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Some properties of the statistical tensors, which govern the angular distribution of radiation emitted by oriented nuclei, are discussed. The discussion is limited to the case of axial symmetry in the spin-Hamiltonian which produces the orientation. An identification of the irreducible tensors, which define the statistical tensors, with those familiar in spin coupling is made. This also permits the matrix elements of the former tensors to be obtained quite easily. The temperature dependence of the statistical tensors for the case of small spin coupling is discussed.

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