Particle mass-dependent stability of a bound state of the Coulomb three-particle system

Tree-particle system stability with particle masses m1, m2 and m3 and charges Z1=Z2±1, Z3=±1 are generally investigated. It is shown that the upper bound of the energy of the ground state and lower state with any given rotational moment J is expressed in terms of the energy of some equivalent system with m1=m2. Using this upper bound and disintigration of energies of the system two first particles symmetrical with respect to masses in Born-Oppenheimer series the region of obvious stability of the system of three particles with arbitrary masses in states with J=0 and 1 momenta is determined. It is significant that such approach being mathematically rigorous requires no calculations of investigated system wave functions. The obtained region of obvious stability at J=0 is wider than found earlier by direct variational calculations, and with J=1 such region is first determined. The results may be used in analysis of states of different three-particle Coulomb systems, including usual and exotic molecules containing nuclei and electrons, muons and positrons as well as three-particle electron-hole formations in a solid