Study of the energy of symmetric mesomolecules

The energy E(m, M) of four-particle mesomolecules X+X+Y-Y- and X+X-Y+Y- is studied as a function of the ratio s = m/M of masses of their constituent p articles. A law of transformation of the reduced energy E(s) = E(m, M)/m an d the wave function of such systems under inversion of s is established. It is shown that the knowledge of the energy of the positronium molecule e(+) e(+)e(-)e(-) determines a series expansion of the reduced energy of mesomol ecules of both types up to terms of third order, inclusive. On the basis of this expansion and an expansion of the Born-Oppenheimer type, analytic app roximations of the function epsilon(s) are constructed. With these approxim ations, a gap in energies of mesomolecules X+X+Y-Y- from the system p(+)p()K(-)K(-) (s = 0.526183) to the positronium molecule e(+)e(+)e(-)e(-) (s = 1) is bridged and the reduced energies of molecules t(+)t(+)d(-)d(-) and pi (+)pi(+)mu(-)mu(-) (equal to - 0.619562 and - 0.587354 au, respectively) ar e predicted. The dissociation energies of all 36 mesomolecules X+X+Y-Y-, wh ich can be composed of electrons, muons, pions, kaons, protons, deuterons, tritons, and their antiparticles, are calculated. It is shown that the X+XY-Y- molecules with arbitrary masses of the particles m and M are stable ag ainst dissociation, whereas the X+X-Y+Y- molecules with large differences i n masses m and M of the particles break down into atoms X+X- and Y+Y-.