Energy expressions for n=3 and 4 systems in a single-j shell

Abstract

For systems with three and four fermions within a single-j shell, analytical expressions for the state energies are presented from a decomposition of the angular momentum. In some important cases the expressions acquire a very simple form. The expression may help us in understanding the structure of isomeric states. The decomposition also makes it possible to construct the algebraic condition for conservation of seniority.

5 pages, 1 figure, printer-friendly version, submitted to Phys. Rev. C

References in corpus (11)

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Cited by in corpus (18)

• Overview of Neutron-Proton Pairing
• Spin-aligned neutron-proton pair mode in atomic nuclei
• A monopole-optimized effective interaction for tin isotopes
• Partial conservation of seniority in $j=9/2$ shell: Analytic and numerical studies
• Multistep shell model description of spin-aligned neutron-proton pair coupling
• $N=Z$ nuclei: A laboratory for neutron-proton collective mode
• Alternate proof of the Rowe-Rosensteel proposition and seniority conservation
• Is Seniority a Partial Dynamic Symmetry in the First $\nu g_{9/2}$ Shell?
• Importance of static quadrupole moments for determining collective aspects of nuclear structure: N=Z calculations with four and eight valence particles
• 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
• Cooperation of anti-aligning and aligning shell-model forces for N=Z
• Coherence features of the spin-aligned neutron-proton pair coupling scheme
• Competition of different coupling schemes in atomic nuclei
• 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
• J=0, J=J_{max} and quadrupole pairing
• Partial conservation of seniority in semi-magic nuclei