Table \[tab:all-order\], the results of Derevianko [*et al.*]{} for $6s$ and $6p$ levels of Cs are presented in the final column; it is seen that our relativistic Hartree-Fock results agree very well.

The core relaxation corrections to $6s$ and $6p$ levels of Cs arising from inclusion of the radiative potential (accounting for vacuum polarization and self-energy) were calculated in Ref. [@rad_pot] and the importance of these effects were noted. The very large corrections for $d$ levels were seen in our recent work on the spectra of the alkaline earths [@radium]. The relaxation effect has also been shown to be important in the transition frequencies of several- and many-electron highly-charged ions [@blundell; @CCJ], particularly for transitions involving $d$ levels [@4p4d], although the relative size of the corrections seen there is significantly smaller than what we have observed in neutral atoms.

Correlation corrections {#sec:correlations}
=======================

  ------------ ---------------- --------------------- ---------------------------------- -------------------------------------- --------------------- ---------------------------------- --------------------------------------
  State         $\epsilon_{\rm                                                                                                                                                           
                     Exp}$                                                                                                                                                               

                                 $\epsilon_{\rm Br}$   $\delta \epsilon^{(1)}_{\rm Br}$   $\delta \epsilon^{(1)}_{\rm Br,fit}$   $\epsilon_{\rm Br}$   $\delta \epsilon^{(1)}_{\rm Br}$   $\delta \epsilon^{(1)}_{\rm Br,fit}$

  $6s_{1/2}$      -0.143098           -0.147671                  -1.588\[-5\]                         -1.470\[-5\]                    -0.143262                  -1.452\[-5\]                         -1.448\[-5\]

  $6p_{1/2}$      -0.092166           -0.093578                  -3.071\[-7\]                         -2.856\[-7\]                    -0.092436                  -2.895\[-7\]                         -2.855\[-7\]

  $6p_{3/2}$      -0.089642           -0.090849                  -3.338\[-8\]                         -3.124\[-8\]                    -0.089848                  -3.164\[-8\]                         -3.129\[-8\]

  $5d_{3/2}$      -0.077035           -0.080029                 -4.970\[-10\]                        -4.409\[-10\]                    -0.078015                 