posted on 2023-06-08, 20:42authored byAndrew W King, Frank Longford, Hazel CoxHazel Cox
High accuracy non-relativistic quantum chemical calculations of the ground state energies and wavefunctions of symmetric three-particle Coulomb systems of the form {m ± 1 m ± 2 m ± 3 } , m 1 = m 2, are calculated using an efficient and effective series solution method in a triple orthogonal Laguerre basis set. These energies are used to determine an accurate lower bound to the stability zone of unit-charge three-particle Coulomb systems using an expression for the width of the stability band in terms of g, the fractional additional binding due to a third particle. The results are presented in the form of a reciprocal mass fraction ternary diagram and the energies used to derive a parameterised function g(a 3), where a 3 =m -1 3 /(m -1 1 +m -1 2 +m -1 3 ) is the reciprocal mass of the uniquely charged particle. It is found that the function is not minimal at a 3 = 0 which corresponds to 8H- nor is it minimal at the positronium negative ion (Ps-) the system with the least absolute energetic gain by association with a third particle; the function g(a 3) is minimal at m 1/m 3 = 0.49, and a possible physical interpretation in terms of the transition from atomic-like to molecular-like is provided.