SU3 isoscalar factors

TL;DR

This paper reviews the properties of SU3 isoscalar factors and Wigner Clebsch-Gordan coefficients, discusses the outer degeneracy problem, and provides an algorithm for their numerical computation respecting symmetry properties.

Contribution

It introduces a recursive algorithm for calculating SU3 isoscalar factors that preserves all known symmetry properties and addresses the outer degeneracy problem.

Findings

Proof of Braunschweig's conjecture on outer degeneracy

Development of a recursive algorithm for isoscalar factors

Comprehensive display of symmetry properties for SU3 coefficients

Abstract

A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture (Braunschweig's) which has been the basis of previous work on the SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar factors are produced, along with an algorithm which allows numerical determination of the factors from the recursion relations. The algorithm produces isoscalar factors which share all the symmetry properties under permutation of states and conjugation which are familiar from the SU2 case. The full set of symmetry properties for the SU3 Wigner-Clebsch-Gordan coefficients and isoscalar factors are displayed.