https://doi.org/10.1140/epja/s10050-025-01781-5
Review
Partial conservation of seniority in semi-magic nuclei
Department of Physics, KTH Royal Institute of Technology, Roslagstullsbacken 21, 106 91, Stockholm, Sweden
a
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Received:
8
September
2025
Accepted:
17
December
2025
Published online:
22
January
2026
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 
, deviations arise for higher-j orbitals where residual interactions can mix states of different seniority. Surprisingly, certain states in systems with 
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 
case, where two 
states with 
and 
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.
© The Author(s) 2026
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