Analytic description of critical point actinides in a transition from octupole deformation to octupole vibrations

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An analytic collective model in which the relative presence of the quadrupole and octupole deformations is determined by a parameter (φο), 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 Β (EL) ratios which depend only on φο, draws the border between the regions of octupole deformation and octupole vibrations in an essentially parameter-independent way, and describes well 2 2 6Th and 226Ra, for which experimental energy data are shown to suggest that they lie close to this border. The similarity of the AQOA results with φο = 45° for ground state band spectra and B(E2) transition rates to the predictions of the X(5) model is pointed out.