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A collective Hamiltonian for the rotation-vibration motion of nuclei isconsidered, in which the axial quadrupole and octupole degrees of freedom arecoupled through the centrifugal interaction. The potential of the systemdepends on the two deformation variables $\beta_2$ and $\beta_3$. The system isconsidered to oscillate between positive and negative $\beta_3$-values, byrounding an infinite potential core in the $(\beta_2,\beta_3)$-plane with$\beta_2>0$. By assuming a coherent contribution of the quadrupole and octupoleoscillation modes in the collective motion, the energy spectrum is derived inan explicit analytic form, providing specific parity shift effects. On thisbasis several possible ways in the evolution of quadrupole-octupolecollectivity are outlined. A particular application of the model to the energylevels and electric transition probabilities in alternating parity spectra ofthe nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.Comment: 25 pages, 13 figures. Accepted in Phys. Rev.

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes