RELATIVISTIC WAVE-EQUATION FOR THE BOUND-STATES OF A SYSTEM OF INTERACTING PARTICLES

A method for obtaining the relativistic wave equation for the bound st ates of a system of interacting charged particles without consideratio n of spin is proposed. An expansion of the wave function of the system in a complete basis of orthonormal wave functions of vacuum states fo r each type of particle is used in this equation. It is shown that thi s equation contains two types of solutions for a proton + electron sys tem. The first type corresponds to Bohr bound states. Exact expression s are obtained for the energy and Bohr radius of the ground state with consideration of the finite mass of the particles. An influence of th e energy of translational motion of the system as a whole on the struc ture of the atomic levels in the laboratory frame is predicted. This e ffect is due to the finite value of n/M, and leads to removal of the d egeneracy of the levels with respect to orbital angular momentum 1, an d partial removal of the degeneracy with respect to its projection. Th e second type of solution represents states of the system with binding energy E-b=M+m-root\M-2-m(2)\ and an exponential wave function dampin g radius equal to the Compton wavelength of the electron. A complete d escription of this state requires consideration of the electronic vacu um polarization. (C) 1997 American Institute of Physics.