An Upper Bound on the Strongly Forbidden $6S_{1/2} \leftrightarrow 5D_{3/2}$ Magnetic Dipole Transition Moment in Ba$^{+}$

We report the results from our first-generation experiment to measure the magnetic-dipole transition moment (M1) between the $6S_{1/2}$ and $5D_{3/2}$ manifolds in Ba$^{+}$. Knowledge of M1 is crucial for the proposed parity-nonconservation experiment in the ion \cite{Fortson93}, where M1 will be a leading source of systematic error. To date, no measurement of M1 has been made in Ba$^{+}$, and moreover, the sensitivity of the moment to electron-electron correlations has confounded accurate theoretical predictions. A precise measurement may help to resolve the theoretical discrepancies while providing essential information for planning a future PNC measurement in Ba$^{+}$. We demonstrate our technique for measuring M1 - including a method for calibrating for stress-induced birefringence introduced by the scientific apparatus - and place an upper bound of $\mathrm{M1} < 93 \pm 39 \times 10^{-5} \mu_{B}$.