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arXiv:2609.33494

Non-dipole effects in a multielectron atom

A. N. Hopersky, A. M. Nadolinsky, Конеев Рустам Викторович

Published Sep 27, 2026• 0 citations
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Abstract

This Letter establishes the analytical structure of the dipole radiation transition operator, taking into account non-dipole effects for a multielectron atom. The results summarize those of Komninos Y. et al., Phys. Rev. A 86, 023420 (2012), obtained in an approximation of a "split" electron of a continuous spectrum. The result for the complete operator of a multipole radiation transition [see formula (10)] can be specified within the framework of the methods of the theory of irreducible tensor operators and for higher multipoles.

DOI
10.48550/arxiv.2609.33494

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This Letter establishes the analytical structure of the dipole radiation transition operator, taking into account non-dipole effects for a multielectron atom. The results summarize those of Komninos Y. et al., Phys. Rev. A 86, 023420 (2012), obtained in an approximation of a "split" electron of a continuous spectrum. The result for the complete operator of a multipole radiation transition [see formula (10)] can be specified within the framework of the methods of the theory of irreducible tensor operators and for higher multipoles.
With the help of mathematical technique of irreducible tensors the multipole expansion for the probability amplitude of spontaneous radiation of a quantum system is derived. It is shown that the found series represents the total radiation amplitude in the form of the sum of radiation amplitudes of electric and magnetis multipole photons. All information about the radiating system is contained in the coefficients of the series which are the irreducible tensors being determined by the current density of transition. The expansion can be used for solving different problems that arise in studying electromagnetic field-quantum system interaction both in long-wave approximation and outside its framework.
The summation of all the higher-order contributions to multiphoton absorption in atoms is presented. The nonperturbative expressions for the transition amplitudes are expressed in terms of continued fractions. They account for the whole perturbation originated by the radiation field on the atom but do not exhibit explicit expression for the level shift. In the case of radiation fields of high intensity the only reliable determination of the level shift involves a careful location of the poles of the resolvent operator. The theory has been tested in considering a two-level atom. An extremely rapid convergence of the continued fractions has been observed, and accurate results concerning high-order resonance shifts have been obtained. The expressions for the transition amplitudes being nonperturbative with regard to the field strength, they can be considered as analytic continuations of the perturbation series. This provides a useful approach to the problem of ultraintense fields.