Partial conservation of seniority in $j=9/2$ shell: Analytic and numerical studies

Abstract

Recent studies show that for systems with four identical fermions in the $j=9/2$ shell two special states, which have seniority $v=4$ and total spins I=4 and 6, are eigenstates of any two-body interaction. These states have good seniority for an arbitrary interaction. In this work an analytic proof is given to this peculiar occurrence of partial conservation of seniority which is the consequence of the special property of certain coefficients of fractional parentage. Further calculations did not reveal its existence in systems with other $n$ and/or $I$ for shells with $j\le 15/2$.

6 pages

References in corpus (9)

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Cited by in corpus (18)

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• Partial conservation of seniority and its unexpected influence on E2 transitions in $g_{9/2}$ nuclei
• Recent progress in configuration-interaction shell model
• Analytic proof of partial conservation of seniority in $j=9/2$ shells
• Overview of Seniority Isomers
• Coherence features of the spin-aligned neutron-proton pair coupling scheme
• Ab initio calculations of anomalous seniority breaking in the $\pi g_{9/2}$ shell for the $N=50$ isotones
• Competition of different coupling schemes in atomic nuclei
• Monopole and Seniority Truncations in the Large-Scale Configuration Interaction Shell Model Approach
• Persistence of the $Z=28$ shell gap in $A=75$ isobars: Identification of a possible $(1/2^{-})$ $\mu$s isomer in ${}^{75}$Co and $\beta$ decay to ${}^{75}$Ni
• Symmetries in the \bm{g_{9/2}} shell
• Large-scale configuration interaction description of the structure of nuclei around ${}^{100}$Sn and ${}^{208}$Pb
• Seniority and $(\frac{9}{2}{)}^n$ configurations in neutron-rich Nickel isotopes
• Partial conservation of seniority in semi-magic nuclei
• Shell Model Symmetries-Honoring Franco Iachello