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 nonidentical 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.

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• Nuclear many-body theory
• Nuclear structure & decays