Ground-state energy and stability of three-particle coulomb systems versus the masses of the particles involved

Abstract

The ground-state energy of three-particle Coulomb systems (trions) is investigated versus the masses of the particles involved. Variational calculations are performed for 34 asymmetric trions X±Y±Z∓ consisting of electrons, muons, pions, kaons, nuclei of hydrogen isotopes and their antiparticles, as well as for more than 100 auxiliary three-particle systems involving particles of masses chosen arbitrarily. Wide bases of Laguerre exponential-polynomial functions depending on perimetric particle coordinates are used. Approximate analytic formulas for the ground-state energies of all trions X±Y±Z∓ with arbitrary particle masses are constructed on the basis of the values found here for the energies of asymmetric trions and the values calculated previously for the energies of symmetric trions X±X±Z∓. Particle-mass regions are determined where trions are stable with respect to dissociation. In addition to symmetric trions X±X±Z∓, which are stable at any particle masses, asymmetric trions X±X±Z∓ possess the stability property if the masses of the particles X and Y exceed the mass of the particle Z, where, by Z, we mean, for example, an electron, a muon, a pion, or a kaon. The t+d+p− and t+d+d− combinations of hydrogen nuclei and antinuclei are also stable with respect to dissociation. The general properties of the ground-state trion energy as a function of the particle masses are discussed.