Irreducible U(3) tensor interactions in the symplectic collective model

The potential V(β, γ) of the Bohr-Mottelson and symplectic collective models is expressed as a linear combination of U(3) irreducible tensor operators in the symplectic enveloping algebra. This many-body collective potential is then projected onto the symplectic two-body tensor operators. The projected two-body potential is shown to give results similar to the many-body potential in ²⁰Ne. Hence, in the symplectic shell model, one has obtained a collective model with two-body forces.