Stability thresholds of quantum systems of three charged particles

General diagram of stability thresholds (existence of bound states) for the ground and excited states, both symmetric and antisymmetric, is obtained in the mass-charge (m, Z) coordinate plane for a three particle Coulomb system of X X Y-type trions with zero total angular momentum. Variational optimization approaches with the use of Gaussian and exponential bases are proposed for high-precision three-particle calculations. A qualitative explanation of the stability diagram is given in the framework of the Born- Oppenheimer adiabatic approximation, by using simple approximating formulas for both symmetric and antisymmetric electronic energy curves