Beryllium atom reinvestigated: A comparison between theory and experiment

We compare the theoretical and experimental energies for the ground state of the beryllium atom and investigate possible sources for the small discrepancy of about 60 {μ}hartrees found by Bunge [Phys. Rev. A 14, 1965 (1976); 17, 486(E) (1978)]. Indications that the correlation energy may be underestimated in Bunge's work have been confirmed by a recent, very extensive multiconfigurational Hartree-Fock (MCHF) calculation. We emphasize that the critical part of the comparison between theory and experiment is the sum of the first and second ionization energies---the third and fourth are known more accurately from theory---and present the theoretical results accordingly. Before a comparison with experimental results can be performed, corrections must be added to account for mass polarization, for the effect of relativity including the Breit interaction and for radiative effects. The previously unknown mass-polarization contribution to the first ionization energy has recently been determined experimentally. Relativity is most important for the 1s electrons and this effect was included in Bunge's work, whereas the relativistic effect on the correlation involving the 2s electrons was neglected. Here, these contributions have been calculated to leading order. A crude estimate of the contribution to the Lamb shift from the 2s electrons is also given. When the revised relativistic corrections are combined with recent results from a very extensive MCHF calculation, the discrepancy in the beryllium ground-state energy is reduced to (10±{}50){μ} hartrees.