New Procedure for Evaluation of U(3) Coupling and Recoupling Coefficients

TL;DR

This paper introduces a new, faster, and more accurate method for calculating U(3) coupling and recoupling coefficients, improving upon previous formulations by eliminating complex sums and binomial coefficients.

Contribution

The paper presents a novel procedure for calculating U(3) coupling coefficients that simplifies computations and enhances accuracy, applicable to nuclear structure studies and general U(3) symmetry systems.

Findings

Faster computation of U(3) coefficients

Elimination of binomial coefficients and alternating sums

Improved accuracy over previous methods

Abstract

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3)->SO(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and hence provides faster and more accurate output of requested results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Arne Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. A C++ library built on this new methodology will be published in a complementary journal that specializes in the management and distribution of such programs.