Spin-orbit splitting levels

In the case of a single-core hole level the spectral function can directly be compared with experiments (XPS, ESCA). However, in cases with two or more core levels the dipole matrix elements must be included to determine the relative strength of the individual core-level spectra. In the case of spin-orbit split levels, this can be done through statistical weighting of the spectra but for core holes in different shells or subshells, the matrix elements have to be included explicitly. In the 4 s., 4 p case one then obtains... 

Here we note that Uf appears as a weighted average of what may be regarded as the potentials for two spin-orbit split levels, and f/ " is related to the difference between these two potentials. The factor of 2 in the numerator of the spin-orbit potential is included for representation of the final expression in terms of the spin operator. Rearranging these expressions, we can write... 

For high rotational levels, or for a moleeule like OFI, for whieh the spin-orbit splitting is small, even for low J, the pattern of rotational/fme-stnieture levels approaehes the Flund s ease (b) limit. In this situation, it is not meaningful to speak of the projeetion quantum number Rather, we first eonsider the rotational angular momentum N exelusive of the eleetron spin. This is then eoupled with the spin to yield levels with total angular momentum J = N + dand A - d. As before, there are two nearly degenerate pairs of levels assoeiated... 

Figure 4. Spin-orbit splitting in AT — 1 and 2 vibronic levels of the state of NCN. Solid lines connect the results of calculations thar employ ab initio computed potential curves [28], For comparison the results obtained by employing experimentally derived potential curves (dashed lines) [30,31] are also given. Full points represent energy differences between P — K — and P — K spin levels, and crosses are differences between P — K + I and P — K levels.

Spin-orbit splittings as well as binding energies of a particular electron level increase with increasing atomic number. The intensity ratio of the peaks from a spin-orbit doublet is determined by the multiplicity of the corresponding levels, equal to 2j + 1. Hence, the intensity ratio of the j = and j = components of the Rh 3d doublet is 6 4 or 3 2. Thus, photoelectron peaks from core levels come in pairs -doublets - except for s levels, which normally give a single peak. 

Levels with a non-zero value of the orbital angular momentum quantum number (1 > 0), i.e. p, d, f,... levels, show spin-orbit splitting. The magnitude of this splitting is too small to be evident in Figure 5.28, hence the double subscript for these levels (i.e. L2 3 represents both the L2 and L3 levels. 

In any future reexamination of the spectrum of the ReFg anion it may be anticipated that a moderately strong band should be found between ca. 5-10 kK., since the spin-orbit splitting of the zT g ground level again amounts to 3/2 f in the first order. 

Let us start with neutral and charged TTF. The experimental spectrum for S2p (Fig. 6.14(a)) corresponding to neutral TTF is disappointingly unstructured, whereas that for charged TTF is clearly rich in structure. As shown in Fig. 1.31, the S2/ core levels are composed of two spin-orbit split components, 2p3/2 and 2pi/2, separated by 1.3 eV, so that the S2p NEXAFS spectra consists of the superposition of both... 

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