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

A collective Hamiltonian for the rotation–vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables β2 and β3. The system is considered to oscillate between positive and negative β3-values, by rounding an infinite potential core in the (β2, β3)-plane with β2 > 0. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole–octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei Nd, Sm, Gd and Dy is presented. PACS: 21.60.Ev; 21.10.Re E-mail: [email protected]