Constructing Wave Functions for Few-Body Systems in a Hyperspherical Basis Using Parentage Scheme of Symmetrization
nvestigating few-body systems with identical particles in a hyperspherical basis yields the problem of obtaining symmetrized hyperspherical functions from functions with arbitrary quantum numbers. This article solves the problem of hyperspherical basis symmetrization for four-,five- ,and six- body systems using Parentage Scheme of Symmetrization. Parentage coefficients corresponding to the , , , , representations of S_4 groups, , , , ,  representations of S_5 groups, and  and  representations of S_6 groups are obtained, and Young operators, acting on N = 4,5,6 body hyperspherical functions symmetrized with respect to (N-1) particles, are derived. The symmetrized N = 4,5,6 body hyperspherical functions are obtained with different values of quantum numbers . The connection between the transformation coefficients for the identical particle systems and the parentage coefficients is demonstrated and the corresponding formulas are introduced.