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Optics and Spectroscopy

Influence of an external electric field on the probabilities of two-photon transitions between 2s, 2p and 1s levels for hydrogen and antihydrogen atoms

Dmitry A. Solovyev, Leonti N Labzowsky, V. Sharipov

Published Jul 1, 2009• 1 citation
Publisher

Abstract

The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( $$ \bar H $$ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and $$ \bar H $$ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.

DOI
10.1134/s0030400x09070030

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The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( Hˉ\bar HHˉ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and Hˉ\bar HHˉ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.
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.
The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen ( Hˉ \bar H Hˉ ) atoms in an external electric field are calculated. These quantities are different for H and Hˉ \bar H Hˉ due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.
We analyze the influence of an external electric field on the nsnsns and npnpnp Rydberg states. The impact of an electric field leads to a significant modification of the decay rate. Namely, the additional (linear and quadratic in the field) terms arise in the differential transition probabilities. In contrast to the quadratic term, the linear summand leads to a difference of the hydrogen (H)(\text{H})(H) and antihydrogen (H‾)(\overline{\text{H}})(H) spectra. However, this difference vanishes after the integration over photon-emission directions and does not contribute to the total emission probability. The quadratic term results in the significant change of the total decay rate and level width, respectively. The analysis of the linear and quadratic terms depending on the field strength is discussed.
We have applied the density matrix and second-order perturbation theory in order to re-analyze the two-photon decay of hydrogen-like ions for the polarization of emitted light. Special attention is paid to the linear polarization of one of the photons, while the spin state of the second photon is supposed to be unobserved. For such an “angle-polarization” correlation of the two photons we investigate the contributions that arise from non electric-dipole terms in the expansion of the electron-photon interaction. Detailed calculations are performed for the 2s 1/2 →1s 1/2 and 3d 5/2 →1s 1/2 transitions in neutral hydrogen as well as in hydrogen-like uranium.