Exotic π atom mass spectrum

This work reviews the theoretical information on the π -atom and definition of nonperturbative to Hamiltonian of interaction according to the basis investigation of the asymptotically behaviour of the loop function of scalar particles in the external electromagnetic field. The constituent masses of the bound state are analytically determined. It is shown that, when determined the mass spectrum of a relativistic bound state π - atom will show that the constituent mass component is usually introduced which differ from a mass of initial particles. In the given paper we determined the constituent mass and the binding energy of π -atom with relativistic and nonperturbative corrections