超越艾略特模型的旋转带
Rotational bands beyond the Elliott model
摘要：
转动带在原子核的光谱中是常见的。受早期描述这些带的液滴的四极形变的启发，艾略特从费米子产生和湮灭算符构建了$\mathrm{SU}(3)$的离散核子表示。从那时起，艾略特的模型就成为描述原子核转动的基础。然而，后来的工作表明，辛扩展$\mathrm{Sp}(3,R)$提供了一个更统一的图片。我们将无核壳模型波函数分解成几种铍同位素的自由定义的子空间，以及$^{20}$ Ne，使用Elliott的$\mathrm{SU}(3)$和$\mathrm{Sp}(3,R)$的二次卡西米尔。由强$B(E2)$值描绘的能带结构在$\mathrm{Sp}(3,R)$而不是$\mathrm{SU}(3)$中具有更一致的描述。{In特别是，我们确认了以前的工作发现，在一些核素强连接的上下带具有相同的基本辛结构。
英文摘要：
Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed a discrete nucleon representations of $\mathrm{SU}(3)$ from fermionic creation and annihilation operators. Ever since, Elliott's model has been foundational to descriptions of rotation in nuclei. Later work, however, suggested the symplectic extension $\mathrm{Sp}(3,R)$ provides a more unified picture. We decompose no-core shell-model nuclear wave functions into symmetry-defined subspaces for several beryllium isotopes, as well as $^{20}$Ne, using the quadratic Casimirs of both Elliott's $\mathrm{SU}(3)$ and $\mathrm{Sp}(3,R)$. The band structure, delineated by strong $B(E2)$ values, has a more consistent description in $\mathrm{Sp}(3,R)$ rather than $\mathrm{SU}(3)$. {In particular, we confirm previous work finding in some nuclides strongly connected upper and lower bands with the same underlying symplectic structure.
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