On the accuracy of valence–shell computations for heavy and super–heavy elements

Recent atomic computations on the (super–) heavy elements have raised the expectation that their low–lying excitation and ionization energies can be calculated with an accuracy of a few hundredth of an eV and, hence, that such computations might help in the identification of new lines. For most many–electron atoms, however, the higher–order relativistic and quantum electrodynamical (QED) effects are included so far only in a rather approximate form. Using different model computations for the neutral and weakly ionized ytterbium (Z = 70) and nobelium atoms (Z = 102), it is shown here that QED effects alone may lead to an uncertainty of 20–50 meV for the excitation energies of all super–heavy elements, and that even for highly–correlated wave functions the theoretical predictions are presently not more accurate than about 0.1 eV. Moreover, in order to support forthcoming spectroscopic measurements on the elements beyond Z = 100, detailed computations have been carried out for the two low–lying $^1{\rm S}_{\,0} - ^{1,3}{\rm P}_{\,1}^{\,o}$ excitation energies of nobelium by using systematically enlarged multiconfiguration Dirac–Fock wave functions