New angular momentum coupling method based on Wigner rotation theory

TL;DR

This paper introduces a novel angular momentum coupling method using Wigner rotation theory that simplifies the construction of many-nucleon states and could enhance computational efficiency in nuclear physics.

Contribution

It presents a new approach to angular momentum coupling that incorporates fermion antisymmetry and restores rotational symmetry through angular momentum projection.

Findings

Allows total angular momentum construction across different j-shells

Fully absorbs fermion antisymmetry restrictions into single-j space

Potentially improves efficiency in nuclear many-body calculations

Abstract

We present a new method for constructing the total angular momentum of many-nucleon states. We find that the restrictions imposed by the fermion antisymmetry on the total state are fully absorbed into the single-j space when the broken rotational symmetry of the product state is restored by angular momentum projection. For different j-shells, any total angular momentum that obeys the selection rule is allowed, just as for non-identical particles. The method based on this reorganization is conceptually different from the traditional J and m schemes and may help to improve the efficiency of angular momentum coupling in nuclear many-body calculations.