Construction of SU(3) irreps in canonical SO(3)-coupled bases

TL;DR

This paper explores alternative methods for constructing SU(3) irreducible representations using SO(3)-coupled bases, highlighting a basis that yields good K quantum numbers in the rotor-model limit.

Contribution

It introduces a new canonical basis for SU(3) irreps that diagonalizes a specific SO(3) invariant, improving the understanding of basis states in the asymptotic rotor-model limit.

Findings

The proposed basis diagonalizes a linear combination of SO(3) invariants.

Basis states have good K quantum numbers asymptotically.

Comparison shows advantages over existing canonical methods.

Abstract

Alternative canonical methods for defining canonical SO(3)-coupled bases for SU(3) irreps are considered and compared. It is shown that a basis that diagonalizes a particular linear combination of SO(3) invariants in the SU(3) universal enveloping algebra gives basis states that have good $K$ quantum numbers in the asymptotic rotor-model limit.