Hyperspherical Elliptic Coordinates and Three-Body Coulomb Problem

We introduce the hyperspherical elliptic coordinates for the study of a class of three-body systems. These new coordinates are well adapted to the singularities of the three-body potential and may be regarded as a generalization of the familiar spheroidal coordinates for diatomic molecules. However, being defined on the hypersphere in six-dimensional space, the new coordinates formally resolve the long-standing difficulties of the Born-Oppenheimer ansatz such as the laborious evaluation of non-adiabatic coupling terms, a separate treatment of the mass-polarization effect, the need for the electronic translational factor, etc.