EN
The approach of Kahana to the electron-positron interaction in an electron gas contains the superfluous assumption that electron scattering on the positron can occur only to momentum states lying outside the Fermi sphere. The perturbed hypernetted-chain approach avoids that assumption, but self-consistency was achieved only in the Born approximation. In the present work a modification of perturbed hypernetted-chain approach allowed to reach self-consistency also at the Kohn-Sham level, at least for 1 ≤ r_s ≤ 3.5. The electron-positron correlation functions obtained in this way are compared to figures resulting from other approaches.