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

TL;DR

This paper demonstrates that certain angular momentum states of four fermions in a specific shell are stationary under any rotationally invariant two-body interaction, revealing a fundamental invariance explaining their occurrence.

Contribution

It establishes the invariance of a specific state space under any rotationally invariant two-body interaction and links this to observed spectral features in certain nuclei.

Findings

States with I=4 and 6 are stationary for any such interaction.

The invariance explains the occurrence of Escuderos-Zamick states.

Relation between these states and levels with I=10 and 12 is established.

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.