Energies and stability of four-particle mesic molecules

The energy and stability of four-particle mesic molecules (quadrions) whose constituents represent charged particles, which interact via Coulomb force s, have been investigated for various masses of constituent particles. From an analysis of the particle-mass dependence of the energy of symmetric qua drions of the X+X+Y-Y- and X+Y+X-Y- types, it has been deduced that the hig hly symmetric positronium molecule e(+)e(+)e(-)e(-) stands out in the sense that it can be used as a reference in the theory of four-particle Coulomb systems: its energy determines the energies of all quadrions to third-order terms in the spread of the particle masses inclusive. Analytic formulas th at determine the energies of X+X+Y-Y- and X+Y+X-Y- mesic molecules featurin g particles of arbitrary masses have been constructed by using calculated d ata on the quadrion energies and the law governing the transformation of th e energy of a specific quadrion under the inversion of the ratio of the par ticle masses. On the basis of these formulas, the previously unknown energi es of the K(+)K(+)e(-)e(-), pi(+)pi(+)e(-)e(-), mu(+)mu(+)e(-)e(-), K(+)K()mu(-)mu(-), K(+)K(+)mu(-)mu(-), and d(+)d(+)p(-)p(-) mesic molecules have been calculated to be (in Hartree atomic units)E = -1.15985, -1.14572, -1.1 4098, -179.76, -223.22, and -1269.3, respectively. It has been shown that a ll symmetric quadrions of the X+X+Y-Y- type are stable with respect to diss ociation. Upper bounds on the energies of asymmetric quadrions have been ob tained on the basis of the energies of symmetric quadrions. It has been est ablished that, among all 406 quadrions that can be composed of electrons, m uons, pions, kaons, protons, and tritons and their antiparticles, 28 symmet ric quadrions of the X+X+Y-Y- type and 92 asymmetric mesic molecules are st able with respect to dissociation.