Octupole deformation in light actinides within an analytic quadrupole octupole axially symmetric model with a Davidson potential

Abstract

The analytic quadrupole octupole axially symmetric model, which had successfully predicted $^{226}\mathrm{Ra}$ and $^{226}\mathrm{Th}$ as lying at the border between the regions of octupole deformation and octupole vibrations in the light actinides using an infinite well potential (AQOA-IW), is made applicable to a wider region of nuclei exhibiting octupole deformation, through the use of a Davidson potential, ${\ensuremath{\beta}}^{2}+{\ensuremath{\beta}}_{0}^{4}/{\ensuremath{\beta}}^{2}$ (AQOA-D). Analytic expressions for energy spectra and $B(E1),B(E2),B(E3)$ transition rates are derived. The spectra of $^{222\text{--}226}\mathrm{Ra}$ and $^{224,226}\mathrm{Th}$ are described in terms of the two parameters ${\ensuremath{\phi}}_{0}$ (expressing the relative amount of octupole vs quadrupole deformation) and ${\ensuremath{\beta}}_{0}$ (the position of the minimum of the Davidson potential), while the recently determined $B(EL)$ transition rates of $^{224}\mathrm{Ra}$, presenting stable octupole deformation, are successfully reproduced. A procedure for gradually determining the parameters appearing in the $B(EL)$ transitions from a minimum set of data, thus increasing the predictive power of the model, is outlined.