Ionization of a Model Atom: Exact Results and Connection with Experiment

TL;DR

This paper provides exact theoretical results on the ionization process of a model atom under a periodic potential, connecting these findings with experimental observations and demonstrating the universality of the ionization behavior.

Contribution

It offers an exact analysis of ionization in a 1D model atom with a time-periodic potential, linking theoretical results with experimental data and universality.

Findings

Survival probability decays exponentially for short times

Late-time decay follows a t^{-3} law

Results are applicable to real atomic systems and experiments

Abstract

We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength $r$ and frequency $\omega$. The survival probability is for small $r$ given by $e^{-\Gamma t}$ for times of order $\Gamma^{-1} \sim r^{-2n}$, where $n$ is the number of ``photons'' required for ionization, with enhanced stability at resonances. For late times the decay is like $t^{-3}$. Results are for a 1d system with a delta function potential of strength $-g(1 + \eta (t))$ but comparison with experiments on the microwave ionization of excited hydrogen atoms and with recent analytical work indicate that many features are universal.