(4) | |
The c(γSLJ) are expansion coefficients, and | |
(5) |
The largest percentage in the composition of a level is called the purity of the level in that coupling scheme. The coupling scheme (or combination of coupling schemes if more than one configuration is involved) that results in the largest average purity for all the levels in a calculation is usually best for naming the levels. With regard to any particular calculation, one does well to remember that, as with other calculated quantities, the resulting eigenvectors depend on a specific theoretical model and are subject to the inaccuracies of whatever approximations the model involves.
Theoretical calculations of experimental energy level structures have
yielded many eigenvectors having significantly less than 50 % purity in
any coupling scheme. Since many of the corresponding levels have
nevertheless been assigned names by spectroscopists, some caution is
advisable in the acceptance of level designations found in the literature.
The ground-state electron configurations of elements heavier than neon are shortened in the table by using rare-gas element symbols in brackets to represent the corresponding electrons. The ground levels of all neutral atoms have reasonably meaningful LS-coupling names, the corresponding eigenvector percentages lying in the range from ~55 % to 100 %. These names are listed in the table, except for Pa, U, and Np; the lowest few ground-configuration levels of these atoms comprise better 5f ^{N}(L_{1}S_{1}J_{1}), 6d_{j}7s^{2} (J_{1 }j) terms than LS-coupling terms. The relatively large spin-orbit interaction of the 6p electrons produces jj-coupling structures for the (6p^{2}_{1/2})_{0}, (6p^{2}_{1/2}6p_{3/2})^{o}_{3/2}, and (6p^{2}_{1/2}6p^{2}_{3/2})_{2} ground levels of the 6p^{2}, 6p^{3}, and 6p^{4} configurations of neutral Pb, Bi, and Po, respectively. As noted in the section jj Coupling of Equivalent Electrons, the jj-coupling names are more appropriate for these atoms than the alternative LS-coupling designations in the table.
The ionization energies in the table are from recent compilations [13, 14]. The uncertainties are mainly in the range from less than one to several units in the last decimal place, but a few of the values may be in error by 20 or more units in the final place; i.e., the error of some of the two place values could be greater than 0.2 eV. Although no more than four decimal places are given here, values for both the neutral and singly-ionized atoms are given to their full accuracies in [14].