In the final two columns, the shifts due to core relaxation are presented, divided into the direct and exchange contributions.

The first-order shift $\delta \epsilon^{(1)}$ is always negative, leading to increased binding, and shifts for the $p$ and $d$ waves are seen to be orders of magnitude smaller than the $s$-wave shift. The direct part of the relaxation potential is of opposite sign to Uehling (see also Fig. \[fig:potentials\]), reducing the binding. The exchange part of the relaxation potential, however, may lead to shifts that are positive or negative. It is interesting that for $6s$, the exchange relaxation contribution is larger than that coming from the direct part. For the other orbitals, we see that the direct part of the relaxation correction dominates, though the exchange part is also very important, particularly for $5d$. Consideration of core relaxation makes the Uehling shift for $6s$ larger, while it leads to a correction of opposite sign for the other orbitals.

While the magnitude of the relaxation correction for $6s$ is about 10% that of the first-order shift, for the other orbitals the situation is very different. For $6p_{1/2}$, the relaxation correction is about twice the size of the first-order shift, which then 