Optical absorption spectra of finite systems from a conserving Bethe-Salpeter equation approach

We present a method for computing optical absorption spectra by means of a Bethe-Salpeter equation approach, which is based on a conserving linear response calculation for electron-hole coherences in the presence of an external electromagnetic field. This procedure allows, in principle, for the determination of the electron-hole correlation function self-consistently with the corresponding single-particle Green function. We analyze the general approach for a "one-shot" calculation of the photoabsorption cross section of finite systems, and discuss the importance of scattering and dephasing contributions in this approach. We apply the method to the closed-shell clusters Na_4, Na^+_9 and Na^+_(21), treating one active electron per Na atom.