DOI: 10.1209/epl/i2003-00114-3
Europhys. Lett., 61 (5) , pp. 606-612 (2003)

Nonrelativistic atom-photon interaction beyond the multipole approximation

D. J. Boers¹ and C. M. J. Wijers<sup>2

1</sup>  Carl von Ossietzky Universität, Fachbereich Physik - 26111 Oldenburg, Germany
²  University of Twente, Department of Applied Physics P.O. Box 217, 7500 AE Enschede, The Netherlands

(Received 27 August 2002; accepted in final form 17 December 2002)

Abstract
We investigate the interaction between the hydrogen atomic orbitals and the quantized modes of the electromagnetic field within the domain of nonrelativistic quantum electrodynamics in the Coulomb gauge. Contrary to the conventional dipole approximation and higher-order multipole approximations, which hold in the long-wavelength regime, we make no such approximations and investigate the rigorous wavelength dependence of the interaction matrix elements. Using analytical as well as numerical considerations, we establish the short-wavelength behaviour in the domain that is beyond the multipole approximation but still within the nonrelativistic regime. Our results differ significantly from the predictions of the dipole approximation. These features are graphically demonstrated in the case of the radiative 1s- 2p_z coupling in the hydrogen atom. We report a previously unnoticed short-wavelength contribution to the interaction that vanishes in the multipole expansion. We note that the convergence properties of radiative energy shifts are incorrectly predicted by the dipole approximation and that the unapproximated result is in fact quickly convergent.

PACS
42.50.Ct - Quantum description of interaction of light and matter; related experiments.
31.30.Jv - Relativistic and quantum electrodynamic effects in atoms and molecules.
31.15.Ar - Ab initio calculations.

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