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

L. Zamick, Y. Y. Sharon, A. Escuderos, T. Hoang, S. J. Q. Robinson

Published 2013-06-19, updated 2014-08-26Version 4

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 or even I T=0 states. Fot I even T=1 states and odd I T=0 states we take J_{B} =8 whilst for odd I T=1 J_{B} is taken to be 7.