Abstract
A group-theoretical method is used for a classification of the nuclear eigenstates in the harmonic oscillator shell model. This classification turns out to be intimately connected with the distinction between good and spurious states. In fact it provides a procedure for the elimination of spurious states. The method makes use of the invariance properties of the system Hamiltonian for several groups of transformations. In particular a group U 3 formerly used for the study of collective rotational effects in the nuclear shell-model is of importance. This group is related to the degeneracy of the 3-dimensional isotropic harmonic oscillator states. Some special examples, illustrating the method, are given.
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