Alternate proof of the Rowe-Rosensteel proposition and seniority conservation

Abstract

For a system with three identical nucleons in a single-$j$ shell, the states can be written as the angular momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these non-orthonormal states form a matrix which coincides with the one derived by Rowe and Rosensteel [Phys. Rev. Lett. {\bf 87}, 172501 (2001)]. The propositions they state are related to the eigenvalue problems of the matrix and dimensions of the associated subspaces. In this work, the propositions will be proven from the symmetric properties of the $6j$ symbols. Algebraic expressions for the dimension of the states, eigenenergies as well as conditions for conservation of seniority can be derived from the matrix.

9 pages, no figure

References in corpus (8)

• Partial conservation of seniority and nuclear isomerism
• Seniority conservation and seniority violation in the g_{9/2} shell
• Energy expressions for n=3 and 4 systems in a single-j shell
• Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles
• $J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
• Number of Spin $I$ States of Identical Particles
• Isospin relations for four nucleons in a single j shell
• Number of states for nucleons in a single-$j$ shell

Cited by in corpus (12)

• Partial conservation of seniority in $j=9/2$ shell: Analytic and numerical studies
• $N=Z$ nuclei: A laboratory for neutron-proton collective mode
• Partial conservation of seniority and its unexpected influence on E2 transitions in $g_{9/2}$ nuclei
• Analytic proof of partial conservation of seniority in $j=9/2$ shells
• Coherence features of the spin-aligned neutron-proton pair coupling scheme
• Total number of $J$ levels for identical particles in a single-$j$ shell using coefficients of fractional parentage
• Competition of different coupling schemes in atomic nuclei
• Exact expressions for the number of levels in single-\textit{j} orbits for three, four and five fermions
• Monopole and Seniority Truncations in the Large-Scale Configuration Interaction Shell Model Approach
• Number of spin-J states and odd-even staggering for identical particles in a single-j shell
• Large-scale configuration interaction description of the structure of nuclei around ${}^{100}$Sn and ${}^{208}$Pb
• Partial conservation of seniority in semi-magic nuclei