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 [4], [31], [22], [211], representations of S_4 groups, [5], [311], [221], [2111], [11111] representations of S_5 groups, and [42] and [51] 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.

This publication has been peer reviewed.
Publication Type: 
Conference Proceedings
Lia L Margolin
Year of Publication: 
Journal, Book, Magazine or Other Publication Title: 
Proc. of 15-th Internat. Conf. on Meson-Nucleon Physics and Nuclear Structure, Carnegie Mellon University, Pittsburg, PA y
Date Published: 
Sunday, June 2, 2019
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