Determination of the ground state energies of the H 2 + , D 2 + and H 2 + molecular ions taking into account relativistic corrections

On the basis of determination of the asymptotic behavior of correlation functions of the corresponding field currents with the corresponding quantum numbers an analytic method for determination of the energy spectrum of three-body Coulomb system is suggested. Our results show that the constituent masses of particles, which we have defined as masses of particles in a bound state, differ from masses of particles in a free-state. The constituent mass to the free state mass relation for the electron is greater than the same mass relation for the proton, deuteron and triton. It was also found that this constituent electron mass has different values in each systems, i.e. in H ₂ ⁺ , D ₂ ⁺ and T ₂ ⁺ hydrogen molecular ions. The contributions of exchange and self-energy diagrams were taken into account in the determination of the energy spectrum of the three-body Coulomb system. Our results show that the self-energy diagram contribution is inversely proportional to the square of the constituent mass of particles. This contribution is sufficient for the electron and is negligible for the proton, deuteron and triton. When defining the energy and the wave function (WF), it is necessary to take into account the contributions of both the exchange and self-energy diagrams.