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

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, ${\beta }^2+{\beta }_0^4/{\beta }^2$ (AQOA-D). Analytic expressions for energy spectra and $B\left(E1\right),B\left(E2\right),B\left(E3\right)$ 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 ${\varphi }_0$ (expressing the relative amount of octupole vs quadrupole deformation) and ${\beta }_0$ (the position of the minimum of the Davidson potential), while the recently determined $B\left(EL\right)$ transition rates of ${}^{224}\mathrm{Ra}$, presenting stable octupole deformation, are successfully reproduced. A procedure for gradually determining the parameters appearing in the $B\left(EL\right)$ transitions from a minimum set of data, thus increasing the predictive power of the model, is outlined.

Figure 1

Excitation energies $E_{n_{\beta },L}$ [Eq. (12)] for $n_{\beta }=0$ and $L=2$ are shown as a function of the free parameters ${\beta }_0$ and ${\varphi }_0$. All quantities shown are dimensionless. See Sec. 2c for further discussion.