Hyperspherical functions with arbitrary permutational symmetry

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Abstract
An algorithm is formulated for the construction of many-particle permutational symmetry adapted functions in hyperspherical coordinates. A recursive procedure is proposed, introducing hyperspherical coefficients of fractional parentage (hscfps). These coefficients are the eigenvectors of the transposition class sum of the symmetric group in an appropriate basis. Only the matrix element of the transposition of the last two particles has to be calculated in each step. This matrix element is obtained by using the hscfps calculated in the preceding step as well as the Raynal-Revai and the T coefficients. The results are applicable to the study of the atomic, molecular, and nuclear few-body problem.