Failure of relativistic codes in the non-relativistic limit: the role of Brillouin configurations
Résumé
In the present letter we solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method. We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We identify the role of single excitations obeying to Brillouin's theorem in this problem. We show that with large scale calculations in which this problem is properly treated, we can reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED