Energy fine-structure splitting

The various transition energies of the gold atom and its ions are shown and compared with experiment [53] in table 2. The nonrelativistic results have errors of several eV. The RCC values, on the other hand, are highly accurate, with an average error of 0.06 eV. The inclusion of the Breit effect does not change the result by much, except for a some improvement of the fine-structure splittings. 

Table 2 CCSD transition energies in Au (eV). IP is the ionization potential, EA denotes electron affinity, and EE — excitation energy relative to the ground state. FS denotes fine-structure splittings.

While including the Breit term has a rather small effect on the excitation energies of Pr " ", it improves the fine-structure splittings (table 7). This is a general phenomenon, and may be traced to including the spin-other-spin interaction in the two-electron Breit term [62]. 

Fig. 7.10 Adiabatic correlation diagram for the Na nd states obtained from the known d state fine structure splitting, the intermediate field energy ordering, and applying the nocrossing rule for states of the same m (from ref. 3).

The data can be represented either as quantum defects for each fine structure series or as a quantum defect for the center of gravity of the level and a fine structure splitting. For the moment we shall use the latter convention, although it is by no means universal. Explicitly, we represent the energy of an nij state, where j = ( + s and s is the electron spin, as... 

In a non-relativistic approximation the usual fine structure (splitting) of the energy terms is considered as a perturbation whereas the hyperfine splitting - as an even smaller perturbation, and they both are calculated as matrix elements of the corresponding operators with respect to the zero-order wave functions. 

Spin-orbit averaged experimental excitations energies of alkaline metals are very well reproduced by this method (cf. Table 5) [220,221]. Unfortunately, fine structure splittings have not been investigated up to now using this approach. 

Figure 19. As Fig. 18, but for the binding energy. A spin-orbit correction derived from the experimental fine-structure splitting of the I atom has been applied for the CCSD(T) results obtained with VTZ, VQZ basis sets and the extrapolation to the basis set limit (stars). 

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