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

TL;DR

This paper investigates how anti-aligning and aligning shell-model forces work together to shape the ground states of nuclei with equal numbers of protons and neutrons, highlighting their combined effects in specific nuclear shells.

Contribution

It demonstrates the cooperative effect of anti-aligning and aligning forces in shell-model interactions, showing their significant role in forming the nuclear ground state structure.

Findings

Ground state is mainly composed of the |phi> state (~80%)

Large negative matrix elements in specific channels promote cooperation

Overlap of ground states with |chi> varies between shells

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.