Abstract A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show that it is also very fast. Applications of the brackets to calculating interaction matrix elements and constructing hyperspherical bases for identical particles are described. Comparisons are done with the programs published previously. Program summary Program Title: HHBRACKETS Program Files doi: http://dx.doi.org/10.17632/77kd74zy5k.1 Licensing provisions: GPLv3 Programming language: Fortran-90 Nature of problem: When solving three-body problems, expansions of hyperspherical harmonics over harmonics similar in form but pertaining to different sets of Jacobi vectors are required. A universal and fast routine that provides the coefficients of such expansions, called hyperspherical brackets or Raynal–Revai coefficients, is needed by researchers in the field. The expansions are used both to calculate interaction matrix elements and construct states (anti)symmetric with respect to particle permutations. Solution method: At the hypermomentum that is minimum possible at given Jacobi orbital momenta, hyperspherical brackets are calculated using an explicit expression that includes only few summations. To calculate the brackets at larger hypermomenta, a recursion relation is employed. It perfectly works up to very high hypermomenta. Attention is paid to avoid difficulties with large quantum numbers.

中文翻译：

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计算三粒子超球面谐波之间变换系数的程序

摘要 提出了一种计算三粒子超球面括号的程序。列出了测试结果，可以看出该程序适用于非常高的超动量和轨道动量值。列出的运行表明它也非常快。描述了括号在计算相互作用矩阵元素和构造相同粒子的超球面基中的应用。与之前发布的程序进行了比较。程序概要 程序名称：HHBRACKETS 程序文件 doi：http://dx.doi.org/10.17632/77kd74zy5k.1 许可条款：GPLv3 编程语言：Fortran-90 问题性质：解决三体问题时，超球面谐波的展开需要形式相似但属于不同雅可比矢量集的谐波。该领域的研究人员需要一个通用且快速的程序来提供这种扩展的系数，称为超球面括号或 Raynal-Revai 系数。展开式既用于计算相互作用矩阵元素，也用于构造关于粒子排列的（反对）对称状态。求解方法：在给定雅可比轨道动量下可能最小的超动量下，使用仅包含少量求和的显式表达式计算超球面括号。为了在更大的超动量下计算括号，采用了递归关系。它完美地适用于非常高的超动量。注意避免大量子数的困难。是该领域研究人员所需要的。展开式既用于计算相互作用矩阵元素，也用于构造关于粒子排列的（反对）对称状态。求解方法：在给定雅可比轨道动量下可能最小的超动量下，使用仅包含少量求和的显式表达式计算超球面括号。为了在更大的超动量下计算括号，采用了递归关系。它完美地适用于非常高的超动量。注意避免大量子数的困难。是该领域研究人员所需要的。展开式既用于计算相互作用矩阵元素，也用于构造关于粒子排列的（反对）对称状态。求解方法：在给定雅可比轨道动量下可能最小的超动量下，使用仅包含少量求和的显式表达式计算超球面括号。为了在更大的超动量下计算括号，采用了递归关系。它完美地适用于非常高的超动量。注意避免大量子数的困难。超球面括号是使用仅包含少量求和的显式表达式计算的。为了在更大的超动量下计算括号，采用了递归关系。它完美地适用于非常高的超动量。注意避免大量子数的困难。超球面括号是使用仅包含少量求和的显式表达式计算的。为了在更大的超动量下计算括号，采用了递归关系。它完美地适用于非常高的超动量。注意避免大量子数的困难。