the most precise results for parity violation in Cs [@DFS1989APV; @DFG2002; @APV2012].

Inclusion of the correlation potential modifies the orbitals of the valence electrons at large distances, $r\gtrsim a_B$. These are the distances that also determine the binding energies of the electrons. Placing fitting factors before the correlation potential $f_{\kappa}\Sigma_{\kappa}$ and fitting to the experimental binding energies may be considered a way of taking into account missed effects in the correlation potential. (Experience has shown that, indeed, fitting of the energies leads to improved wave functions at all distances.)

In Table \[tab:sigma\] we present the Uehling shift for the valence orbitals of Cs with the correlation potential taken into account. We present results both for $\Sigma^{(2)}$ and $\Sigma^{(\infty)}$ to see how sensitive the Uehling correction is to the correlation corrections. The values presented in this table do not include the large effects of core relaxation.

It is seen from Table \[tab:sigma\] that the effect of the correlations is large. They increase the $6s$ level shift by around $50\%$ and they exceed the relaxation correction for this level. The relative corrections for the other waves is even larger, though for these waves the relaxation effect dominates.

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  Atom   State         $\epsilon_{\rm HF}$   