Wave functions of the Q.Q interaction in terms of unitary 9-j coefficients

TL;DR

This paper demonstrates that wave functions for two protons and two neutrons in the g_{9/2} shell under a quadrupole-quadrupole interaction can be closely approximated by single sets of unitary 9j coefficients, simplifying their description.

Contribution

The study shows that wave functions in the g_{9/2} shell with Q.Q interaction are well represented by unitary 9j coefficients, providing a simplified analytical approach.

Findings

Strong overlap between Q.Q wave functions and U9j coefficients.

U9j coefficients effectively approximate wave functions for various states.

Comparison with realistic interactions confirms the validity of the U9j approximation.

Abstract

We obtain wave functions for 2 protons and 2 neutrons in the g_{9/2} shell expressed as column vectors with amplitudes D(J_{p},J_{n}). When we use a quadrupole-quadrupole interaction (Q.Q) we get, in many cases, a very strong overlap with wave functions given by a single set of unitary 9j coefficients --U9j= ((jj)^{2j} (jj^{J_{B}} \ (jj)^{J_{p}} (jj)^{J_{n}})^{I}. Here J_{B}=9 for even I T =0 states. For both even and odd T=1 states we take JB equal to 8 whilst for odd I, T=0 we take JB to be 7. We compare the Q.Q results with those of a more realistic interaction.