The problem of two electrons in an external field and the method of integral equations in optics |
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Authors: | O N Gadomsky K K Altunin |
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Institution: | (1) Ul’yanovsk State University, 432700 Ul’yanovsk, Russia |
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Abstract: | This paper solves the problem of the interaction, via the field of virtual photon field with the emission or absorption of
a real photon, of two atomic electrons located at arbitrary distances from one another. The interaction is interpreted as
a third-order QED effect in the coordinate representation. The role of intermediate states with positive and negative frequencies
is studied. A general expression is derived for the matrix elements of the operator of the effective electron-electron interaction
energy for different types of quantum transitions. The expression makes it possible to calculate the probabilities of the
corresponding transitions and to examine various patterns of induction of polarizing fields by one atom at the point occupied
by the other atom. The exchange of virtual photons between the atoms located at arbitrary distances from one another is shown
to lead to additional terms in the operators of spin-orbit and spin-spin coupling of the atomic electrons, over and above
those in the corresponding Breit operators. It is shown that there is an important difference between the induction of polarizing
fields and the transfer of optical photons. In particular, it is found that when polarizing fields are induced, a situation
may arise in which the disappearance (production) of a photon takes place at the point occupied by one atom, while absorption
(emission) of the same photon occurs at the place occupied by the other atom. A block diagram of an experimental device that
could be used to study this property of polarizing fields is presented. Finally, a method of deriving integral field equations
is proposed. The method is based on allowing for polarizing fields, and its effectiveness is demonstrated by the example of
electric dipole and spin transitions in the spectrum of interacting atomic electrons.
Zh. éksp. Teor. Fiz. 114, 1555–1577 (November 1998) |
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