Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems

Non-relativistic quantum chemical calculations of the particle mass, m ± 2 , corresponding to the dissociation threshold in a range of Coulomb three-particle systems of the form {m ± 1 m ± 2 m ± 3 } , are performed variationally using a series solution method with a Laguerre-based wavefunction. These masses are used to calculate an accurate stability boundary, i.e., the line that separates the stability domain from the instability domains, in a reciprocal mass fraction ternary diagram. This result is compared to a lower bound to the stability domain derived from symmetric systems and reveals the importance of the asymmetric (mass-symmetry breaking) terms in the Hamiltonian at dissociation. A functional fit to the stability boundary data provides a simple analytical expression for calculating the minimum mass of a third particle required for stable binding to a two-particle system, i.e., for predicting the bound state stability of any unit-charge three-particle system.