Construction of SO ( 5 ) ⊃ SO ( 3 ) spherical harmonics and Clebsch–Gordan coefficients

Abstract The SO (5) ⊃ SO (3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU (1, 1) × SO (5) basis. We present a computer code for explicit construction of the SO (5) ⊃ SO (3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO (3)-coupled basis. ... Title of program: GammaHarmonic Catalogue Id: AECY_v1_0 Nature of problem Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S 4 . Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors). Versions of this program held in the CPC repository in Mendeley Data AECY_v1_0; GammaHarmonic; 10.1016/j.cpc.2008.12.039 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 SO(5)⊃SO(3)球谐函数是核集体模型角向波函数展开的天然基矢。其为近期提出的、在SU(1,1)×SO(5)基下对核集体模型哈密顿量进行对角化的代数方法奠定了基础。本文提供一套用于显式构造SO(5)⊃SO(3)球谐函数的计算机代码，并借助该代码计算了在SO(3)耦合基下开展集体模型计算所需的克莱布希-高登系数（Clebsch-Gordan coefficients）。…… 程序标题：GammaHarmonic 目录编号：AECY_v1_0 问题本质 在四维球面S⁴上显式构造SO(5)⊃SO(3)球谐函数；计算SO(3)约化矩阵元以及SO(5)⊃SO(3)克莱布希-高登系数（同标因子）。 该程序收录于Mendeley Data中的CPC（Computer Physics Communications）程序库版本为AECY_v1_0；GammaHarmonic；DOI:10.1016/j.cpc.2008.12.039 本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019年）