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Abstract
The correct description of crystal field (CF) effect in a periodic lattice takes into account the band states exacts, rejecting the conventional one ion crystal field model having no regard for translational invariance of electronic states and indistinguishability of electrons. Although the efficiency of the traditional crystal field model is in many cases quite satisfactory, the model is based on incoherent and false assumptions; therefore, one can hardly expect quantitatively correct results particularly for typical band and metallic systems. The difficulties faced by CF theory were overcome by Stevens who proposed a new method of looking at crystal field which is compatible with the latticeperiodicity. In this approach, the crystal field potential emerges in a natural way from general Hamiltonian defined for the whole system. This is a perturbation scheme for degenerate systems employing the projection operators and the second quantization method.
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