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

Abstract

The existence of states with angular momenta $I = 4$ and~6 of four fermions in an angular momentum $j = 9/2$ 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 $I = 0$ 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 $I = 4$ 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 $I = 10$ and 12. Aspects of the observed spectra of $^{94}$Ru, $^{96}$Pd, and $^{74}$Ni are discussed in the light of this relation.