论文标题
Wigner旋转基质在高角度动量处的有效且有效的算法
An effective and efficient algorithm for the Wigner rotation matrix at high angular momenta
论文作者
论文摘要
Wigner旋转矩阵（$ d $函数）是Angular-Momentum-Procotion Operator的一部分，在现代核结构模型中起着至关重要的作用。但是，它的数值评估遭受了严重的错误和不稳定性，这是一个长期存在的问题，这阻碍了核高旋转状态的精确计算。最近，塔吉玛[物理学。 C Rev. C 91，014320（2015）]通过建议高精度傅立叶方法来解决问题迈出了重要的一步，该方法依赖于配方 - 操纵软件。在本文中，我们提出了一种基于Jacobi多项式的Wigner $ d $函数的有效且有效的算法。我们通过一些测试计算将我们的方法与传统的Wigner方法和Tajima傅立叶方法进行了比较，并证明我们的算法始终可以以与傅立叶方法相似的高精度给出稳定的结果，在某些情况下（对于特殊的$ j，m，m，k $和$θ$）我们的方法更加准确。此外，我们的方法是独立的，并且记忆消耗较少。在本文中，提供了相关的测试代码和子例程作为补充材料。
The Wigner rotation matrix ($d$-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a long-standing problem that its numerical evaluation suffers from serious errors and instability, which hinders precise calculations for nuclear high-spin states. Recently, Tajima [Phys. Rev. C 91, 014320 (2015)] has made a significant step toward solving the problem by suggesting the high-precision Fourier method, which however relies on formula-manipulation softwares. In this paper we propose an effective and efficient algorithm for the Wigner $d$ function based on the Jacobi polynomials. We compare our method with the conventional Wigner method and the Tajima Fourier method through some testing calculations, and demonstrate that our algorithm can always give stable results with similar high-precision as the Fourier method, and in some cases (for special sets of $j, m, k$ and $θ$) ours are even more accurate. Moreover, our method is self-contained and less memory consuming. A related testing code and subroutines are provided as Supplemental Material in the present paper.
