Abstract
SU(3) recoupling techniques are used to give explicit constructions of the spurious states in the SU(3) scheme of the harmonic oscillator shell model. A compact formula is derived for all spurious states of excitation 1&Z.xl;hω in 1p shell nuclei. Spurious states of excitation 1&Z.xl;hω in heavier nuclei can be written down from a general formula whenever the needed fractional parentage coefficients are known. Calculation of spurious states of excitation 2&Z.xl;hω are illustrated with the simple example, 16O. It is shown how the purely non-spurious parts can be projected out of specific core excited states such as those of the weak coupling model for hole and particle states of high SU(3) symmetry. Most of the SU(3) recoupling coefficients needed for the construction of spurious states can be simply related to ordinary SU(2) Racah coefficients.
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