Abstract
The existence of states with angular momenta and 6 of four fermions in an angular momentum shell that are stationary for any rotationally invariant two-body interaction despite the presence of other states with the same angular momentum, the Escuderos-Zamick states, is shown to be equivalent to the invariance to any such interaction of the span of states generated from states by one-body operators. This invariance is verified by exact calculation independently of previous verifications of the equivalent statement. It explains the occurrence of the Escuderos-Zamick states for just and 6. The action of an arbitrary interaction on the invariant space and its orthogonal complement is analyzed, leading to a relation of the Escuderos-Zamick energy levels to levels with and 12. Aspects of the observed spectra of , , and are discussed in the light of this relation.
- Received 7 June 2022
- Accepted 22 July 2022
DOI:https://doi.org/10.1103/PhysRevC.106.024308
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