Energies, fine structures, and isotope shifts of the 1s22snlexcited states of the beryllium atom

The energies and wave functions of the 1${\mathit{s}}^2$2snl states of beryllium are calculated with a full-core plus correlation method. Eight excited states (2p ${}_{}{}^{1,3}{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$, 3s ${}_{}{}^{1,3}{}_{}{}^{}$S, 3p ${}_{}{}^{1,3}{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$, and 3d ${}_{}{}^{1,3}{}_{}{}^{}$D) 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 ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$, 3s ${}_{}{}^{1,3}{}_{}{}^{}$S, 3p ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$, and 3d ${}_{}{}^3{}_{}{}^{}$D states, the predicted energies agree with experiment to about 1 ${\mathrm{cm}}^{\mathrm{-}1}$. However, the discrepancies are larger for 2p ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$, 3p ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$, and 3d ${}_{}{}^1{}_{}{}^{}$D. The relativistic corrections are found to be critically important in these comparisons. The predicted fine-structure splittings for 2p ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_{2,1,0}^{\mathit{o}}$ are 2.360 and 0.637 ${\mathrm{cm}}^{\mathrm{-}1}$. They agree well with the 2.35 and 0.64 ${\mathrm{cm}}^{\mathrm{-}1}$ in the experiment. The predicted