New methods and results in the three-body Coulomb problem (Q5948474)

An approximate symmetry of the three-body Coulomb problem revealed via approximate separability of the hyperspherical adiabatic Hamiltonian in hyperspherical elliptic coordinates is discussed. In the zeroth order this symmetry leads to a completely separable representation of the three-body wave function. Taking into account the non-adiabatic couplings, as well as the non-separable part of the Coulomb potential by mixing a few zeroth-order states, permits one to obtain accurate results for systems with arbitrary masses and charges of particles, and for a wide spectrum below the three-body breakup threshold.