Phase-Amplitude Method in Atomic Physics. II. Z Dependence of Spin-Orbit Coupling

The spin-orbit interaction for p electrons is shown to occur in the K shell for all atoms and to vary with atomic number Z according to Δμ∝Hα²(0, Z)/Z, where Δμ is the difference in quantum defect between the fine-structure levels evaluated at the series limit, α(0, Z) is the amplitude function for a nonrelativistic zero-energy p wave at $r=0$, and H is a relativistic correction factor. The quantity Δμ is evaluated and found to vary as Z2.33, which is in remarkable agreement with experiment. In addition to this gross behavior, the variation of α²(0, Z)/Z exhibits a structure tied to the Periodic Table. This structure derives from the influence of the valence region of the atomic potential, which affects the spin-orbit interaction through the normalization factor α(0, Z). Neither inner screening effects, embodied in Casimir's σ(Z) parameter, nor deviations of the atomic potential from Zr^-1 in the interaction region appear very relevant to this problem.