Precision Radio Frequency Spectroscopy in the $^{137}$Ba$^+$ 5D$_{5/2}$ Manifold

As atomic theorists' computational techniques become increasingly accurate and sophisticated, precision experiments are necessary to confirm the results of these calculations. The substructure of the long-lived 5D$_{5/2}$ level of $^{137}$Ba$^{+}$ is an ideal testing ground, where calculations are limited by uncertainty in the wavefunctions used. The intervals of this hyperfine manifold are parameterized to first-order by the well-studied nuclear magnetic dipole moment ($\mu$) and the electric quadrupole moment (Q). However, the presence of a nuclear magnetic octupole moment, $\Omega$, as well as second-order corrections in the hyperfine interaction of the same magnitude as $\Omega$, offer additional contributions which are measurable using precision radio-frequency (rf) spectroscopy.\footnote{Phys. Rev. A 77, 052503 (2008)} By accurately measuring hyperfine intervals with transitions that are insensitve to magnetic field to first order, and using results from the 5D$_{3/2}$ level,\footnote{Opt. Express 20, 21379-21384 (2012)} we can extract $\Omega$ as well as the magnitude of the second order corrections to compare with theory.