Ionization of a Model Atom by Perturbations of the Potential

TL;DR

This paper investigates how a particle bound by a delta-function potential responds to time-dependent changes in the potential, revealing nonperturbative analytical results on survival probability and decay behavior in both one and three dimensions.

Contribution

It provides analytical solutions for the wave function evolution under parametric excitation in a simplified model, highlighting decay dynamics and dependence on pulse strength and duration.

Findings

Survival probability follows a power-law decay with exponent depending on pulse strength.

Strong short pulses induce exponential decay over intermediate times.

Analytical results applicable in both one and three dimensions.

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.