Deduction of the Quantum Numbers of Low-Lying States of 6-Nucleon Systems Based on Symmetry

Abstract

The inherent nodal structure in the wave functions of 6-nucleon systems is investigated using group theory. The existence of a group of six low-lying states composed of mainly an $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ component is deduced. In addition to the ${}\left(4,2\right)$ spatial permutation symmetry, the ${}\left(2,2,2\right)$ symmetry is found to be also important for the low-lying states.