Simplified and more efficient computations of angular-momentum-coupled Goldstone diagrams

Abstract

Motivated by the work of Kuo et al. (Ann Phys 132:237–276, 1981), we develop a simple method to compute Goldstone diagrams in the angular momentum coupled scheme. By redefining the cross-coupled matrix elements, we leverage symmetry properties more effectively, leading to simplified diagram factorization rules and promoted computational efficiency. We have successfully applied the rules to one-body tensor operators, and extended similar formulations to two-body tensor operators beyond the work of Kuo et al. (1981).