Interparticle potential up to next-to-leading order for gravitational,electrical, and dilatonic forces

Long-range forces up to next-to-leading order are computed in the framework of the Einstein–Maxwell-dilaton system by means of a semiclassical approach to gravity. As has been recently shown, this approach is effective if one of the masses under consideration is significantly greater than all the energies involved in the system. Further, we obtain the condition for the equilibrium of charged masses in the system.