Precision measurements on the $^{138}$Ba$^+$ $6s^2S_{1/2}-5d^2D_{5/2}$ clock transition

Measurement of the $^{138}$Ba$^+$ ${}^2S_{1/2} - {}^2D_{5/2}$ clock transition frequency and $D_{5/2}$ Land\'e $g_J$ factor are reported. The clock transition frequency $\nu_{\mathrm{Ba}^+}=170\,126\,432\,449\,333.31\pm(0.39)_\mathrm{stat}\pm(0.29)_\mathrm{sys}\,$Hz, is obtained with accuracy limited by the frequency calibration of the maser used as a reference oscillator. The Land\'{e} $g_J$-factor for the ${}^2D_{5/2}$ level is determined to be $g_{D}=1.200\,367\,39(24)$, which is a 30-fold improvement on previous measurements. The $g$-factor measurements are corrected for an ac-magnetic field from trap-drive-induced currents in the electrodes, and data taken over a range of magnetic fields underscores the importance of accounting for this systematic.