Crystal field theory and the Shubnikov point groups

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Abstract
Two pieces of theory which have so far remained unconnected, crystal field theory and the theory of corepresentations of non-unitary groups, are brought together here for the study of the splitting of atomic energy levels in a crystalline field with the symmetry of one of the magnetic (Shubnikov) point groups. The cases of the various possible relative strengths of the crystalline field and of spin-orbit coupling are considered. Tables are presented which enable the splitting of any atomic energy level to be obtained very easily in a crystalline field with the symmetry of any one of the 58 magnetic point groups. Examples of the use of these tables are given. A discussion is given of the relevance of Kramers' theorem to the energy levels of electrons in surroundings with the symmetry of any one of the 58 magnetic point groups.

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