Ionization of a Model Atom by Perturbations of the Potential

Abstract

We study the time evolution of the wave function of a particle bound by an attractive $\delta$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state $|\theta (t){|}^2$, following a pulse of strength $r$ and duration $t$, behaves as $|\theta (t){|}^2-|\theta (\infty ){|}^2\sim t^{-\alpha }$, with both $\theta (\infty )$ and $\alpha$ depending on $r$. On the other hand a sequence of strong short pulses produces an exponential decay over an intermediate time scale.

21 pages in a TeX file, 5 figures in ps files, changed content [email protected], [email protected]

References in corpus (3)

• Nonautonomous Hamiltonians
• On the Influence of Pulse Shapes on Ionization Probability
• Analytical Treatment of Stabilization

Cited by in corpus (6)

• Decay versus survival of a localized state subjected to harmonic forcing: exact results
• Complete ionization for a non-autonomous point interaction model in d = 2
• On the Atomic Photoeffect in Non-relativistic QED
• Ionization in damped time-harmonic fields
• Nonperturbative analysis of a model quantum system under time periodic forcing
• Exact theory and numeric results for short pulse ionization of simple model atom in one dimension