Analytic Wave Functions. III. The Spin-Orbit, Spin-Other Orbit, and Spin-Spin Interactions

In two earlier papers we have described our methods and programs for calculations of certain classes of atomic wave functions. In this paper we consider the application of the wave functions so obtained to the calculation of the spin-orbit, spin-other-orbit, and spin-spin interactions. As an example we consider oxygen with the electron distribution ${\mathrm{}\left(1s\right)\mathrm{}}^2{\mathrm{}\left(2s\right)\mathrm{}}^2{\mathrm{}\left(2p\right)\mathrm{}}^4$. In first approximation we suppose the spin-orbit interaction diagonal in the wave functions of the Slater diagram. These calculations then remove the horizontal degeneracy from the diagram. We assume the Coulomb potential for the spin-orbit calculation and show the relative contributions of the nucleus and various type electrons to the result. Although the order of the splitting is as observed, the observed asymmetry is not obtained. In second approximation the off-diagonal elements of the spin-orbit interaction are included. The desired asymmetry of the fine structure is obtained, and the agreement with experiment is satisfactory. The spin-other-orbit and spin-spin interactions are calculated for the diagonal first approximation.