Nuclear magnetic octupole moment and the hyperfine structure of the5D3/2,5/2states of theBa+ion

Abstract

The hyperfine structure of the long-lived $5{D}_{3/2}$ and $5{D}_{5/2}$ levels of ${\text{Ba}}^{+}$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $\ensuremath{\Omega}$ 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 $5{D}_{J}$ fine-structure manifold allows one to extract $\ensuremath{\Omega}$ 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 ${\text{Ba}}^{+}$ experiments.