Structure of the Configurations of High Azimuthal Quantum Number in Cu II and the Rare Gases

Abstract

The energy levels of configurations such as $d^{9}f$, $d^{9}g$ of Cu II and $p^{5}d$, $p^{5}f$ of the rare gases are split into two widely separated groups by the spin-orbit interaction of the almost closed shell. These groups have the two levels of the parent doublet as limits. The splitting within these groups is due to the small electrostatic interaction between the core and the outer electron and the spin-orbit interaction of the outer electron. It is found that if one neglects all of these except the leading term in the electrostatic interaction, the theory predicts that all levels should be double, two levels of different $J$ value having the same energy. It further predicts definitely, without unknown constants, all details of the relative arrangement of these energy levels in the two groups. In the rare-gas configurations and Cu II $d^{9}f$, the levels tend to occur in these pairs and follow this arrangement approximately but the interactions which are neglected in this picture are not entirely negligible. Knowledge of the simple limiting structure should nevertheless be of value in such cases. Cu II $3d^{9}5g$ however fits the simple picture in all details; the levels are observed to occur in pairs with precisely the energies predicted. Thus the 20 levels of this complex configuration are represented by simpler formulas and with better agreement (0.20 ${\mathrm{cm}}^{-1\mathrm{}}$ average discrepancy) than in any other case which has been treated theoretically.