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

Abstract

We have carried out configuration-interaction calculations for $^{4}F^{e,o}$ states of Li and ${\mathrm{Be}}^{+}$ and for the lowest $^{4}D^{e,o}$ states of ${\mathrm{Be}}^{+}$ 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 ${\mathrm{Li}}^{+}$ $2p4f^{1,3}F$ states have also been considered. The nonrelativistic result for the Li $1s2p4f^{4}F\ensuremath{\rightarrow}1s2s4f^{4}F^{o}$ transition is ${\ensuremath{\lambda}}_{\mathrm{air}}=5474.3\ifmmode\pm\else\textpm\fi{}0.4$ \AA{}. Including relativistic, radiative, and mass-polarization corrections for the $1s2p^{3}P$ and $1s2s^{3}S$ ${\mathrm{Li}}^{+}$ cores we get $\ensuremath{\lambda}=5471.7\ifmmode\pm\else\textpm\fi{}0.4$ \AA{}, in excellent agreement with a $\ensuremath{\lambda}=5471.9\ifmmode\pm\else\textpm\fi{}1.4$ \AA{} recently observed in the beam-foil source. Stronger support for our basic assumption comes from three calculated (experimental) wavelengths $\ensuremath{\lambda}=3406.0\ifmmode\pm\else\textpm\fi{}0.3(3405.6\ifmmode\pm\else\textpm\fi{}0.6), 4330.1\ifmmode\pm\else\textpm\fi{}0.5(4330.2\ifmmode\pm\else\textpm\fi{}0.5), \mathrm{and} 3510.8\ifmmode\pm\else\textpm\fi{}0.5(3510.8\ifmmode\pm\else\textpm\fi{}0.5)$ \AA{} in the Be ${\mathrm{ii}}^{**}$ spectrum. Furthermore, three lines (the first two above and $\ensuremath{\lambda}=981$ \AA{}) have been reassigned and three new wavelengths are predicted for this spectrum. The $1s2s4f\ifmmode\pm\else\textpm\fi{}1s2p3d$ nature of the $^{4}F^{o}(1)$ and $^{4}F^{o}(2)$ states in ${\mathrm{Be}}^{+}$ is responsible for the uncommon situation that $^{4}F^{o}(1)$ is below $1s2s4d ^{4}D^{o}(2)$, thus explaining the failure of some of the earlier assignments. The lowest ${\mathrm{Be}}^{+}$ $1s2s2p^{4}P^{o}$ state is found 115.845\ifmmode\pm\else\textpm\fi{}0.016 eV above the ${\mathrm{Be}}^{+}$ $1{s}^{2}2s$ ground state, in fair agreement with a recent experimental value of 115.7\ifmmode\pm\else\textpm\fi{}0.1 eV. The He and ${\mathrm{Li}}^{+}$ $2p4f^{1,3}F$ states decay to $1s4f^{1,3}F$ states with wavelengths too close to the resonance transition $2p\ensuremath{\rightarrow}1s$ of the corresponding one-electron system to be observed in beam-foil experiments. The ${\mathrm{Li}}^{+}$ $2p4f ^{1,3}F$ states, however, decay to $2p3d ^{1,3}D$ states with $\ensuremath{\lambda}=3825.4\ifmmode\pm\else\textpm\fi{}0.1 \mathrm{and} 4352.2\ifmmode\pm\else\textpm\fi{}0.1$ \AA{}, respectively, and they should be susceptible of experimental observation.