For two neutrons and two protons or two neutron holes and two proton holes in a single $j$-shell, the state $|\varphi \rangle$ with isospin and seniority zero and the lowest angular momentum zero state $|\chi \rangle$ 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 $1f_{7/2}$ and $1g_{9/2}$ 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 $|\varphi \rangle$ and $|\chi \rangle$ with comparable coefficients. Interaction matrix elements in other channels influence significantly the ratio of these coefficients. The state $|\varphi \rangle$ makes up about 80% of the calculated ground states. The overlaps of the latter with $|\chi \rangle$ are less in the $1g_{9/2}$ shell than in the $1f_{7/2}$ shell.

• Received 21 May 2013

DOI:https://doi.org/10.1103/PhysRevC.88.034329