Nonexponential decay law of the 2P-1S transition of the H-atom

TL;DR

This paper numerically analyzes the decay probability of the hydrogen 2P state, revealing deviations from exponential decay at very short and long times, including Zeno and anti-Zeno effects.

Contribution

It provides a detailed numerical evaluation of the survival probability for the hydrogen 2P state, extending previous analytic studies with precise spectral function calculations.

Findings

Deviations from exponential decay at very short and long times.

Identification of Zeno and anti-Zeno regions in decay behavior.

Long-time decay follows a t^{-4} power law.

Abstract

We evaluate numerically the survival probability $P(t)$ for the unstable 2P excited state of the hydrogen atom, which decays into the ground-state 1S emitting one photon ($\tau \sim 1.595$ ns), thus extending the analytic study of Facchi and Pascazio, Physics Letters A 241 (1998). To this end, we first determine the analytic expression of the spectral function of the unstable state, which allows for an accurate evaluation of $P(t)$. As expected, for short and long times $P(t)$ shows deviations from the exponential law: a `Zeno' region occurs at extremely short times (up to $\sim 0.3$ attosec, followed by a longer `anti-Zeno' domain (up to $\sim 50$ attosec); at long times above $125 \tau$, the decay law scales as $t^{-4}$.