#### Interplay of γ-Rigid and γ-Stable Collective Motion in Neutron Rich Rare Earth Nuclei

R. Budaca, A.I. Budaca
National Institute of Physics and Nuclear Engineering, 077125, Romania
Abstract. A simple exactly separable version of the Bohr Hamiltonian which combines the γ-stable and γ-rigid collective motion is used to describe few neutron rich rare earth nuclei. The coupling between the two types of collective motion is managed through a rigidity parameter. Considering a potential of the form u(β)+v(γ)/β2 adapted to the current problem and restricting the γ-stable part of the Hamiltonian to stiff oscillations around the γ value of the rigid motion one obtains an exact separation of variables. Moreover, the separated potential for β>/i> variable is chosen such that in the lower limit of the rigidity parameter, the model recovers exactly the ES-X(5) or ES-D solutions, while in the upper limit it tends to the prolate $\gamma$-rigid solutions X(3) or X(3)-D. The experimental realization of the model is found in few transitional rare earth nuclei around N=96 where a singular behaviour is observed.

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