Nuclear magnetic octupole moment and the hyperfine structure of the $5D_{3/2,5/2}$ states of the Ba$^+$ ion

TL;DR

This paper analyzes the hyperfine structure of Ba$^+$ ion's $5D$ states to develop a method for extracting nuclear magnetic octupole moments using relativistic many-body calculations and hyperfine measurements.

Contribution

It introduces a procedure to extract nuclear magnetic octupole moments from hyperfine structure data of Ba$^+$ ion's $5D$ states, combining ab initio calculations with experimental techniques.

Findings

Relativistic many-body perturbation theory computes electronic matrix elements.

Simultaneous hyperfine measurements can isolate nuclear octupole moments.

Accurate extraction of nuclear moments is feasible with current trapped ion techniques.

Abstract

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 $\Omega$ 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 $5D_J$ fine-structure manifold allows one to extract $\Omega$ 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 Ba$^+$ experiments.