Indirect spin-orbit interaction in high-LRydberg states with2S1/2cores

Abstract

In high-L Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-L term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a {sup 2}S{sub 1/2} state. However, observations in barium Rydberg states and recent observations in Rydberg states of Si{sup 2+} reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, Si{sup 2+}, and barium.