SU(2) × SU(2) scalars in the enveloping algebra of SU(4)

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Abstract
We build an integrity basis for the SU(2) × SU(2) scalars belonging to the enveloping algebra of SU(4). We prove that it contains seven independent invariants in addition to the Casimir operators of SU(4) and SU(2) × SU(2). We form a complete set of commuting operators by adding to the latter two linear combinations of the former the operators Ω and Φ first introduced by Moshinsky and Nagel. We then solve the state labeling problem that occurs in the reduction SU(4) ⊆ SU(2) × SU(2) by diagonalizing simultaneously Ω and Φ. Their eigenvalues are calculated numerically in all irreducible representations of SU(4) that are encountered in light nuclei up to and including the s–d shell. Finally we build the propagation operators for the widths of the fixed supermultiplet, spin and isospin spectral distributions by taking appropriate linear combinations of SU(2) × SU(2) invariants of degree less than or equal to four, and we tabulate the averages of these operators in the above‐mentioned irreducible representations of SU(4).

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