Ionization of a Model Atom by Perturbations of the Potential

Details Ionization of a Model Atom by Perturbations of the Potential Ionization of a Model Atom by Perturbations of the Potential

1999-05-19

arxiv.org/abs/math-ph/9905015v2

Physics

Mathematical Physics

21 pages in a TeX file, 5 figures in ps files, changed content lebowitz@math.rutgers.edu, rokhlenko@math.rutgers.edu

Scientific paper

10.1063/1.533320

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.

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