\ensuremath{-}11}$ sec near the ionization threshold, the nonexponential decay corrections are sufficiently large to suggest that perhaps it is possible to test the validity of the fundamental exponential "law" within the realm of atomic physics.

Physical Review LettersMar 28, 197739 citations

Algebraic decay of the survival probability in chaotic helium

Peter Schlagheck, Andreas Buchleitner

We demonstrate that the classical helium atom exhibits algebraic decay of the survival probability in the autoionizing $\mathrm{eZe}$ configuration. Excitation towards asymptotic orbits of marginal stability is identified as the cause of the nonexponential decay. Since one electron travels along a bound Kepler trajectory of infinite excitation in these orbits, we argue that the classical decay law will prevail in the quantum dynamics of a wave packet launched along the $\mathrm{eZe}$ configuration.We demonstrate that the classical helium atom exhibits algebraic decay of the survival probability in the autoionizing $\mathrm{eZe}$ configuration. Excitation towards asymptotic orbits of marginal stability is identified as the cause of the nonexponential decay. Since one electron travels along a bound Kepler trajectory of infinite excitation in these orbits, we argue that the classical decay law will prevail in the quantum dynamics of a wave packet launched along the $\mathrm{eZe}$ configuration.

Physical Review AJan 11, 200112 citations

Radiative decay of autoionized states of potassium and rubidium atoms

G.G. Bogachev

Dec 1, 19740 citations

On a realistic interpretation of spontaneous decay processes

Walter Meissner

Chaos Solitons & FractalsMay 1, 19966 citations

A rigorous evaluation of the time evolution amplitude

G(t)

for an isolated autoionizing state has yielded the result ${{|G(t)|}^{2}}_{t\ensuremath{\rightarrow}\ensuremath{\infty}}={e}^{\ensuremath{-}\frac{\ensuremath{\Gamma}t}{\ensuremath{\hbar}}+\frac{{\ensuremath{\hbar}}^{2}}{{\ensuremath{\pi}}^{2}(4{E}^{2}+{\ensuremath{\Gamma}}^{2}){t}^{2}}}$ where

E

is the energy above the ionization threshold and $\ensuremath{\Gamma}$ the width. For states with lifetimes in the region ${10}^{\ensuremath{-}8}$-${10}^{\ensuremath{-}11}$ sec near the ionization threshold, the nonexponential decay corrections are sufficiently large to suggest that perhaps it is possible to test the validity of the fundamental exponential "law" within the realm of atomic physics.

We demonstrate that the classical helium atom exhibits algebraic decay of the survival probability in the autoionizing

\mathrm{eZe}

configuration. Excitation towards asymptotic orbits of marginal stability is identified as the cause of the nonexponential decay. Since one electron travels along a bound Kepler trajectory of infinite excitation in these orbits, we argue that the classical decay law will prevail in the quantum dynamics of a wave packet launched along the

\mathrm{eZe}

configuration.