T=0 Green's function for the exciton

Abstract

The excitons as electronic excitations of an insulator are obtained from the full manybody Hamiltonian by means of T=0Green's function techniques. Exciton amplitudes and energies are obtained via the vertex-part equation from an eigenvalue equation which in the Wannier limit is the effective-mass equation. A formula is obtained for the frequency dependent effective interaction whose static limit (ω=0) goes over into the Haken-Schottky dielectric-constant interaction for excitons of large electron-hole separations. A simple criterion will result to answer the question on when one is allowed to replace the frequency dependent interaction by its ω=0 limit.