A. Rokhlenko (rokhlenk@math.rutgers.edu) and J. L. Lebowitz, (lebowitz@sakharov.rutgers.edu)
Ionization of a Model Atom by Perturbations of the Potential
(31K, Tex manuscript with 5 ps files of figures)
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.