On the existence of four-particle Coulomb systems

Whether bound states of Coulomb systems composed of four particles with unit charges (quadrions), a ⁺ b ⁺ c ⁻ d ⁻, exist is demonstrated to be determined by the masses of the constituent particles. Relations that make it possible to establish the existence of a large number quadrions with different masses of the particles are derived. The energies of reference quadrions of different symmetry, a positronium molecule, a ⁺ a ⁺ a ⁻ a ⁻, a ⁺ b ⁺ a ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻, are determined and groups of stable asymmetric quadrions corresponding to them are identified. A relationship between the stability of a number of quadrions and three-particle systems (trions) was found. The results shows that, among all the 406 four-particle independent combinations of electrons, muons, pions, kaons, protons, deuterons, and tritium nuclei or their antiparticles, there are 227 bound quadrions.