The role of quantal fluctuations in the optical response of small metal clusters

We present an ab--initio calculation of the line shape of the photoabsorption spectrum of Na_8 and Na_9+ clusters at zero temperature, including for the first time the polarization effect driven by the electron-plasmon coupling. The latter are found to yield a significant lowering of the energy centroid of the plasmons, whereas the main effect the electron-phonon coupling is to smooth the spectrum