Numerical investigations of different orders of relativistic effects in atomic shells

Abstract

Different orders in α2 of the hydrogenic energy levels are discussed. The spurious contribution of − 0.2Z5 α3 of the first order Douglas-Kroll-Hess (DKH) Hamiltonian is cancelled at the second order DKH level, which recovers the energy up to the order of Z6 α4 at least to a large extent and includes also a significant part of the higher order terms. Concerning the valence shell energies of many electron atoms, their behavior is more similar to the one of the hydrogen-like 1 s than of the respective nlj levels. The convergence of the α2 expansion becomes unsatisfactory for the very heavy elements.