More on Odd-J Pairing in Nuclei

TL;DR

This paper explores the effects of using an interaction with only odd J energies non-zero in nuclear pairing, highlighting simplifications, degeneracies, and comparisons with more realistic interactions.

Contribution

It introduces a simplified interaction focusing on odd J energies and analyzes its implications for nuclear wave functions and degeneracies.

Findings

High overlaps can be misleading in wave function approximations.

A single set of unitary 9-j coefficients often provides accurate wave functions.

Degeneracies are prevalent and explained in the context of odd-J pairing interactions.

Abstract

We point out a simplicity that arises when we use an interaction in which only an energy with odd J is non-zero. The emphasis is on J=J_{\text{max}} and in particular J=9^{+} in the g_{9/2} shell. It is noted that high overlaps can be deceptive. In many cases a single set of unitary 9-j coefficients gives either an exact or a surprisingly good approximation to the wave function of a non-degenerate state. The many degeneracies that occur in these calculations are discussed and explained. As a counterpoint, we compare the results with an interaction in which both the J=0 and J=J_{\text{max}} two-body matrix elements are equal (and attractive). Comparisons with a more realistic interaction are also made.