The Effect of Retardation on the Interaction of Two Electrons

TLDR

An approximate wave equation incorporating (v/c)^2 terms for two‑electron interaction is reduced to spin‑dependent forms (48) and (36), with the non‑retarded case given by (10) and (36). The equation is derived first in configuration space and then via the Heisenberg‑Pauli wave‑field theory, using only first‑order Coulomb terms. Retardation introduces previously unknown terms that modify the fine structure of orthohelium, making the corrected equations (6) and (48) necessary and significant mainly for low‑atomic‑number elements.

Abstract

An approximate wave-equation (6) is set up which takes into account terms of the order ${(\frac{v}{c})}^{2}$ in the interaction of two electrons. This equation (6) is reduced to a form (48) which can be interpreted in terms of electronic spins. Disregarding the effect of retardation the two electrons are described by formula (10). This is reduced to a form (36) which can also be described in terms of spins. It is shown that the retarded equation (48) differs from the non-retarded (36) by terms which affect the fine structur of orthohelium and which have not been known so far.The derivation of the wave-equation (6) is made first in configuration space and later by the Heisenberg-Pauli theory of wave-fields. The latter method is used only to terms of the first order in the Coulomb interaction. It is shown from the consideration of (36) that it cannot be the correct equation and that the modifications due to retardation introduced in (6) and (48) are necessary. These modifications are appreciable only for spectra of elements with low atomic number.