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The existence of states with angular momenta $I = 4$ and~6 of four fermionsin an angular momentum $j = 9/2$ shell that are stationary for any rotationallyinvariant two-body interaction despite the presence of other states with thesame angular momentum, the Escuderos-Zamick states, is shown to be equivalentto the invariance to any such interaction of the span of states generated from$I = 0$ states by one-body operators. This invariance is verified by exactcalculation independently of previous verifications of the equivalentstatement. It explains the occurrence of the Escuderos-Zamick states for just$I = 4$ and 6. The action of an arbitrary interaction on the invariant spaceand its orthogonal complement is analyzed, leading to a relation of theEscuderos-Zamick energy levels to levels with $I = 10$ and 12. Aspects of theobserved spectra of $^{94}$Ru, $^{96}$Pd, and $^{74}$Ni are discussed in thelight of this relation.

physical review. c

Relation to a property of the angular momentum zero space of states of  four fermions in an angular momentum $j = 9/2$ shell unexpectedly found to be  stationary for any rotationally invariant two-body interaction