The numerical calculation results of the integral equations for a two fermion system

The two-particle system is described by integral equations with a kernel depending on the total system energy. These equations are reduced to the eigenvalue problem with the operator depending on the eigenvalue. This nonlinear eigenvalue problem is solved with the help of an iteration method have been proposed previously. The energy spectrum of the two-fermion equal-mass system is obtained for two cases: first, total spin equals 0 and, second, total spin equals 1. The hyperfine-structure interval in the ground state of positronium and dimuonium, the frequency of the transition from the 1S ground state to the 2S metastable state in orthopositronium, the decay rate of parapositronium and paradimuonium are calculated. The results agree well with experimental data