Retarded interactions of electrons
https://doi.org/10.25587/2222-5404-2023-20-3-20-32
Abstract
Multielectron atoms and ions, especially ions with a high degree of ionization, observed in natural and laboratory conditions, are relativistic systems in which the orbital quantum number loses its ordinary meaning. It becomes a bad quantum number, and in this case, there is a need for a relativistic approach to study these systems, i.e., research in the j-representation natural for relativism. It requires considering not only electrical and magnetic, but also retarded interactions between the electrons of such systems due to the finiteness of the speed of light in a vacuum. In the article, the relativistic energy operator of retarded interactions between electrons in the v2/c2 approximation (part of the Breit operator) is reduced to two different forms using the method of Racah irreducible tensor operators. These forms are expressed in terms of standard irreducible tensor operators used in the theory of the atom, nucleus, and solid-state physics. The resulting expressions for the operator of the energy of retarded interactions are presented in a form natural for the relativistic approach, i.e. in j - representation. The energy operator of the retarded interactions is a two-electron interaction that is a direct multiplication of operators (matrices in the Pauli representation) which affects different electrons. Therefore, the two-electron wave function is represented as a direct multiplication of one-electron wave functions, that is Dirac-type bispinors. All this allows using the method of Raсah irreducible tensor operators in calculating the matrix element. The matrix elements of the energy operator of the retarded interactions are represented in terms of the standard values of the atom and nucleus theory.
About the Authors
I. S. Kychkin
M.K. Ammosov North-Eastern Federal University
Russian Federation
Russian Federation
Kychkin Innokentij Savvich ‒ Doctor of Physical and Mathematical Sciences, Professor, Department of General and Experimental Physics, Institute of Physics and Technology
Yakutsk
V. I. Sivtsev
M. K. Ammosov North-Eastern Federal University
Russian Federation
Russian Federation
Sivtsev Vasilij Ivanovich ‒ Candidate of Physical and Mathematical Sciences, Associate Professor, Department of General and Experimental Physics, Institute of Physics and Technology
Yakutsk
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Review
For citations:
Kychkin I.S., Sivtsev V.I. Retarded interactions of electrons. Vestnik of North-Eastern Federal University. 2023;20(3):20-32. (In Russ.) https://doi.org/10.25587/2222-5404-2023-20-3-20-32
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