原子核的解剖学：通过群论分解阐明多体波函数
The anatomy of atomic nuclei: illuminating many-body wave functions through group-theoretical decomposition
摘要：
利用现代计算机，我们可以计算原子核的多体波函数，其分量之多令人震惊，即$ > 10^{10}$。但是，除了复制和/或预测实验之外，我们还能从数百亿个分量的向量中学到什么？描述波函数的一种方法是通过群的不可约表示。我简要地讨论了核波函数的群论表征的历史，重点是使用Lanczos型方法有效地将任意波函数分解成群irreps。虽然分解结果往往是分散在许多irreps，但人们仍然发现强大的模式。首先，沿着旋转带的群分解显示出一致的共性，支持共享“内在形状”的图像;这也被称为\textit{quasi-dynamical symmetry}。第二，使用唯象力和\textit{ab initio}力的波函数的群分解通常非常相似，尽管它们的起源和维数有很大的不同。这两个结果表明，群理论分解可以提供一个强大的“解剖”的许多核波函数。这反过来又支持了使用基于几何的多体框架进行计算的想法。
英文摘要：
With modern computers we can compute nuclear many-body wave functions with an astounding number of component, $ > 10^{10}$. But, aside from reproducing and/or predicting experiments, what do we learn from vectors with tens of billions of components? One way to characterize wavefunctions is through irreducible representations of groups. I discuss briefly the history of group-theoretical characterization of nuclear wavefunctions, with an emphasis of using Lanczos-type methods to efficiently dissect arbitrary wavefunctions into group irreps. Although the resulting decompositions are often fragmented over many irreps, one nonetheless finds powerful patterns. First, group decompositions along rotational bands show coherent commonalities, supporting the picture of a shared "intrinsic shape;" this is also called \textit{quasi-dynamical symmetry}. Second, group decompositions for wave functions using both phenomenological and \textit{ab initio} forces are often very similar, despite vastly different origins and dimensionalities. Both of these results suggest a group theoretical decomposition can provide a robust "anatomy" of many nuclear wave functions. This in turn supports the idea of using symmetry-based many-body frameworks for calculations.
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