Dirac's Equation and the Spin-Spin Interactions of Two Electrons

An improvement is made on a previous attempt to treat two particles by means of Dirac's equation. The approximate equation (1) below is considered in successive steps. The first step, following Oppenheimer, includes the electrostatic energy exactly, rather than to the first in power in $e^2$. This makes it possible to use it as a good starting point in the calculation of spectral terms. The second step brings in the energy due to the interaction of the electric currents. It is given by (9) below. Maxwell's equations and the conservation of energy (see (8.5)) demand the validity of the diagonal matrix elements of this expression as a first order perturbation energy, independently of theories of light quanta. The interactions of the particles with themselves give additive constants in the energy within the limits of the approximation used. Within the same limits the results are in agreement with experiment.