Energies, fine structures, and isotope shifts of the 1s²2snl excited states of the beryllium atom

The energies and wave functions of the 1s²2snl states of beryllium are calculated with a full-core plus correlation method. Eight excited states (2p ^1,3P^o, 3s ^1,3S, 3p ^1,3P^o, and 3d ^1,3D) are studied. A restricted variational method is used to extrapolate a better nonrelativistic energy. The relativistic corrections are calculated with first-order perturbation theory. The calculated excitation energies (relative to the ground state) are compared with experiment. For the 2p ³P^o, 3s ^1,3S, 3p ³P^o, and 3d ³D states, the predicted energies agree with experiment to about 1 cm^-1. However, the discrepancies are larger for 2p ¹P^o, 3p ¹P^o, and 3d ¹D. The relativistic corrections are found to be critically important in these comparisons. The predicted fine-structure splittings for 2p ³P_2,1,0^o are 2.360 and 0.637 cm^-1. They agree well with the 2.35 and 0.64 cm^-1 in the experiment. The predicted ¹⁰–⁹Be 2s ¹S–3d ¹D isotope shift is 14.08 GHz. This also agrees with the 14.05(4) GHz in the experiment. The lifetime of the 1s²2s2p ³P₁^o is calculated using the intermediate-coupling scheme.