Nuclear magnetic octupole moment and the hyperfine structure of the 5D3Õ2,5Õ2 states of the Ba+ ion

The hyperfine structure of the long-lived 5D3/2 and 5D5/2 levels of Ba + ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the firstand 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 5DJ fine-structure manifold allows one to extract 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.