Exciton—phonon interaction in the degenerate‐band case

To consider the combined effect of valence‐band degeneracy and polar electron‐phonon interaction on the exciton binding energy in tetrahedral semiconductors two methods are generalized that have been introduced by Haken for the case of single isotropic parabolic energy bands. The first of these methods starts from polarons that form the exciton, while the second couples the bare exciton to the phonon field. In both methods the spherical part of the Luttinger matrix is used to describe the kinetic energy of the hole. There result effective Hamiltonians in configurationspin space with phonon‐induced electron‐hole interaction potentials. These consist essentially of Haken's potentials averaged over light and heavy hole bands but also contain a tensor force term. Renormalized masses must be inserted in the kinetic energy part only in the first method where the polaron is the starting point.