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One- and two-photon transitions in the hydrogen atom are analyticallyevaluated in the absence and in the presence of an external electric field. Theemission probabilities are different for the hydrogen and anti-hydrogen atomsdue to the existence of contributions, linear in electric field. The magnitudeof these contributions is evaluated within the nonrelativistic limit. TheCoulomb Green function method is applied. Different nonrelativistic "forms" forthe decay probabilities in combination with different gauge choices areconsidered. The three-photon E1E1E1 2p-1s transition probability is alsoevaluated and possible applications of the results are discussed.

journal of physics. b, atomic molecular and optical physics/journal of physics. b, atomic, molecular and optical physics

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