Breit Interaction and Parity Non-conservation in Many-Electron Atoms
  We present accurate {\em ab initio} non-perturbative calculations of the Breit correction to the parity non-conserving (PNC) amplitudes of the $6s-7s$ and $6s-5d_{3/2}$ transitions in Cs, $7s-8s$ and $7s-6d_{3/2}$ transitions in Fr, $6s-5d_{3/2}$ transition in Ba$^+$, $7s-6d_{3/2}$ transition in Ra$^+$, and $6p_{1/2} - 6p_{3/2}$ transition in Tl. The results for the $6s-7s$ transition in Cs and $7s-8s$ transition in Fr are in good agreement with other calculations while calculations for other atoms/transitions are presented for the first time. We demonstrate that higher-orders many-body corrections to the Breit interaction are especially important for the $s-d$ PNC amplitudes. We confirm good agreement of the PNC measurements for cesium and thallium with the standard model . 
V. A. Dzuba, V. V. Flambaum, and M. S. Safronova