Constructing Wave Functions for Few Body Systems in a Hyperspherical Basis

Investigating 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.

Carnegie Mellon University
L.L. Margolin
Presentation Date: 
Tuesday, June 4, 2019
Event or Conference: 
15-th International Conference on Meson-Nucleon Physics
Presentation Type: 
Paper Presentation
Boyer's Domain: 
Presentation Attachment(s): 
Presentation Location: 
Carnegie Mellon University
Pittsburg, PA
United States
Associated Awards: 
$2500 Travel Award from MMC
Abstract: 
Investigating 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.