Program to calculate coefficients of transformations between three-particle hyperspherical harmonics

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 summaryProgram Title: HHBRACKETSProgram Files doi:http://dx.doi.org/10.17632/77kd74zy5k.1Licensing provisions: GPLv3Programming language: Fortran-90Nature 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.