Multiplets of intermediate width

In this most realistic case the van Vleck formula adopts the form of 

By introducing the particular susceptibility function common for a multiplet +J IVitO) 2 

The zero-order van Vleck coefficients are determined as the relative energies of levels of the 25+1 Lj multiplet, as 

The determination of the second-order van Vleck coefficients E M is the most laborious step. The magnetic field gives rise to matrix elements between the different multiplets of a term the non-vanishing matrix elements are of the form 

The energy contribution in second-order perturbation theory is 

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Multiplets of intermediate width appropriate to 4f-complexes (Table 21, Fig. 10)... 

Fig. 8.17. Multiplet width as compared with thermal energy (a) wide multiplets (b) multiplets of intermediate width (c) narrow multiplets.

Terms of the magnetic susceptibility formula for multiplets of intermediate width... 

Table 21 Magnetic susceptibility for multiplets of the intermediate width...

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