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Physical Review A

Intensity distribution shift for the resonant photon scattering on the hydrogen atom

Leonti N Labzowsky, Соловьёв Дмитрий Анатольевич

Published Aug 26, 2002• 5 citations
Publisher

Abstract

The role of nonresonant (NR) corrections in the resonant photon scattering process on the hydrogen atom is discussed. It is shown that the average energy of the emitted photons may not coincide with the average energy of the incident photons defined by the photon source spectral function. The discrepancy is due to the NR corrections and to the interaction with the vacuum.

DOI
10.1103/physreva.66.024503

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The role of nonresonant (NR) corrections in the resonant photon scattering process on the hydrogen atom is discussed. It is shown that the average energy of the emitted photons may not coincide with the average energy of the incident photons defined by the photon source spectral function. The discrepancy is due to the NR corrections and to the interaction with the vacuum.
It is shown that the average energy of the emitted photons does not coincide with the average energy of the incident photons in the process of resonant photon scattering on an atom. This happens because of the asymmetry of the natural line profile caused by the nonresonant corrections and by the dependence of the transition rates on the frequency. In the case of the Lyman-α transition in hydrogen, . The effect can be much larger if ‘artificial’ asymmetry of the intensity distribution in the photon source with respect to the resonance frequency takes place. In the latter case, the difference is close to the accuracy of the recent experiments on the Lyman-α frequency measurements.
The process of nonresonant photon scattering on a hydrogen atom is considered as a microscopic model for a quantum-mechanical description of the reflection of light on a mirror. Multiple reflections of this kind then can serve as a model for light storage within a system of mirrors. In combination with modern high-precision measurements of atomic transition frequencies, such a storage of light could allow for new information on the time variation of fundamental constants, such as the fine-structure constant. The intensity distribution shift arising due to the inherent asymmetry of the natural line profile sets an ultimate limit for the preservation of the photon light frequency during storage. In the case of a ‘hydrogen mirror’ this shift appears to be much larger than the relative accuracy of about 10 −15 required in measurements of a time dependence of the fine-structure constant. Possibilities of achieving the required accuracy are discussed.
We investigate nonresonant contributions to resonant Rayleigh-scattering cross sections of atoms. The problematic nonresonant contributions set a limit to the accuracy to which atomic spectra determine energy levels. We discuss the off-resonance effects in one-photon transitions. We also show that off-resonance contributions for the 1S–2S two-photon transition in atomic hydrogen are negligible at current and projected levels of experimental accuracy. The possibility of a differential measurement for the detection of off-resonance effects in one-photon transitions in atomic hydrogen is discussed. PACS Nos.: 31.15-p, 12.20Ds
In the present paper, we consider nonresonant corrections to $2s\text{\ensuremath{-}}ns/nd$ transition frequencies in hydrogen for the experiments based on two-photon spectroscopy. A detailed study of angular correlations of quantum interference effects within the framework of rigorous quantum electrodynamics is given. Closed expressions for the resonant two-photon-scattering cross sections on an atomic level with dependence on all atomic quantum numbers including fine and hyperfine structure are derived. These expressions are applied for the description of experiments based on two-photon spectroscopy with fixing of incident (outgoing) photon polarizations. We demonstrate that, for certain experimental geometries, nonresonant corrections could be significant for the determination of Rydberg constant and proton charge radius.
In the experimental observation of radiationless resonant Raman scattering, features that differ from the idealized case can arise when the spectral width of the incident photon distribution is comparable to the width of pertinent atomic energy levels. These features include nonlinear dispersion of the peak maxima and changes in the symmetry and width of the ejected-electron lines with changes in the average incident photon energy. Under certain conditions, the electron line shapes can become highly asymmetric or even double peaked. The origin of these features in actual experiments is explored through a model calculation for large spectral widths. Some possible applications of these effects are pointed out.