Theoretical studies of core-excited states of two- and three-electron atoms

We have carried out configuration-interaction calculations for ⁴Fe,o states of Li and Be⁺ and for the lowest ⁴De,o states of Be⁺ in an effort to test the accuracy that can be achieved in transition-energy calculations by assuming transferability of relativistic, radiative, and mass-polarization corrections among similar electron cores. He and Li⁺ 2p4f1,3F states have also been considered. The nonrelativistic result for the Li 1s2p4f⁴F→1s2s4f⁴Fᵒ transition is λₐᵢᵣ=5474.3±0.4 {}. Including relativistic, radiative, and mass-polarization corrections for the 1s2p³P and 1s2s³S Li⁺ cores we get λ=5471.7±0.4 {}, in excellent agreement with a λ=5471.9±1.4 {} recently observed in the beam-foil source. Stronger support for our basic assumption comes from three calculated (experimental) wavelengths ${λ}=3406.0±{}0.3(3405.6±{}0.6), 4330.1±{}0.5(4330.2±{}0.5), and 3510.8±{}0.5(3510.8±{}0.5)in the Be{ii}**$ spectrum. Furthermore, three lines (the first two above and ${λ}=981) have been reassigned and three new wavelengths are predicted for this spectrum. The1s2s4f±{}1s2p3d$ nature of the $⁴Fᵒ(1)$ and $⁴Fᵒ(2)$ states in ${Be}⁺$ is responsible for the uncommon situation that $⁴Fᵒ(1)$ is below $1s2s4d ⁴Dᵒ(2)$, thus explaining the failure of some of the earlier assignments. The lowest ${Be}⁺$ $1s2s2p⁴Pᵒstate is found 115.845±0.016 eV above the{Be}⁺$ $1{s}²2sground state, in fair agreement with a recent experimental value of 115.7±0.1 eV. The He and{Li}⁺$ $2p4f1,3F$ states decay to $1s4f1,3F$ states with wavelengths too close to the resonance transition $2p{→}1s$ of the corresponding one-electron system to be observed in beam-foil experiments. The ${Li}⁺$ $2p4f 1,3F$ states, however, decay to $2p3d 1,3D$ states with ${λ}=3825.4±{}0.1 and 4352.2±{}0.1$ {}, respectively, and they should be susceptible of experimental observation.