Spectroscopy of the Hydrogen and Anti-Hydrogen Atoms in External Fields

Abstract

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.

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

“…However, we should note that this result yields only a minor contribution for small nuclear charges Z when it is evaluated within the 'velocity' form [20]. In this case a major contribution arises from the negativeenergy intermediate states and scales like (αZ) 8 in atomic units [13,14].…”

“…The relation (8) involves the nonrelativistic electron momentum operator p = −i∇, the electron spin operator ŝ = 1 2 σ (σ are the Pauli matrices) and (...) A A denotes the matrix element with the Schrödinger wavefunctions. In the dipole approximation the first term of the integrand in equation (7) describes the E1 photon emission, that in the case of A = 1s, A = 2s is forbidden by parity; the second term corresponds to the M1 photon emission.…”

“…However, we should note that this result yields only a minor contribution for small nuclear charges Z when it is evaluated within the "velocity" gauge [21]. In this case a major contribution arises from the negative-energy intermediate states and scales like (αZ) 8 in atomic units [14], [15]. The two-photon 2p 1/2 → γ(E1) + γ(E2) + 1s transition rate for hydrogen and hydrogen-like ions is proportional to (αZ) 8 in atomic units.…”

“…The possibility of the CPT-tests is connected with the modern extra-accurate resonance frequency measurements in hydrogen [4,5]. In [6][7][8] it was shown that a specific difference in the H and H atomic spectra arises even in the absence of the CPT-violation, if an external electric field is present. In principle, a difference also arises for the frequency measurements if nonresonant (NR) corrections are taken into account.…”

“…The two-photon 2p 1/2 → γ (E1) + γ (E2) + 1s and 2p 1/2 → γ (E1) + γ (M1) + 1s transition rates for hydrogen and hydrogen-like ions are proportional to mα 2 (αZ) 8 while the leading contribution to the 2p 1/2 level width is mα(αZ) 4 in relativistic units. Thus, the two-photon transitions represent the higher order corrections to the life time of the 2p 1/2level when compared to the lowest order (αZ) 3 ln(αZ) (in relativistic units) radiative corrections derived in [21,22].…”