Calculation of the Exchange Energy for Excitons in the Two-Body Model

The exchange energy for the Wannier exciton is calculated by solving a previously derived two-body Hamiltonian $H^{\mathrm{}\left(2\right)\mathrm{}}$. The solution of the eigenvalue problem of $H^{\mathrm{}\left(2\right)\mathrm{}}$ in the effectivemass approximation is performed with a numerical diagonalization method. The values obtained for the exchange energy in several II-VI compounds are between 10 and 20% of the binding energy of the pure hydrogenlike exciton. The comparison with experimental results shows a satisfactory agreement.