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

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). Copyright © 1976 American Institute of Physics.SCOPUS: ar.j