Influence of external electric fields on multi-photon transitions between the 2s, 2p and 1s levels for hydrogen and anti-hydrogen atoms and hydrogen-like ions

TL;DR

This paper analytically evaluates one- and two-photon transitions in hydrogen and anti-hydrogen atoms under external electric fields, revealing differences in emission probabilities and exploring multi-photon transition probabilities with potential applications.

Contribution

It provides analytical calculations of multi-photon transition probabilities in hydrogen and anti-hydrogen atoms influenced by external electric fields, highlighting linear field effects.

Findings

Emission probabilities differ for hydrogen and anti-hydrogen due to electric field contributions.

Electric fields induce linear modifications in transition probabilities.

Three-photon transition probabilities are also evaluated.

Abstract

One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability is also evaluated and possible applications of the results are discussed.