of results of exact QED calculations for $d$-level shifts performed in frozen atomic cores, e.g., in the work [@sapchengd].

Our results for Na through to E119 are presented in Table \[tab:all-order\]. First-order shifts, shifts with core relaxation included, and shifts with core relaxation and electron-core correlations (to be discussed in the next section) are given. We see similar corrections for the other atoms that we saw for Cs. The effect of relaxation on $s$ levels is significant but moderate, about $(5-20)\%$. On the other hand, for all other levels, the magnitude and sign of the Uehling shift is determined by the core relaxation correction. There is orders of magnitude enhancement of the $d$ level shifts for all alkali atoms studied. For Cs, the $d$ levels experience a four-orders of magnitude enhancement. There is an almost 8 orders of magnitude enhancement for the $3d_{5/2}$ level in Na. The relative size of this correction tends to decrease for atoms with higher $Z$, though remains very sizeable everywhere. For Rb, Cs, and Fr, the Uehling shifts for $d$ levels are larger than those for $p$ levels. For Cs, the $d$ level shifts are only ten times smaller than the $s$ level shifts.

In 