The classification of hidden crossings in the three-body Coulomb problem: separable and conventional hyperspherical representations

A classification of hidden crossings in the three-body Coulomb problem is d eveloped on the basis of hyperspherical adiabatic approach and approximate separability of the hyperspherical adiabatic eigenvalue problem in hypersph erical elliptic coordinates. For the case when two of three particles arc i dentical we found two main types of hidden crossings which generalize the w ell-known S and T series of hidden crossings in the two-Coulomb-centre prob lem and reveal essential mechanisms of nonadiabatic transitions. The unstab le periodic trajectories associated with these two types of hidden crossing s are discussed. The results are illustrated by the calculations for the po sitronium negative ion eee(+) with zero total angular momentum.