Critical masses for three Coulombic particles

Three masses M 1 , M 2 , M 3 bearing charges +Q, -Q, +Q, respectively, are stable (have at least one energy eigenvalue below the continuum) if the lighter of the two like-charged particles is more massive than a certain critical mass, M c . Bounds for M c over the full range of masses for the other two particles have been computed using the full non-relativistic Hamiltonian for three particles interacting by Coulomb potentials. The global map of all masses covers molecule-like systems and atom-like systems, as well as exotic systems. The authors use a non-adiabatic method which applies over the whole range of masses. The author's results are compared with well known critical masses of a positron binding with a hydrogen atom. Independent estimates of critical masses are also found in three special cases using first-order perturbation theory. Although the Born-Oppenheimer approximation is not adequate to estimate critical masses, it does provide a useful interpretation and satisfactory estimates of generalised critical masses.