Calculation of oscillator (Talmi–Moshinsky–Smirnov) brackets

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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 summaryProgram Title: OSBRACKETSCPC Library link to program files:https://doi.org/10.17632/4m594wzv94.1Licensing provisions: GPLv3Programming language: Fortran-90Nature 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.