Abstract
A simple analytic expression is reported for U(6) matrix elements in the totally symmetric irreducible representations relevant to the interacting boson model. With respect to the SU(3) symmetry-adapted basis, the U(6) generators are given explicitly as SU(3) reduced matrix elements. The two-body Hamiltonian is expressed as a linear combination of SU(3) tensor operators. In particular, the Casimir invariants of the SU(5), O(6), and O(5) algebras are given in terms of SU(3) tensors. By using 9-(\ensuremath{\lambda}\ensuremath{\mu}) coefficients, the SU(3) tensor method is extended to the proton-neutron interacting boson model.
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