Numerical calculation of the energy spectrum of a two-fermion system Original Research Article

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 we have proposed previously. The energy spectrum of the two-fermion equal mass system is obtained for two cases, firstly total spin equal 0, and secondly total spin equal 1. The hyperfine structure interval in the ground state of positronium and the frequency of the transition from the 1S ground state to the 2S metastable state in orthopositronium are compared with experimental data.