Partial conservation of seniority in semi-magic nuclei

TL;DR

This paper explores the phenomenon where certain seniority states in semi-magic nuclei remain partially conserved despite the breaking of seniority symmetry in higher-$j$ orbitals, supported by theoretical, numerical, and experimental evidence.

Contribution

It provides a comprehensive review of partial seniority conservation, especially in the $j=9/2$ case, including analytical proofs, numerical studies, and experimental validation.

Findings

Certain $v=4$ states in $j=9/2$ remain unmixed under arbitrary interactions.

Partial seniority conservation is supported by experimental data across multiple nuclear regions.

Symbolic shell-model approaches help analyze wave functions and symmetries in these systems.

Abstract

The concept of seniority plays a central role in nuclear structure physics by classifying many-body states according to the number of unpaired nucleons. While exact seniority conservation holds in single-$j$ systems with $j \leq 7/2$, deviations arise for higher-$j$ orbitals where residual interactions can mix states of different seniority. Surprisingly, certain states in systems with $j \geq 9/2$ exhibit partial conservation of seniority, remaining solvable even when the symmetry is expected to break. This paper reviews the theoretical foundation of the seniority scheme, its connection to pairing interactions and coefficients of fractional parentage, and the conditions under which solvability persists. Particular emphasis is placed on the $j=9/2$ case, where two $v=4$ states with $I=4$ and $I=6$ remain unmixed under arbitrary interactions. We discuss analytical proofs of their existence, numerical studies, and supporting experimental evidence from semi-magic nuclei across five regions of the nuclear chart. Extensions to symbolic shell-model approaches are also presented, highlighting their utility in exploring wave functions and symmetries in many-body systems.