New methods and results in the three-body Coulomb problem

An approximate symmetry of the three-body Coulomb problem revealed via appr oximate separability of the hyperspherical adiabatics Hamiltonian in hypers pherical elliptic coordinates is discussed. In the zeroth order this symmet ry leads to a completely separable representation of the three-body wave fu nction. Taking into account the non-adiabatic couplings, as well as the Iro n-separable part of the Coulomb potential by mixing a few zeroth-order stat es, permits one to obtain accurate results for systems with arbitrary masse s and charges of particles, and for a wide spectrum below the three-body br eakup threshold.