A program to calculate the oscillator brackets, or Talmi–Moshinsky–Smirnov coefficients, is presented. The recursion with respect to radial quantum numbers is employed. The listed runs show that the program is very fast and it produces accurate results up to very high oscillator excitations. The amount of computations per bracket does not increase with the increase of quantum numbers. In one of the presented versions, the program provides the sets of all existing brackets of a given parity pertaining to oscillator excitations and total angular momenta which lie within given ranges. In the other version, the subsets of such brackets having given angular momenta are produced. Such type arrays of the brackets are quite convenient for majority of applications. These arrays are made compact due to use of suitable combinations of partial angular momenta as array arguments. The program is easy to implement and follow. Comparisons are made with results of programs based on the explicit expression for the brackets.

Program summary

Program Title: OSBRACKETS

CPC Library link to program files: https://doi.org/10.17632/4m594wzv94.1

Licensing provisions: GPLv3

Programming language: Fortran-90

Nature of problem: Single-particle basis oscillator states are widely used for studying the structure of various many-body systems. To compute matrix elements of two-body operators, the Talmi-Smirnov transformation of oscillator states is performed. Coefficients of this transformation are called oscillator brackets. Often it is necessary to retain large sets of basis oscillator states in calculations. Therefore, a fast program to compute the brackets is needed. The program should provide accurate results up to high oscillator excitations.

Solution method: At zero radial quantum numbers oscillator brackets are calculated using an explicit expression that includes only few summations. Starting from such brackets, recurrence relations are employed to calculate the brackets of the general type. These relations prove to work perfectly up to very high oscillator excitations.

中文翻译：

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振荡器（Talmi–Moshinsky–Smirnov）括号的计算

提出了一个计算振荡器括号或Talmi-Moshinsky-Smirnov系数的程序。采用关于径向量子数的递归。列出的运行结果表明，该程序非常快，并且即使在非常高的振荡器激励下也能产生准确的结果。每个括号的计算量不会随着量子数的增加而增加。在给出的版本之一中，程序提供了与给定奇偶性有关的所有现有括号的集合，这些集合与位于给定范围内的振荡器激励和总角动量有关。在另一种形式中，产生具有给定角力矩的这种托架的子集。托架的这种类型的阵列对于大多数应用而言非常方便。由于使用了部分角动量的适当组合作为数组参数，这些数组变得紧凑。该程序易于实施和遵循。基于括号的显式表达式与程序结果进行比较。

计划摘要

节目名称： OSBRACKETS

CPC库链接到程序文件： https : //doi.org/10.17632/4m594wzv94.1

许可条款： GPLv3

编程语言： Fortran-90

问题的性质：单粒子基振荡器状态被广泛用于研究各种多体系统的结构。为了计算两体算子的矩阵元素，执行了振荡器状态的Talmi-Smirnov变换。这种变换的系数称为振荡器括号。通常在计算中必须保留大量基本振荡器状态。因此，需要一个快速的程序来计算括号。该程序应提供准确的结果，直至高振荡器激励。

求解方法：在零径向量子数下，使用仅包含很少的求和的显式来计算振荡器括号。从此类括号开始，采用递归关系来计算常规类型的括号。这些关系证明可以在非常高的振荡器激励下完美工作。