结合六次势能的轴对称四极-八极模型
Axially Symmetric Quadrupole-Octupole Model incorporating Sextic Potential
AI总结：
本文提出结合六次势能的轴对称四极-八极模型(AQOA-S)，推导了能谱与跃迁率的解析表达式，在Ra和Th同位素中与实验数据高度吻合，优于Davidson势模型。
摘要：
我们提出了分析性四极八极轴对称模型的扩展应用，该模型最初使用无限深势阱（IW）研究轻锕系元素中的八极形变与振动。本研究通过引入六次势能替代 Davidson 势，将模型适用性扩展至更广泛的八极形变原子核。与传统模型（如采用无限方势阱的 AQOA-IW 和采用 Davidson 势的 AQOA-D）类似，我们提出的模型称为 AQOA-S。采用现象学表示为 $v(\ ildeβ) = a_1\ ilde β^2+a_2\ ilde β^4+a_3\ ilde β^6$ 的六次势能，我们可推导出能谱与跃迁率（B(E1), B(E2), B(E3)）的解析表达式。模型能谱主要由两个关键参数决定：$ϕ_0$ 表示八极与四极应变之间的平衡，$α$ 是通过六次势能调节能谱形状与行为的关键因子。在应用方面，本研究涵盖五种同位素，即 $^{222-226}$Ra 和 $^{224,226}$Th。值得注意的是，我们的模型与相应实验数据表现出显著一致性，特别是对于最近确定的 $^{224}$Ra 的 B(EL) 跃迁率，超越了采用 Davidson 势的模型性能。$^{224}$Ra 中八极形变的稳定性使这些发现具有特殊意义。
英文摘要：
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 $v(\tildeβ) = a_1\tilde β^2+a_2\tilde β^4+a_3\tilde β^6$, 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: $ϕ_0$, indicating the balance between octupole and quadrupole strain, and $α$, 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.
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