& 3.072 & 2.778 & 2.822 & 2.749\
$+4p$ & 2.014 & 2.823 & 2.148 & 1.904 & 1.685\
$+4s$ & 2.239 & 3.126 & 2.380 & 2.058 & 1.792\
$+3d$ & 2.131 & 2.956 & 2.173 & 1.822 & 1.541\
$+3p$ & 2.007 & 2.208 & 0.941 & 0.276 & -0.198\
$+3s$ & 1.932 & 2.037 & 0.688 & -0.040 & **[-0]{}.**[558]{}\
****

As to the second-order corrections $\eta_X$, these are proportional to various products of electronic matrix elements of magnetic-dipole and electric-quadrupole hyperfine interactions. Based on our accuracy estimates for $A$ and $B$, we conservatively assign $\sim 10\%$ theoretical uncertainty to such matrix elements. Thereby, we expect a $\sim 10\%$ theoretical uncertainty in the second-order HFS constants. In addition, the second-corrections contain summation over intermediate states; in our calculations we truncated the entire sum to a single contribution from the lowest-energy $F_{5/2}$ state. We examined contributions from other 12 lowest-energy intermediate states and found that $\eta_{\mu\mu}$, $\eta_{\mu{Q}}$, $\eta_{QQ}$ are modified by less than 4%, 8%, and 20%, respectively. Thus the overall theoretical uncertainty in second-order corrections is in the order of 10%.

Projected Experimental Accuracy {#sec:Experimental}
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Experimental Procedure
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The measurement of the hyperfine intervals $\Delta W_i$ 