Scaling relations for the ground-state energies of three-particle systems with Coulomb interaction

A general approximate expression for the nonrelativistic ground-state energies of Coulomb systems with charges $Z_a$=$Z_b$=±1 and $Z_c$=∓1 and arbitrary masses $m_a$, $m_b$, and $m_c$ is suggested. The results obtained with use of this expression are in excellent agreement with precise variational and adiabatic calculations of three-particle electron, muon, and excitonic molecular systems and can be used for the prediction of ground-state energies of yet-untested systems.