Screening in the exchange term of the electron-hole interaction of the Bethe-Salpeter equation

The Bethe-Salpeter equation (BSE), governing the dynamics of a particle-hole pair in a many-body system, is considered for the case in which the two-particle propagator is constructed from a finite set of particle-hole states. It is shown that in this case, it may be appropriate to screen the exchange kernel of the BSE with a background dielectric function ${\epsilon }_{\mathrm{BG}}.$ An application to the computation of optical excitation spectra in quantum dots is discussed.