Solvability of eigenvalues in jn configurations

TL;DR

This paper investigates the conditions under which eigenvalues in jn nuclear configurations are solvable, revealing that eigenstates with certain symmetries exhibit eigenvalues as linear combinations of two-body energies with rational coefficients.

Contribution

It demonstrates that eigenstates of any two-body interaction have solvable eigenvalues, especially those with definite seniority and no other states with the same spin J.

Findings

Eigenvalues can be linear combinations of two-body energies with rational coefficients.

States with definite seniority exhibit partial dynamical symmetry.

Eigenstates with no other states of the same J have solvable eigenvalues.

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.