Nuclear collective motion of heavy nuclei with axial quadrupole and octupole deformation

A quadrupole-octupole axially symmetric model is constructed for the unified description of alternate parity bands corresponding to octupole vibration or a stable deformation. The model depends on two parameters whose clear physical meaning allows a systematic description of the rotation-vibration dynamics of alternate parity bands analyzed for isotopic sequences of Ra, Th, U, and Pu nuclei. A critical point is identified in the $A=224–228$ mass region of the Ra and Th nuclei marking different stages of the transition between static and dynamic octupole deformation. Model predictions are performed for energies of unobserved states of the yrast sequence and of the excited bands as well as for the $E1, E2$, and $E3$ transition rates, which reproduce the available experimental data and exhibit a specific spin dependence for the transitional nuclei.

Figure 1

The original potential $u_L\left(\varphi \right)$ Eq. (2.8) for $L=0$ and $L=8$ with an infinite barrier at $\varphi \to 0$ is presented along with its modified inner part $v\left(\varphi \right)$ Eq. (2.9), represented by an inverted (red curve) and a normal parabola (purple curve) when $|{\varphi }_c|={10}^{\circ }$ and, respectively, $|{\varphi }_c^{\prime }|={70}^{\circ }$. The corresponding conjunction points of the exact and modified potential regions are marked by horizontal dashed lines.

Figure 2

Comparison between the harmonic approximation [23] and the diagonalization results for $W_L$ when the barrier is infinite.

Figure 3

Comparison between theoretical and experimental absolute energies (column 1) and $\mathrm{\Delta }L=1$ staggering measure (column 2) for ${}^{224}\mathrm{Ra}$ [42], ${}^{226}\mathrm{Ra}$ [44], and ${}^{228}\mathrm{Ra}$ [46] nuclei. The last column depicts the evolution of the corresponding ${\tilde{u}}_L\left(\varphi \right)$ potential for few selected angular momentum values with the dashed horizontal lines noting the matching points $\pm {\varphi }_c$.

Figure 4

Same as in Fig. 3, but for ${}^{224}\mathrm{Th}$ [42], ${}^{226}\mathrm{Th}$ [48], and ${}^{228}\mathrm{Th}$ [46].

Figure 5

Same as in Fig. 3, but for ${}^{230}\mathrm{Th}$ [49], ${}^{232}\mathrm{Th}$ [50], and ${}^{234}\mathrm{Th}$ [52].

Figure 6

Same as in Fig. 3, but for ${}^{230}\mathrm{U}$ [49], ${}^{232}\mathrm{U}$ [53], and ${}^{234}\mathrm{U}$ [52].

Figure 7

Same as in Fig. 3, but for ${}^{236}\mathrm{U}$ [54], ${}^{238}\mathrm{U}$ [55], and ${}^{240}\mathrm{U}$ [56].

Figure 8

Same as in Fig. 3, but for ${}^{236}\mathrm{Pu}$ [54], ${}^{238}\mathrm{Pu}$ [55], and ${}^{240}\mathrm{Pu}$ [57].