as $\mu_\mathrm{eff} \sim B_\mathrm{o}\mu_\mathrm{B}^2/\Delta W$. Barring any “accidental” near-degeneracies ($\Delta W\! < \!10\mbox{ MHz}$), a precision of $1 \mbox{ Hz}$ should be achievable with our current level of magnetic field control.

Accuracy
--------

The potential systematic effects that are expected for this system can be divided into those that will be common to measurements of ground state splittings, and those that are unique to the ${}^2\!\!\;F_{7/2}^o$ state. The former group includes the nonlinear Zeeman shifts from static magnetic fields, differential Stark shifts from the trap fields, blackbody and time-dilation shifts, off-resonant shifts of the levels being measured due to the microwave probe field, and hyperfine-induced third-order corrections [@Safronova2010b]. Since ground-state splittings have been measured below the target precision of $1\mbox{ Hz}$ for many years [@Fisk1997; @Werth1987], the techniques to avoid effects such as these have already been demonstrated and are expected to be sufficient for reaching the comparatively modest target accuracy of $1\mbox{ Hz}$. In particular, taking the expected zero-field splittings from the coefficients in Table \[Table:HFS\] suggests that the largest second- and fourth-order Zeeman shifts will be on the $F =4 \!\leftrightarrow \!3$ transition, which will contribute a systematic shift of less than $1\mbox{ Hz}$ at $B_\mathrm{o} =5\mbox{ mG}$.

