Solvability of eigenvalues in jn configurations

Abstract

Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the interaction and are rational non-negative num- bers. It is shown here that a state which is an eigenstate of any two-body interaction has this solvability property. This includes, in particular, any state with spin J if there are no other states with this J in the jn configuration. It is also shown that eigenstates with solvable eigenvalues have definite seniority v and thus, exhibit partial dynamical symmetry.

References in corpus (2)

• Partial conservation of seniority and nuclear isomerism
• Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles

Cited by in corpus (10)

• Partial Dynamical Symmetries
• Spin-aligned neutron-proton pairs in $N=Z$ nuclei
• Partial conservation of seniority in $j=9/2$ shell: Analytic and numerical studies
• Seniority in quantum many-body systems. I. Identical particles in a single shell
• Analytic proof of partial conservation of seniority in $j=9/2$ shells
• Partial conservation of seniority in nuclei
• Symmetries in the \bm{g_{9/2}} shell
• SU(3) partial dynamical symmetry and nuclear shapes
• Partial conservation of seniority in semi-magic nuclei
• Relation to a property of the angular momentum zero space of states of four fermions in an angular momentum $j=9/2$ shell unexpectedly found to be stationary for any rotationally invariant two-body interaction