Exact results for ionization of a model atom

O. Costin, J. L. Lebowitz, A. Rokhlenko

Research output: Contribution to journalConference articlepeer-review


We investigate some fundamental aspects of the process underlying electron production via atomic ionization by external fields. Using a combination of exact analytic and controlled numerical methods we obtain in [1] rigorous qualitative and quantitative results for a model atom having one bound state with energy hbarω0. In particular we prove that this system will be fully ionized by a time periodic field η(t) of arbitrary frequency ω and arbitrary strength r for almost all shapes of η(t). (There are however exceptional η(t) for which full ionization fails). In the case of a harmonic η(t)=sin(ω t) the survival probability of the bound state for small r is given by e-1 for times of order Γ, with Γ-r2n, where n is the minimum number of "photons" required for ionization (with large modification at resonances). For late times the survival probability is oscillatory with an envelope that decays like t-3. The onset of the power law, replacing the exponential regime, occurs earlier when r is large. This can lead to a decrease in ionization rates when the strength of the ionizing field is increased and corresponds to what is called stabilization, a phenomenon which has been observed experimentally. These and other comparisons with analytical works and experiments indicate that the main features of the ionization behaviour we obtain are in fact quite universal. These include the large dynamic Stark shifts for strong fields and above ionization threshold peaks, with period hbarω, in the kinetic energy of the ejected electrons.

Original languageEnglish (US)
Pages (from-to)O1D6
JournalIEEE International Conference on Plasma Science
StatePublished - 2001
Event28th IEEE International Conference on Plasma Science/ 13th IEEE International Pulsed Power Conference - Las Vegas, NV, United States
Duration: Jun 17 2001Jun 22 2001

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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