Partial dynamical SU(3) symmetry and the nature of the lowest K=0 collective excitation in deformed nuclei

We discuss the implications of partial dynamical SU(3) symmetry (PDS) for the structure of the lowest K =0⁺ (K=0₂) collective excitation in deformed nuclei. We consider an interacting boson model Hamiltonian whose ground and γ bands have good SU(3) symmetry, while the K=0₂ band is mixed. It is shown that the double-phonon components in the K=0₂ wave function arise from SU(3) admixtures which, in turn, can be determined from absolute E2 rates connecting the K=0₂ and ground bands. An explicit expression is derived for these admixtures in terms of the ratio of K=0₂ and γ bandhead energies. The SU(3) PDS predictions are compared with existing data and with broken-SU(3) calculations for ¹⁶⁸Er.