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 (H) and antihydrogen (H) 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. PACS number(s): 31.30. Jv, 12.20. Ds,

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The resonant spectra of hydrogen and anti-hydrogen atoms in the presence of an external electric field are compared theoretically. It is shown that nonresonant corrections to the transition frequency contain terms linear in the electric field. The existence of these terms does not violate space and time parity and leads to a difference in the resonant spectroscopic measurements for hydrogen and anti-hydrogen atoms in an external electric field. The one-photon 1s − 2p and the two-photon 1s − 2s resonances are investigated.

The spectroscopical properties of hydrogen (H) and anti-hydrogen [Formula: see text] atoms in external electric and magnetic fields are discussed. This problem became important in connection with the recent experimental success in production of [Formula: see text] atoms. The main features of these experiments are briefly reviewed. The proposals for the search of the CPT violation via comparison of the H and [Formula: see text] spectra are shortly discussed. The spectroscopical differences between H and [Formula: see text] atoms in external magnetic fields and in parallel magnetic and electric fields are described in detail. It is proven that the positions of the maxima of the frequency distributions for transition probabilities in external electric field for H and [Formula: see text] atoms will deviate if the non-resonant corrections to the Lorentz line profile are taken into account.