Cooperation of anti-aligning and aligning shell-model forces for N=Z

Abstract

For two neutrons and two protons or two neutron holes and two proton holes in a single j-shell, the state |phi> with isospin and seniority zero and the lowest angular momentum zero state |chi> produced by an attractive interaction of quasinucleon pairs with angular momentum 2j have a large overlap for all relevant j and large contents of quasinucleon pairs with angular momenta 2j and 0, respectively. In the 1f7/2 and 1g9/2 shells, the large negative matrix elements of the effective interaction in these two channels relative to most of the rest therefore_cooperate_ to produce a ground state which is essentially a linear combination of |phi> and |chi> with comparable coefficients. Interaction matrix elements in other channels influence significantly the_ratio_ of these coefficients. The state |phi> makes up about 80 % of the calculated ground states. The overlaps of the latter with |chi> are_less_ in the 1g9/2 shell than in the 1f7/2 shell.