Demonstration of moleculelike normal modes of Coulombic three-body systems in hyperspherical coordinates

The adiabatic channel wave functions of Coulombic three-body systems are investigated in mass-weighted hyperspherical coordinates. We consider the ABA Coulombic systems, where two of the particles are identical, and examine the density distribution functions at fixed hyperradii R for different systems as the mass ratio {λ}=mA/mB varies from the atomic limit ({λ}{→}0, as in H^-) to the molecular limit ({λ}{→}{∞}, as in H₂⁺). The bonding and antibonding as well as the rovibrational characters of the three-body systems are illustrated by these density plots.