Calculation of oscillator (Talmi–Moshinsky–Smirnov) brackets

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.本文提出了一款用于计算振子括号（oscillator brackets）——即塔尔米-莫什金斯基-斯米尔诺夫系数（Talmi–Moshinsky–Smirnov coefficients）——的程序。该程序采用针对径向量子数的递推算法。所展示的运行测试结果表明，本程序运算效率极高，即便针对极高阶的振子激发场景，也能输出高精度结果。单个振子括号的计算量不会随量子数的增大而增加。在所提供的两类程序版本中，其一可生成给定宇称、且振子激发与总角动量处于指定范围内的全部有效振子括号集合；其二则可生成指定角动量对应的此类振子括号子集。这类振子括号数组适配绝大多数应用场景，通过将分角动量进行合理组合作为数组参数，实现了数组的紧凑化存储。本程序易于实现与理解，本文还将本程序的计算结果与基于振子括号显式表达式开发的程序所得结果进行了对比验证。