![Upper radial component of the Cs 6s orbitals. Thick solid line corresponds to the relativistic HF orbital, dashed line is the Brueckner orbital, and the thin solid line is the rescaled relativistic HF orbital, which is seen to coincide with the Brueckner orbital for $r \lesssim a_B$ (see inset).[]{data-label="fig:Cs6sOrbitals"}](fig2.pdf){width="\columnwidth"}

It is worth emphasizing the effect of the correlation potential on the valence electron wave functions. The wave functions are modified by the correlation potential in the region $r\gtrsim a_B$; see Fig. \[fig:Cs6sOrbitals\], where we illustrate the relativistic Hartree-Fock and Brueckner upper radial component for the $6s$ orbital of Cs. For $r<a_B$, the Brueckner wave functions are proportional to the Hartree-Fock wave functions, $\varphi_{\rm Br}(r<a_B)=c\varphi(r<a_B)$. The effect that the correlation corrections have in this region is simply in the normalization of the wave functions. Obviously, since the Uehling potential acts at a distance close to the nuclear radius, $\langle \varphi_{\rm Br}|V_{\rm Ueh}|\varphi_{\rm Br}\rangle =c^2\langle
\varphi|V_{\rm Ueh}|\varphi\rangle$. If the range of the correction to the Hartree-Fock potential $\delta V_{\rm HF}^{\rm Ueh}$ were within $a_B$, then $\langle \varphi_{\rm Br}|V_{\rm Ueh}+\delta V_{\rm HF}^{\rm Ueh}|\varphi_{\rm Br}\rangle =c^2\langle
\varphi|V_{\rm Ueh}+\delta V_{\rm HF}^{\rm Ueh}|\varphi\rangle$ also, i.e., $\delta \epsilon _{\rm Br}=c^2 \delta \epsilon= (\delta
\epsilon^{(1)}_{\rm Br}/\delta \epsilon^{(1)})\delta \epsilon$. 