Analytic Description of Critical Point Actinides in a Transition from Octupole Deformation to Octupole Vibrations

An analytic collective model in which the relative presence of the quadrupole and octupole deformations is determined by a parameter (phi_0), while axial symmetry is obeyed, is developed. The model [to be called the analytic quadrupole octupole axially symmetric model (AQOA)] involves an infinite well potential, provides predictions for energy and B(EL) ratios which depend only on phi_0, draws the border between the regions of octupole deformation and octupole vibrations in an essentially parameter-independent way, and describes well 226-Th and 226-Ra, for which experimental energy data are shown to suggest that they lie close to this border. The similarity of the AQOA results with phi_0=45 degrees for ground state band spectra and B(E2) transition rates to the predictions of the X(5) model is pointed out. Analytic solutions are also obtained for Davidson potentials, leading to the AQOA spectrum through a variational procedure.Comment: LaTeX, 27 pages, including 14 postscript figure

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 $\beta_2$ and $\beta_3$. The system is considered to oscillate between positive and negative $\beta_3$-values, by rounding an infinite potential core in the $(\beta_2,\beta_3)$-plane with $\beta_2>0$. 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 $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.Comment: 25 pages, 13 figures. Accepted in Phys. Rev.