Title: Axially Symmetric Quadrupole-Octupole Model incorporating Sextic Potential Show Chinese title

Title: 包含六次势的轴对称四极-八极模型

Abstract: We present an extended application of the analytic quadrupole octupole axially symmetric model, originally employed to study the octupole deformation and vibrations in light actinides using an infinite well potential (IW). In this work, we extend the model's applicability to a broader range of nuclei exhibiting octupole deformation by incorporating a sextic potential instead of the Davidson potential.Similarly to conventional models, such as AQOA-IW (for infinite square potential) and AQOA-D (for the Davidson potential), our proposed model is referred to as AQOA-S. By employing the sextic potential, phenomenologically represented as $v(\tilde\beta) = a_1\tilde \beta^2+a_2\tilde \beta^4+a_3\tilde \beta^6$, we can derive analytical expressions for the energy spectra and transition rates (B(E1), B(E2), B(E3)). The energy spectra of the model are essentially governed by two critical parameters: $\phi_0$, indicating the balance between octupole and quadrupole strain, and $\alpha$, a key factor in adjusting the shape and behavior of the spectra through the sextic potential. In terms of applications, the study encompasses five isotopes, namely $^{222-226}$Ra and $^{224,226}$Th. Significantly, our model demonstrates remarkable agreement with the corresponding experimental data, particularly for the recently determined B(EL) transition rates of $^{224}$Ra, surpassing the performance of the model that employs the Davidson potential. The stability of the octupole deformation in $^{224}$Ra adds particular significance to these findings. Show Chinese abstract

Abstract: 我们展示了一种解析四极-八极轴对称模型的扩展应用，该模型最初用于使用无限深势阱（IW）研究轻锕系元素中的八极形变和振动。 在这项工作中，我们将模型的应用范围扩展到更多表现出八极形变的核素，通过引入六次势代替Davidson势来实现这一点。与传统的模型类似，例如AQOA-IW（用于无限方势阱）和AQOA-D（用于Davidson势），我们的提议模型被称为AQOA-S。通过采用六次势，以经验公式表示为$v(\tilde\beta) = a_1\tilde \beta^2+a_2\tilde \beta^4+a_3\tilde \beta^6$，我们可以推导出能谱和跃迁几率（B(E1)、B(E2)、B(E3)）的解析表达式。 模型的能谱主要受两个关键参数的影响：$\phi_0$，它表示八极和四极应变之间的平衡；以及$\alpha$，这是通过六次势调整能谱形状和行为的关键因素。 在应用方面，本研究涵盖了五个同位素，即$^{222-226}$铀和$^{224,226}$钍。 尤为重要的是，我们的模型与相应的实验数据表现出显著的一致性，特别是在最近确定的$^{224}$铀的B(EL)跃迁几率上，优于采用Davidson势的模型。 $^{224}$铀中八极形变的稳定性使这些发现具有特别的意义。