Nuclear magnetic octupole moment and the hyperfine structure of the 5D_3/2,5/2 states of the Ba⁺ ion

The hyperfine structure of the long-lived 5D_3/2 and 5D_5/2 levels of Ba⁺ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments Ω is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire 5D_J fine-structure manifold allows one to extract Ω without contamination from the second-order corrections. Measurements to the required accuracy should be possible with a single trapped barium ion using sensitive techniques already demonstrated in Ba⁺ experiments.