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 discrete nucleon representations of 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 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 ²⁰Ne, using the quadratic Casimirs of both Elliott’s SU(3) and Sp(3, R). The band structure, delineated by strong B(E2) values, has a more consistent description in Sp(3, R) rather than SU(3). In particular, we confirm previous work finding in some nuclides strongly connected upper and lower bands with the same underlying symplectic structure.

旋转带在原子核的光谱中很常见。受到液滴四极变形对这些带的早期描述的启发，Elliott 根据费米子的产生和湮灭算符构建了 SU(3) 的离散核子表示。从那时起，Elliott 的模型一直是描述原子核旋转的基础。然而，后来的工作表明辛扩展 Sp(3, R ) 提供了一个更统一的图片。我们使用 Elliott 的 SU(3) 和 Sp(3, R )的二次 Casimir将无核壳模型核波函数分解为几种铍同位素以及²⁰ Ne 的对称定义子空间。能带结构，由强B ( E2) 值，在 Sp(3, R ) 而不是 SU(3) 中有更一致的描述。特别是，我们证实了先前在一些核素中发现的具有相同潜在辛结构的强烈连接的上带和下带。