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The matrix representation of a 4th and 6th degree octahedral potential in a complete basis of f2LSJ functions belonging to a particular row of each of the 5 irreducible representations of the octahedral group Oh is presented. The matrices are 7×7, 3×3, two of 9×9, and 12×12 when spin-orbit and electrostatic interaction are included. Bases for the 5 irreducible representations are presented as linear combinations of M states for integral J values ranging from 0 to 6. Reduced matrix elements (independent of M or row of representation) are also given including a 2nd degree potential as well so that matrices for any other symmetry can readily be formed in the f2 configuration. Sufficient information is given to define the phases of the states so that other interactions such as spin-orbit can readily be included.
Satten et al. (Mon,) studied this question.
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