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}{sub 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}{sub 0}, draws the border between the regions of octupole deformation and octupole vibrations in an essentially parameter-independent way, and describes well {sup 226}Th and {sup 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}{sub 0}=45 deg. 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 of the form {beta}{sup 2}+{beta}{sub 0}{sup 4}/{beta}{sup 2}, leading to the AQOA spectrum through a variational procedure.