Energies of Symmetric Three-Particle Coulomb Systems

T. K. Rebane and A. V. Filinsky¹⁾

Research Institute of Physics (Petrodvorets), St. Petersburg State University,
ul. Pervogo Maya 100, Petrodvorets, St. Petersburg, 198904 Russia

Received January 17, 1997

Abstract—The parametric dependence of the eigenvalue of the Hamiltonian on the particle masses and preci-
sion 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 XX (symmetric trions) consisting of
singly charged particles X and 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 ener-
gies 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.

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