Russell-Saunders terms from

Example 7.3-1 (a) Into which states does the Russell-Saunders term d2 3F split in an intermediate field of Oh symmetry (b) Small departures from cubic symmetry often occur as a result of crystal defects, substituent ligands, and various other static and dynamic perturbations. If some of the IRs of O do not occur in the group of lower symmetry, then additional splittings of degenerate levels belonging to such IRs must occur. Consider the effect of a trigonal distortion of D3 symmetry on the states derived in (a) above. 

Example 8.2-1 Examine the effect of spin-orbit coupling on the states that result from an intermediate field of O symmetry on the Russell-Saunders term 4F. Correlate these states with those produced by the effect of a weak crystal field of the same symmetry on the components produced by spin-orbit coupling on the 4F multiplet. 

Exercise 8.2-1 Verify the DPs necessary to determine the spin-orbit splitting of the intermediate-field states derived from the Russell-Saunders term 4F. 

We are now in position to derive the electronic states arising from a given electronic configuration. These states have many names spectroscopic terms (or states), term symbols, and Russell-Saunders terms, in honor of spectroscopists H. N. Russell and F. A. Saunders. Hence, the scheme we use to derive these states is called Russell-Saunders coupling. It is also simply referred to as L-S coupling. 

Nickel(II) is a 3d ion. From this configuration the Russell-Saunders terms G,... 

The value of performing intermultiplet spectroscopy has been demonstrated by optical results on ionic systems. Well defined atomic spectra from intra-4f transitions have been measured up to 6 eV in all the trivalent lanthanides (except, of course, promethium) [Dieke (1968), Morrison and Leavitt (1982) see fig. 1 based on Carnall et al. (1989)]. Each level is characterised by the quantum numbers L, S, J, F), where L and 5 are the combined orbital and spin angular momenta of the 4f electrons participating in the many-electron wavefunctions, and J is the vector sum of L and 5. The quantum number F represents the other labels needed to specify the level fully. It is usually the label of an irreducible representation of the crystal field and we shall omit it. The Coulomb potential is responsible for separating the 4f states into Russell-Saunders terms of specific L and S, while the spin-orbit interaction is diagonal in J and so splits these terms into either 25-1-1 or 2L -I-1 levels with 7 = L - 5 to L -f 5. Provided the spin-orbit interaction is weaker than the Coulomb interaction, as is the case in the lanthanides, the resulting levels consist of relatively pure L, 5, J), or in spectroscopic notation states. These 27-1-1 manifolds are then weakly... 

Fig. 1. Energy levels of trivaient lanthanides below 43000 cm (5.3 eV) arranged according to the number q of 4f electrons. Excited levels known frequently to luminesce are indicated by a black triangle. The excited levels corresponding to hypersensitive transitions from the ground state are marked with a square. For each lanthanide, J is given to the right (in the notation of atomic spectroscopy, ] is added to the Russell-Saunders terms as lower-right subscripts). When the quantum numbers S and L are reasonably well-defined, the terms are indicated to the left. It may be noted that the assignments and F< in thulium(lll) previously were inverted these two levels with 7 = 4 actually have above 60% of H and F character, respectively. Calculated 7-levels are shown as dotted lines. They are taken from Carnall et al. (1968) who also contributed decisively to the identification of numerous observed levels, mainly by using the Judd-Ofelt parametrization of band intensities.

The crystal-field splitting of the and Russell-Saunders terms can be unravelled from high-resolution emission spectra of both srid Di trarrsitions and excitation spectra of the (/ = 0-2) F (/ = 0 and 1) transi-... 

One of the excited configurations for Zn " " is 3d 4p. Derive all the Russell-Saunders terms arising from this configuration. Can you say anything about which term has the... 

Table 7.6 Crystal field splitting of Russell-Saunders terms arising from d" configurations in an octahedral crystal field. The spin multiplicity, not included in this tabie, is the same for the crystal field terms as for the parent Russell-Saunders term...

Table 11.4 Spin-orbit levels arising from f electron ground state Russell-Saunders terms...

This completes our discussion of the excited states of f electron systems. For completeness, however, Table 11.8 gives a more complete list of the Russell-Saunders terms arising from all f" configurations. It does not include the effects of spin-orbit coupling, which have to be worked out for each case individually. The reader may find it a helpful exercise to select a configuration from Table 11.8 and use it to construct a table similar to Table 11.7. 

As an example, for the lowest spin-orbit coupled state for the electronically excited lithium atom (ls 2p 3p ), L, i = 2, S,ou,i = 3/2, and J = 1/2, the term symbol is Pi/2. These are called Russell-Saunders term symbols because it is assumed that the individual orbital angular momentum are more strongly coupled than the spin-orbit coupling. If spin-orbit coupling is ignored, the J term is omitted from the term symbol. 

To derive the term type (species) from the electronic configuration, Russell-Saunders coupling is assumed as defined eailier,... 

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