An Analysis of the Symmetry in ABA Coulomb Systems

The nodal structures of quantum states of three-body ABA systems composed of two identical fermions and another one with an opposite charge are investigated. We expand the wavefunction in the body frame and show that the effect of symmetry such as rotation, space inversion, and permutation is to impose nodal surfaces on the components of the wavefunction. Based on the nodal surface, a classification of quantum states of ABA systems is presented. It is found that the quantum symmetry plays a crucial role in determing the energy levels and structures of the low-lying states.