Degeneracies with the Q.Q interaction in a single j shell

TL;DR

This paper explores degeneracies caused by the Q.Q interaction in a single j shell, providing new examples, discussing their peculiarities, and suggesting methods to resolve potential confusions.

Contribution

It presents three new examples of degeneracies involving T=0 and T=2 states and discusses how to address these degeneracies in nuclear shell model calculations.

Findings

Identified three new degenerate pairs involving T=0 and T=2 states.

Highlighted an unusual peculiarity in the original degeneracy example.

Suggested steps to remove degeneracies to avoid confusion.

Abstract

Previously [1] it was shown that for a configuration of 2 protons and 2 neutrons in the g_{9/2}shell there is a certain degeneracy that occurs when the quadrupole-quadrupole interaction (Q.Q) is used to to obtain the wave functions.. We here show 3 other examples of such degenerate pairs, all, as before, involving T=0 and T=2 states. . More important we discuss an unusual peculiarity of the original example. Also we point out that degeneracies can be confusing and steps can be taken to remove them.