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FTMC（立陶宛物理与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出SU3HOB-cgvcs程序包，从外部Su{}库获取同位因子，复现精度达约10^-13，证明可基于通用SU(3) Clebsch-Gordan库构建自包含的SU(3)方案HOB程序。
AI 中文摘要
我们提出SU3HOB-cgvcs，这是一个Fortran 2008程序包，可针对任意质量比参数d计算通用的Talmi-Moshinsky简谐振子变换括号。这些括号采用Kalinauskas等人的方法在SU(3)基中构建，该变换简化为对含反射的Talmi-Moshinsky矩阵的Wigner d函数的单次求和，权重为链U(6)⊃U(3)×U(2)的SU(3)⊃SO(3)同位因子乘积。SU3HOB-cgvcs从已建立的外部Clebsch-Gordan库Su{}中获取这些同位因子，该库通过矢量相干态（VCS）方法计算这些同位因子。我们将Su{}的形式体系与我们的形式体系衔接，这需要两项修正：重新插入依赖于每个态径向量子数的符号/相位因子，以及解析处理平凡的(0,0)表示。该程序包逐括号复现了Kamuntavičius等人的通用Talmi-Moshinsky括号程序，复现精度达到机器精度（约10^-13），并证明可在通用SU(3) Clebsch-Gordan库之上构建自包含的SU(3)方案HOB程序。
英文摘要
We present SU3HOB-ladder, a Fortran 2008 package computing the general Talmi-Moshinsky harmonic-oscillator transformation brackets for an arbitrary mass-ratio parameter d in the SU(3) basis. The bracket reduces to a single sum over Wigner d-functions of the reflection-containing Talmi-Moshinsky matrix, weighted by products of SU(3) > SO(3) isofactors of the chain U(6) > U(3)xU(2); the isofactors are d-independent, so they are built once per block (E,L) and reused for every d. We obtain them from the U(2) pseudo-spin generators of that same chain: because the U(3) and U(2) labels inside [E] of U(6) are complementary, the highest-weight states are the null space of the raising operator J_+ = a^dag(1).a(2) and the remaining members of each multiplet follow by lowering, so that no SU(3) recoupling machinery, K-matrix or outer-multiplicity resolution is required at any point. We compare this construction with two alternatives that produce the same brackets - the same scheme with isofactors taken from the vector-coherent-state library Su3cgvcs, and the classical Talmi-Moshinsky sum of Kamuntavicius et al. - over every block up to E=50. Evaluating the classical sum with its factorials in logarithmic form rather than as tabulated binomials removes the range limit that otherwise caps it near E ~ 12, and makes it an absolute check on the bracket values over the whole range where its cost is bearable. Against that check the two routes agree to within a factor of a few at every shell, while the ladder construction is faster by three orders of magnitude; it is also the only one of the three usable over the whole range, retaining max|HOB.HOB^T - I| <~ 2x10^-6 at E=50, where the library route has become unusable and the classical route is prohibitively slow.
CommentsCode: https://github.com/Augustinaz/SU3HOB-ladder, archived at doi:10.5281/zenodo.22150397. v2 replaces the SU3HOB-cgvcs paper of v1: the isofactors are now built internally from U(2) pseudo-spin ladder operators, the external-library route of v1 is retained as one of three routes compared, and v1's unqualified machine-precision claim is corrected to the range in which it was measured
