Degeneracy crystal field approximation

For Ce atoms the 4f level has the total angular momentum S = f and a total number of rotational levels N( = 2S +1 = 6. The crystal field usually splits the degeneracy, but if the level splitting is sufficiently small, all N( substates can participate in spin fluctuation. The theory of the resonance level remains qualitatively the same, but the large Nf value allows the so-call l/N approximation, which helps to simplify the calculation of the level width (Bickers et al. 1985, 1987). At zero temperature the resonance is found to have an asymmetric lineshape with a level width measured by k T. When the temperature is increased the line drops in height and shifts in energy as shown in fig. 28. Although the theory introduces a new parameters in addition... 

The L multiplet is split into levels labeled by their J eigenvalues, J = L + S, L -I- S — 1,..., L — S, where each J level has a 2J -I-1 degeneracy. It is this J degeneracy which is split by the crystal field [9,10]. Usually, the lowest J level is relatively isolated, the ligand field splittings are approximately 100-1000 cm and only the lowest few crystal field states as indicated above provide the main contribution to the measured magnetic susceptibility. The effects of the various interactions are shown in Fig. 18.1 for the f configuration. 

Ep = 2 edcv /wto is approximately 21 meV for most of the III-V and II-VI semiconductors, no is the linear refractive index, and Kpi, is a material independent constant (1940 cm (eV) for a two-parabolic-band model). It should be mentioned that the above model does not correctly account for the degeneracy of the valence band (heavy hole, light hole, and spin-orbit/crystal-field split-off bands) and assumes single parabolic conduction and valence bands. Using the Kane band structure with three valence bands and including excitonic effects have been shown to produce larger TPA coefficients [227]. 

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