The $SU(3)\supset SO(3)$ missing label problem and the analytical Bethe ansatz

Abstract

The missing label for basis vectors of SU (3) representations corresponding to the reduction SU (3) ⊃ SO(3) can be provided by the eigenvalues of SO(3) scalars in the enveloping algebra of su(3). There are only two such independent elements of degree three and four. It is shown how the one of degree four can be diagonalized using the analytical Bethe ansatz.