Abstract
Relativistic effects also influence the motion of electrons. They are described in the framework of the Pauli equation but with a velocity operator from the more general Dirac theory. The moving electrons generate an electromagnetic field beyond the electric field due to the nuclei. It describes the electron-electron interaction and depends on the position, momentum and spin operator of each individual electron in a self-consistent manner. The electromagnetic field is calculated up to the second order in the ratio of electron velocity and speed of light. Besides the well-known scalar-relativistic corrections, the Darwin and mass-correction terms, and the spin-orbit interaction known for isolated atoms, an additional relativistic effect, the Breit interaction, is described by the coupling of the vector potential to the mechanical momentum and of the magnetic field to the electron spin. In addition to the non-relativistic mutual Coulomb interaction of the electrons, the longitudinal one, a relativistic transverse interaction appears, which, however, can be neglected in non-magnetic systems or systems where the spin-orbit coupling predominates the magnetic dipole-dipole interaction.
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Bechstedt, F. (2015). Hamiltonian of Interacting Electrons. In: Many-Body Approach to Electronic Excitations. Springer Series in Solid-State Sciences, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44593-8_2
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DOI: https://doi.org/10.1007/978-3-662-44593-8_2
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