Energies of symmetric three-particle Coulomb systems

The parametric dependence of the eigenvalue of the Hamiltonian on the particle masses and precision values calculated for 45 reference systems within the variational approach implemented for the basis of Laguerre functions of perimetric particle coordinates are used to construct explicit formulas that determine the energies of the ground states of all three-particle Coulomb systems X+/-X+/-Y-/+ (symmetric trions) consisting of singly charged particles X+/- and Y-/+ with arbitrary masses. These formulas can be applied to any symmetric three-particle atomic, molecular, and mesic molecular systems and to electron-hole systems in solids. The energies of the ground states of 63 symmetric trions corresponding to all possible combinations of electrons, positrons, muons, pions, kaons, and hydrogen nuclei and antinuclei are calculated on the basis of these formulas.