116Ru and 118Ru have been studied via β-delayed γ-ray spectroscopy of nuclei produced in fragmentation reactions at the Radioactive Ion-Beam Factory (RIBF) facility. Level schemes with positive-parity states up to spin J=6 have been constructed. The results have been discussed in terms of the interacting boson model, the algebraic collective model, and total Routhian surfaces. We conclude that the very neutron-rich nuclei still show many features associated with triaxial γ-soft nuclei, represented by the O(6) symmetry, but are approaching a spherical structure, the U(5) symmetry, with increasing neutron number towards the N=82 shell closure. In 118Ru, hints of a shape transition in the ground state have been observed.
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