Elsevier

Nuclear Physics A

Volume 170, Issue 1, 19 July 1971, Pages 34-54
Nuclear Physics A

The use of SU(3) in the elimination of spurious center of mass states

https://doi.org/10.1016/0375-9474(71)90681-6Get rights and content

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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    ††

    Operated for the US Atomic Energy Commission under contract with Union Carbide Corporation.

    NSF Senior Postdoctoral Fellow on leave of absence from Department of Physics, University of Michigan, Ann Arbor, Michigan.

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