富中子钐和钆同位素中的四极-十六极关联
Quadrupole-hexadecapole correlations in neutron-rich samarium and gadolinium isotopes
AI总结：
本文利用 Gogny 能量密度泛函与 sdg 相互作用玻色子模型映射方法，研究了富中子 Sm 和 Gd 同位素的四极-十六极关联，发现较轻核中存在显著十六极效应，并验证了该方法的可靠性。
摘要：
我们对中子数 $N=88-106$ 的偶偶 Sm 和 Gd 同位素中的四极-十六极关联效应进行了广泛研究。计算在 Gogny 能量密度泛函（EDF）框架下采用 D1S 参数化，并结合 $sdg$ 相互作用玻色子模型（IBM）进行。将四极-十六极约束的自洽平均场势能面映射到 $sdg$ 玻色子哈密顿量的期望值上。该过程从微观上确定了 $sdg$-IBM 哈密顿量的参数。计算得到的激发能和跃迁强度与使用更简单的 $sd$-IBM 得到的结果以及实验数据进行了比较。基于 Gogny-EDF 映射的 $sdg$-IBM 对所研究原子核光谱性质的再现效果与先前基于相对论 EDF 的 $sdg$ 玻色子映射计算相当，表明无论采用相对论还是非相对论 EDF，轴向四极-十六极方法都是可靠的。与映射的 $sd$-IBM 相比，映射的 $sdg$-IBM 改善了较轻 Sm 和 Gd 同位素中的部分结果，这意味着这些原子核中存在显著的十六极关联。对于 $N \geq 94$ 的原子核，十六极效应较小，两种玻色子模型之间唯一显著差异体现在对 $E0$ 单极跃迁的描述上。
英文摘要：
We present an extensive study of quadrupole-hexadecapole correlation effects in even-even Sm and Gd isotopes with neutron number $N=88-106$. The calculations are performed in the framework of the Gogny energy density functional (EDF) with the D1S parametrization and the $sdg$ interacting boson model (IBM). The quadrupole-hexadecapole constrained self-consistent mean-field potential energy surface is mapped onto the expectation value of the $sdg$-boson Hamiltonian. This procedure determines the parameters of the $sdg$-IBM Hamiltonian microscopically. Calculated excitation energies and transition strengths are compared to the ones obtained with a simpler $sd$-IBM, as well as with the experimental data. The Gogny-EDF mapped $sdg$-IBM reproduces spectroscopic properties of the studied nuclei as reasonably as in the case of the previous $sdg$-boson mapping calculations that were based on the relativistic EDF, indicating that the axial quadrupole-hexadecapole method is sound regardless of whether relativistic or nonrelativistic EDF is employed. The mapped $sdg$-IBM improves some of the results in lighter Sm and Gd isotopes compared to the mapped $sd$-IBM, implying the existence of significant hexadecapole correlations in those nuclei. For those nuclei with $N \geq 94$, hexadecapole effects are minor, and the only significant difference between the two boson models can be found in the description of $E0$ monopole transitions.
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