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

We obtain wave functions for two protons and two 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 $\left(Q·Q\right)$ we get, in many cases, a very strong overlap with wave functions given by a single set of unitary 9-$j$ coefficients—$\mathrm{U}9j=\langle {\left(jj\right)}^{2j}{\left(j{j}^{J_B}\right|{\left(jj\right)}^{J_p}{\left(jj\right)}^{J_n})}^I\rangle$. Here $J_B=9$ for even $IT=0$ states. For both even and odd $T=1$ states we take $J_B$ equal to 8 whilst for odd $I,T=0$ we take $J_B$ to be 7. We compare the $Q·Q$ results with those of a more realistic interaction.